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Overview
Comment: Merge changes from HEAD, including libtommath 0.36 Tarball | ZIP archive | SQL archive family | ancestors | descendants | both | kennykb-numerics-branch files | file ages | folders 14146661ef14906d03c4cc3e5468bb0a30d17a1d kennykb 2005-09-26 20:16:53
Context
 2005-09-27 18:42 [kennykb-numerics-branch] * generic/tcl.h: Changed name of the new Tcl_Obj i... check-in: 2d7e29783f user: dgp tags: kennykb-numerics-branch 2005-09-26 20:16 Merge changes from HEAD, including libtommath 0.36 check-in: 14146661ef user: kennykb tags: kennykb-numerics-branch 2005-09-23 16:47 [kennykb-numerics-branch] * unix/Makefile.in: Added -DMP_PREC=4 switch to all c... check-in: 29be091cd8 user: dgp tags: kennykb-numerics-branch
Changes

Changes to ChangeLog.

  1 2 3 4 5 6 7 .. 46 47 48 49 50 51 52 53 54 55 56 57 58 59   2005-09-23 Don Porter [kennykb-numerics-branch] * unix/Makefile.in: Added -DMP_PREC=4 switch to all compiles so * win/Makefile.in: that minimum memory requirements of mp_int's * win/makefile.vc: will not be quite so large. [Bug 1299153]. ................................................................................ but mp_add_d was producing an inconsistent zero value with a sign field of MP_NEG, something like a value of -0, which other routines in libtommath can't handle. * generic/tclExecute.c: Dropped all creation of "bigOne" values and just use tommath routines that accept the value "1" directly. 2005-09-15 Don Porter [kennykb-numerics-branch] Merge updates from HEAD. * generic/tclStringObj.c (TclAppendFormattedObjs): Revision to eliminate one round of string copying.  > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 .. 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76  2005-09-26 Kevin Kenny [kennykb-numerics-branch] Merge updates from HEAD. 2005-09-26 Kevin Kenny * libtommath/: Updated to release 0.36. * generic/tommath.h: Regenerated. * generic/tclTomMathInterface.h: Added ten missing aliases for mp_* functions to avoid namespace pollution in Tcl's exported symbols. [Bug 1263012] 2005-09-23 Don Porter [kennykb-numerics-branch] * unix/Makefile.in: Added -DMP_PREC=4 switch to all compiles so * win/Makefile.in: that minimum memory requirements of mp_int's * win/makefile.vc: will not be quite so large. [Bug 1299153]. ................................................................................ but mp_add_d was producing an inconsistent zero value with a sign field of MP_NEG, something like a value of -0, which other routines in libtommath can't handle. * generic/tclExecute.c: Dropped all creation of "bigOne" values and just use tommath routines that accept the value "1" directly. 2005-09-15 Miguel Sofer * doc/ParseCmd.3: copy/paste fix [Bug 1292427] 2005-09-15 Don Porter [kennykb-numerics-branch] Merge updates from HEAD. * generic/tclStringObj.c (TclAppendFormattedObjs): Revision to eliminate one round of string copying. 

Changes to doc/ParseCmd.3.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118  '\" '\" Copyright (c) 1997 Sun Microsystems, Inc. '\" '\" See the file "license.terms" for information on usage and redistribution '\" of this file, and for a DISCLAIMER OF ALL WARRANTIES. '\" '\" RCS: @(#) $Id: ParseCmd.3,v 1.18.2.2 2005/05/05 17:55:22 kennykb Exp$ '\" .so man.macros .TH Tcl_ParseCommand 3 8.3 Tcl "Tcl Library Procedures" .BS .SH NAME Tcl_ParseCommand, Tcl_ParseExpr, Tcl_ParseBraces, Tcl_ParseQuotedString, Tcl_ParseVarName, Tcl_ParseVar, Tcl_FreeParse, Tcl_EvalTokens, Tcl_EvalTokensStandard \- parse Tcl scripts and expressions .SH SYNOPSIS ................................................................................ structure of the command (see below for details). If an error occurred in parsing the command then \fBTCL_ERROR\fR is returned, an error message is left in \fIinterp\fR's result, and no information is left at \fI*parsePtr\fR. .PP \fBTcl_ParseExpr\fR parses Tcl expressions. Given a pointer to a script containing an expression, \fBTcl_ParseCommand\fR parses the expression. If the expression was parsed successfully, \fBTcl_ParseExpr\fR returns \fBTCL_OK\fR and fills in the structure pointed to by \fIparsePtr\fR with information about the structure of the expression (see below for details). If an error occurred in parsing the command then \fBTCL_ERROR\fR is returned, an error message is left in \fIinterp\fR's result, and no information is left at \fI*parsePtr\fR.   | |  1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118  '\" '\" Copyright (c) 1997 Sun Microsystems, Inc. '\" '\" See the file "license.terms" for information on usage and redistribution '\" of this file, and for a DISCLAIMER OF ALL WARRANTIES. '\" '\" RCS: @(#) $Id: ParseCmd.3,v 1.18.2.3 2005/09/26 20:16:53 kennykb Exp$ '\" .so man.macros .TH Tcl_ParseCommand 3 8.3 Tcl "Tcl Library Procedures" .BS .SH NAME Tcl_ParseCommand, Tcl_ParseExpr, Tcl_ParseBraces, Tcl_ParseQuotedString, Tcl_ParseVarName, Tcl_ParseVar, Tcl_FreeParse, Tcl_EvalTokens, Tcl_EvalTokensStandard \- parse Tcl scripts and expressions .SH SYNOPSIS ................................................................................ structure of the command (see below for details). If an error occurred in parsing the command then \fBTCL_ERROR\fR is returned, an error message is left in \fIinterp\fR's result, and no information is left at \fI*parsePtr\fR. .PP \fBTcl_ParseExpr\fR parses Tcl expressions. Given a pointer to a script containing an expression, \fBTcl_ParseExpr\fR parses the expression. If the expression was parsed successfully, \fBTcl_ParseExpr\fR returns \fBTCL_OK\fR and fills in the structure pointed to by \fIparsePtr\fR with information about the structure of the expression (see below for details). If an error occurred in parsing the command then \fBTCL_ERROR\fR is returned, an error message is left in \fIinterp\fR's result, and no information is left at \fI*parsePtr\fR. 

Changes to generic/tclStrToD.c.

 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ... 155 156 157 158 159 160 161 162 163 164 165 166 167 168 .... 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 .... 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 .... 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026   * interconversion among 'double' and 'mp_int' types. * * Copyright (c) 2005 by Kevin B. Kenny. All rights reserved. * * See the file "license.terms" for information on usage and redistribution * of this file, and for a DISCLAIMER OF ALL WARRANTIES. * * RCS: @(#) $Id: tclStrToD.c,v 1.1.2.38 2005/09/23 04:03:43 dgp Exp$ * *---------------------------------------------------------------------- */ #include #include #include ................................................................................ mp_int* significand, int nSigDigs, int exponent)); static double MakeNaN _ANSI_ARGS_(( int signum, Tcl_WideUInt tag )); static double RefineApproximation _ANSI_ARGS_((double approx, mp_int* exactSignificand, int exponent)); static double BignumToBiasedFrExp _ANSI_ARGS_(( mp_int* big, int* machexp )); static double Pow10TimesFrExp _ANSI_ARGS_(( int exponent, double fraction, int* machexp )); static double SafeLdExp _ANSI_ARGS_(( double fraction, int exponent )); ................................................................................ * must have at least 18 chars */ double v, /* Number to convert. Must be * finite, and not NaN */ int *signum ) /* Output: 1 if the number is negative. * Should handle -0 correctly on the * IEEE architecture. */ { double f; /* Significand of v. */ int e; /* Power of FLT_RADIX that satisfies * v = f * FLT_RADIX**e */ int lowOK, highOK; mp_int r; /* Scaled significand. */ mp_int s; /* Divisor such that v = r / s */ mp_int mplus; /* Scaled epsilon: (r + 2* mplus) == v(+) * where v(+) is the floating point successor * of v. */ mp_int mminus; /* Scaled epsilon: (r - 2*mminus) == v(-) * where v(-) is the floating point * predecessor of v. */ mp_int temp; int rfac2 = 0; /* Powers of 2 and 5 by which large */ int rfac5 = 0; /* integers should be scaled. */ int sfac2 = 0; int sfac5 = 0; int mplusfac2 = 0; int mminusfac2 = 0; double a; char c; int i, k, n; /* * Take the absolute value of the number, and report the number's sign. * Take special steps to preserve signed zeroes in IEEE floating point. * (We can't use fpclassify, because that's a C9x feature and we still * have to build on C89 compilers.) */ #ifndef IEEE_FLOATING_POINT if (v >= 0.0) { *signum = 0; } else { *signum = 1; v = -v; } #else union { Tcl_WideUInt iv; double dv; } bitwhack; bitwhack.dv = v; if (bitwhack.iv & ((Tcl_WideUInt) 1 << 63)) { *signum = 1; bitwhack.iv &= ~((Tcl_WideUInt) 1 << 63); v = bitwhack.dv; } else { *signum = 0; } #endif /* * Handle zero specially. */ if ( v == 0.0 ) { *string++ = '0'; *string++ = '\0'; return 1; } /* * Develop f and e such that v = f * FLT_RADIX**e, with * 1.0/FLT_RADIX <= f < 1. */ f = frexp(v, &e); #if FLT_RADIX > 2 n = e % log2FLT_RADIX; if (n > 0) { n -= log2FLT_RADIX; e += 1; f *= ldexp(1.0, n); } e = (e - n) / log2FLT_RADIX; #endif if (f == 1.0) { f = 1.0 / FLT_RADIX; e += 1; } /* * If the original number was denormalized, adjust e and f to be denormal * as well. */ if (e < DBL_MIN_EXP) { n = mantBits + (e - DBL_MIN_EXP)*log2FLT_RADIX; f = ldexp(f, (e - DBL_MIN_EXP)*log2FLT_RADIX); e = DBL_MIN_EXP; n = (n + DIGIT_BIT - 1) / DIGIT_BIT; } else { n = mantDIGIT; } /* * Now extract the base-2**DIGIT_BIT digits of f into a multi-precision * integer r. Preserve the invariant v = r * 2**rfac2 * FLT_RADIX**e by * adjusting e. */ a = f; n = mantDIGIT; mp_init_size(&r, n); r.used = n; r.sign = MP_ZPOS; i = (mantBits % DIGIT_BIT); if (i == 0) { i = DIGIT_BIT; } while (n > 0) { a *= ldexp(1.0, i); i = DIGIT_BIT; r.dp[--n] = (mp_digit) a; a -= (mp_digit) a; } e -= DBL_MANT_DIG; lowOK = highOK = (mp_iseven(&r)); /* * We are going to want to develop integers r, s, mplus, and mminus such * that v = r / s, v(+)-v / 2 = mplus / s; v-v(-) / 2 = mminus / s and * then scale either s or r, mplus, mminus by an appropriate power of ten. ................................................................................ * f is multiplied to yield v and by which 1 is multiplied to yield s, * mplus, and mminus. */ if (e >= 0) { int bits = e * log2FLT_RADIX; if (f != 1.0/FLT_RADIX) { /* * Normal case, m+ and m- are both FLT_RADIX**e */ rfac2 += bits + 1; sfac2 = 1; mplusfac2 = bits; mminusfac2 = bits; } else { /* * If f is equal to the smallest significand, then we need another * factor of FLT_RADIX in s to cope with stepping to the next * smaller exponent when going to e's predecessor. */ rfac2 += bits + log2FLT_RADIX + 1; sfac2 = 1 + log2FLT_RADIX; mplusfac2 = bits + log2FLT_RADIX; mminusfac2 = bits; } } else { /* * v has digits after the binary point */ if (e <= DBL_MIN_EXP-DBL_MANT_DIG || f != 1.0/FLT_RADIX) { /* * Either f isn't the smallest significand or e is the smallest * exponent. mplus and mminus will both be 1. */ rfac2 += 1; sfac2 = 1 - e * log2FLT_RADIX; mplusfac2 = 0; mminusfac2 = 0; } else { /* * f is the smallest significand, but e is not the smallest * exponent. We need to scale by FLT_RADIX again to cope with the * fact that v's predecessor has a smaller exponent. */ rfac2 += 1 + log2FLT_RADIX; sfac2 = 1 + log2FLT_RADIX * (1 - e); mplusfac2 = FLT_RADIX; mminusfac2 = 0; } } /* ................................................................................ /* * Free memory, and return. */ mp_clear_multi(&r, &s, &mplus, &mminus, &temp, NULL); return k; } /* *---------------------------------------------------------------------- * * TclInitDoubleConversion -- * * Initializes constants that are needed for conversions to and from   | > > < > > < | < < < < < < < < < < < < < < < < < < < < < < < < < < > | | < < < < | < < < < < < < < < < < < < < < < > > < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < > | | | | | | > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ... 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 .... 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 .... 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 .... 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097   * interconversion among 'double' and 'mp_int' types. * * Copyright (c) 2005 by Kevin B. Kenny. All rights reserved. * * See the file "license.terms" for information on usage and redistribution * of this file, and for a DISCLAIMER OF ALL WARRANTIES. * * RCS: @(#) $Id: tclStrToD.c,v 1.1.2.39 2005/09/26 20:16:53 kennykb Exp$ * *---------------------------------------------------------------------- */ #include #include #include ................................................................................ mp_int* significand, int nSigDigs, int exponent)); static double MakeNaN _ANSI_ARGS_(( int signum, Tcl_WideUInt tag )); static double RefineApproximation _ANSI_ARGS_((double approx, mp_int* exactSignificand, int exponent)); static double AbsoluteValue(double v, int* signum); static int GetIntegerTimesPower(double v, mp_int* r, int* e); static double BignumToBiasedFrExp _ANSI_ARGS_(( mp_int* big, int* machexp )); static double Pow10TimesFrExp _ANSI_ARGS_(( int exponent, double fraction, int* machexp )); static double SafeLdExp _ANSI_ARGS_(( double fraction, int exponent )); ................................................................................ * must have at least 18 chars */ double v, /* Number to convert. Must be * finite, and not NaN */ int *signum ) /* Output: 1 if the number is negative. * Should handle -0 correctly on the * IEEE architecture. */ { int e; /* Power of FLT_RADIX that satisfies * v = f * FLT_RADIX**e */ int lowOK, highOK; mp_int r; /* Scaled significand. */ mp_int s; /* Divisor such that v = r / s */ int smallestSig; /* Flag == 1 iff v's significand is * the smallest that can be represented. */ mp_int mplus; /* Scaled epsilon: (r + 2* mplus) == v(+) * where v(+) is the floating point successor * of v. */ mp_int mminus; /* Scaled epsilon: (r - 2*mminus) == v(-) * where v(-) is the floating point * predecessor of v. */ mp_int temp; int rfac2 = 0; /* Powers of 2 and 5 by which large */ int rfac5 = 0; /* integers should be scaled. */ int sfac2 = 0; int sfac5 = 0; int mplusfac2 = 0; int mminusfac2 = 0; char c; int i, k, n; /* Split the number into absolute value and signum. */ v = AbsoluteValue(v, signum); /* * Handle zero specially. */ if ( v == 0.0 ) { *string++ = '0'; *string++ = '\0'; return 1; } /* * Find a large integer r, and integer e, such that * v = r * FLT_RADIX**e * and r is as small as possible. Also determine whether the * significand is the smallest possible. */ smallestSig = GetIntegerTimesPower(v, &r, &e); lowOK = highOK = (mp_iseven(&r)); /* * We are going to want to develop integers r, s, mplus, and mminus such * that v = r / s, v(+)-v / 2 = mplus / s; v-v(-) / 2 = mminus / s and * then scale either s or r, mplus, mminus by an appropriate power of ten. ................................................................................ * f is multiplied to yield v and by which 1 is multiplied to yield s, * mplus, and mminus. */ if (e >= 0) { int bits = e * log2FLT_RADIX; if (!smallestSig) { /* * Normal case, m+ and m- are both FLT_RADIX**e */ rfac2 = bits + 1; sfac2 = 1; mplusfac2 = bits; mminusfac2 = bits; } else { /* * If f is equal to the smallest significand, then we need another * factor of FLT_RADIX in s to cope with stepping to the next * smaller exponent when going to e's predecessor. */ rfac2 = bits + log2FLT_RADIX + 1; sfac2 = 1 + log2FLT_RADIX; mplusfac2 = bits + log2FLT_RADIX; mminusfac2 = bits; } } else { /* * v has digits after the binary point */ if (e <= DBL_MIN_EXP-DBL_MANT_DIG || !smallestSig) { /* * Either f isn't the smallest significand or e is the smallest * exponent. mplus and mminus will both be 1. */ rfac2 = 1; sfac2 = 1 - e * log2FLT_RADIX; mplusfac2 = 0; mminusfac2 = 0; } else { /* * f is the smallest significand, but e is not the smallest * exponent. We need to scale by FLT_RADIX again to cope with the * fact that v's predecessor has a smaller exponent. */ rfac2 = 1 + log2FLT_RADIX; sfac2 = 1 + log2FLT_RADIX * (1 - e); mplusfac2 = FLT_RADIX; mminusfac2 = 0; } } /* ................................................................................ /* * Free memory, and return. */ mp_clear_multi(&r, &s, &mplus, &mminus, &temp, NULL); return k; } /* *---------------------------------------------------------------------- * * AbsoluteValue -- * * Splits a 'double' into its absolute value and sign. * * Results: * Returns the absolute value. * * Side effects: * Stores the signum in '*signum'. * *---------------------------------------------------------------------- */ static double AbsoluteValue (double v, /* Number to split */ int* signum) /* (Output) Sign of the number 1=-, 0=+ */ { /* * Take the absolute value of the number, and report the number's sign. * Take special steps to preserve signed zeroes in IEEE floating point. * (We can't use fpclassify, because that's a C9x feature and we still * have to build on C89 compilers.) */ #ifndef IEEE_FLOATING_POINT if (v >= 0.0) { *signum = 0; } else { *signum = 1; v = -v; } #else union { Tcl_WideUInt iv; double dv; } bitwhack; bitwhack.dv = v; if (bitwhack.iv & ((Tcl_WideUInt) 1 << 63)) { *signum = 1; bitwhack.iv &= ~((Tcl_WideUInt) 1 << 63); v = bitwhack.dv; } else { *signum = 0; } #endif return v; } /* *---------------------------------------------------------------------- * * GetIntegerTimesPower -- * * Converts a floating point number to an exact integer times a * power of the floating point radix. * * Results: * Returns 1 if it converted the smallest significand, 0 otherwise. * * Side effects: * Initializes the integer value (does not just assign it), * and stores the exponent. * *---------------------------------------------------------------------- */ static int GetIntegerTimesPower(double v, /* Value to convert */ mp_int* rPtr, /* (Output) Integer value */ int* ePtr) /* (Output) Power of FLT_RADIX by which * r must be multiplied to yield v*/ { double a; double f; int e; int i; int n; /* * Develop f and e such that v = f * FLT_RADIX**e, with * 1.0/FLT_RADIX <= f < 1. */ f = frexp(v, &e); #if FLT_RADIX > 2 n = e % log2FLT_RADIX; if (n > 0) { n -= log2FLT_RADIX; e += 1; f *= ldexp(1.0, n); } e = (e - n) / log2FLT_RADIX; #endif if (f == 1.0) { f = 1.0 / FLT_RADIX; e += 1; } /* * If the original number was denormalized, adjust e and f to be denormal * as well. */ if (e < DBL_MIN_EXP) { n = mantBits + (e - DBL_MIN_EXP)*log2FLT_RADIX; f = ldexp(f, (e - DBL_MIN_EXP)*log2FLT_RADIX); e = DBL_MIN_EXP; n = (n + DIGIT_BIT - 1) / DIGIT_BIT; } else { n = mantDIGIT; } /* * Now extract the base-2**DIGIT_BIT digits of f into a multi-precision * integer r. Preserve the invariant v = r * 2**rfac2 * FLT_RADIX**e by * adjusting e. */ a = f; n = mantDIGIT; mp_init_size(rPtr, n); rPtr->used = n; rPtr->sign = MP_ZPOS; i = (mantBits % DIGIT_BIT); if (i == 0) { i = DIGIT_BIT; } while (n > 0) { a *= ldexp(1.0, i); i = DIGIT_BIT; rPtr->dp[--n] = (mp_digit) a; a -= (mp_digit) a; } *ePtr = e - DBL_MANT_DIG; return (f == 1.0 / FLT_RADIX); } /* *---------------------------------------------------------------------- * * TclInitDoubleConversion -- * * Initializes constants that are needed for conversions to and from 

 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24   * Conservation Through Innovation, Limited, with their permission. * * Copyright (c) 1998 by Sun Microsystems, Inc. * * See the file "license.terms" for information on usage and redistribution * of this file, and for a DISCLAIMER OF ALL WARRANTIES. * * RCS: @(#) $Id: tclThreadTest.c,v 1.17.2.3 2005/08/29 18:38:45 dgp Exp$ */ #include "tclInt.h" #ifdef TCL_THREADS /* * Each thread has an single instance of the following structure. There * is one instance of this structure per thread even if that thread contains * multiple interpreters. The interpreter identified by this structure is * the main interpreter for the thread.   | > >  7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26   * Conservation Through Innovation, Limited, with their permission. * * Copyright (c) 1998 by Sun Microsystems, Inc. * * See the file "license.terms" for information on usage and redistribution * of this file, and for a DISCLAIMER OF ALL WARRANTIES. * * RCS: @(#) $Id: tclThreadTest.c,v 1.17.2.4 2005/09/26 20:16:53 kennykb Exp$ */ #include "tclInt.h" extern int Tcltest_Init( Tcl_Interp* ); #ifdef TCL_THREADS /* * Each thread has an single instance of the following structure. There * is one instance of this structure per thread even if that thread contains * multiple interpreters. The interpreter identified by this structure is * the main interpreter for the thread. 

Changes to generic/tclTomMath.h.

 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 .. 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 .. 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120   * to adapt the API to Tcl's linkage conventions. * * Copyright (c) 2005 by Kevin B. Kenny. All rights reserved. * * See the file "license.terms" for information on usage and redistribution * of this file, and for a DISCLAIMER OF ALL WARRANTIES. * * RCS: @(#) $Id: tclTomMath.h,v 1.1.2.6 2005/09/16 15:35:54 dgp Exp$ */ #ifndef TCLTOMMATH_H #define TCLTOMMATH_H 1 #include #include ................................................................................ #define TOOM_MUL_CUTOFF TclBNToomMulCutoff #define TOOM_SQR_CUTOFF TclBNToomSqrCutoff #define mp_s_rmap TclBNMpSRmap #define bn_reverse TclBN_reverse #define fast_s_mp_mul_digs TclBN_fast_s_mp_mul_digs #define mp_add TclBN_mp_add #define mp_and TclBN_mp_and #define mp_clamp TclBN_mp_clamp #define mp_clear TclBN_mp_clear #define mp_clear_multi TclBN_mp_clear_multi #define mp_cmp TclBN_mp_cmp #define mp_cmp_d TclBN_mp_cmp_d #define mp_cmp_mag TclBN_mp_cmp_mag ................................................................................ #define mp_div_3 TclBN_mp_div_3 #define mp_exch TclBN_mp_exch #define mp_expt_d TclBN_mp_expt_d #define mp_grow TclBN_mp_grow #define mp_init TclBN_mp_init #define mp_init_copy TclBN_mp_init_copy #define mp_init_multi TclBN_mp_init_multi #define mp_init_size TclBN_mp_init_size #define mp_karatsuba_mul TclBN_mp_karatsuba_mul #define mp_lshd TclBN_mp_lshd #define mp_mod_2d TclBN_mp_mod_2d #define mp_mul TclBN_mp_mul #define mp_mul_2 TclBN_mp_mul_2 #define mp_mul_2d TclBN_mp_mul_2d #define mp_mul_d TclBN_mp_mul_d #define mp_neg TclBN_mp_neg #define mp_or TclBN_mp_or #define mp_radix_size TclBN_mp_radix_size #define mp_read_radix TclBN_mp_read_radix #define mp_rshd TclBN_mp_rshd #define mp_shrink TclBN_mp_shrink #define mp_sqrt TclBN_mp_sqrt #define mp_sub TclBN_mp_sub #define mp_to_unsigned_bin TclBN_mp_to_unsigned_bin #define mp_to_unsigned_bin_n TclBN_mp_to_unsigned_bin_n #define mp_toom_mul TclBN_mp_toom_mul #define mp_toradix_n TclBN_mp_toradix_n #define mp_unsigned_bin_size TclBN_mp_unsigned_bin_size #define mp_xor TclBN_mp_xor #define mp_zero TclBN_mp_zero #define s_mp_add TclBN_s_mp_add #define s_mp_mul_digs TclBN_s_mp_mul_digs #define s_mp_sub TclBN_s_mp_sub #endif   | > > > > > > > > > >  5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 .. 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 .. 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130   * to adapt the API to Tcl's linkage conventions. * * Copyright (c) 2005 by Kevin B. Kenny. All rights reserved. * * See the file "license.terms" for information on usage and redistribution * of this file, and for a DISCLAIMER OF ALL WARRANTIES. * * RCS: @(#) $Id: tclTomMath.h,v 1.1.2.7 2005/09/26 20:16:53 kennykb Exp$ */ #ifndef TCLTOMMATH_H #define TCLTOMMATH_H 1 #include #include ................................................................................ #define TOOM_MUL_CUTOFF TclBNToomMulCutoff #define TOOM_SQR_CUTOFF TclBNToomSqrCutoff #define mp_s_rmap TclBNMpSRmap #define bn_reverse TclBN_reverse #define fast_s_mp_mul_digs TclBN_fast_s_mp_mul_digs #define fast_s_mp_sqr TclBN_fast_s_mp_sqr #define mp_add TclBN_mp_add #define mp_add_d TclBN_mp_add_d #define mp_and TclBN_mp_and #define mp_clamp TclBN_mp_clamp #define mp_clear TclBN_mp_clear #define mp_clear_multi TclBN_mp_clear_multi #define mp_cmp TclBN_mp_cmp #define mp_cmp_d TclBN_mp_cmp_d #define mp_cmp_mag TclBN_mp_cmp_mag ................................................................................ #define mp_div_3 TclBN_mp_div_3 #define mp_exch TclBN_mp_exch #define mp_expt_d TclBN_mp_expt_d #define mp_grow TclBN_mp_grow #define mp_init TclBN_mp_init #define mp_init_copy TclBN_mp_init_copy #define mp_init_multi TclBN_mp_init_multi #define mp_init_set TclBN_mp_init_set #define mp_init_size TclBN_mp_init_size #define mp_karatsuba_mul TclBN_mp_karatsuba_mul #define mp_karatsuba_sqr TclBN_mp_karatsuba_sqr #define mp_lshd TclBN_mp_lshd #define mp_mod TclBN_mp_mod #define mp_mod_2d TclBN_mp_mod_2d #define mp_mul TclBN_mp_mul #define mp_mul_2 TclBN_mp_mul_2 #define mp_mul_2d TclBN_mp_mul_2d #define mp_mul_d TclBN_mp_mul_d #define mp_neg TclBN_mp_neg #define mp_or TclBN_mp_or #define mp_radix_size TclBN_mp_radix_size #define mp_read_radix TclBN_mp_read_radix #define mp_rshd TclBN_mp_rshd #define mp_shrink TclBN_mp_shrink #define mp_set TclBN_mp_set #define mp_sqr TclBN_mp_sqr #define mp_sqrt TclBN_mp_sqrt #define mp_sub TclBN_mp_sub #define mp_sub_d TclBN_mp_sub_d #define mp_to_unsigned_bin TclBN_mp_to_unsigned_bin #define mp_to_unsigned_bin_n TclBN_mp_to_unsigned_bin_n #define mp_toom_mul TclBN_mp_toom_mul #define mp_toom_sqr TclBN_mp_toom_sqr #define mp_toradix_n TclBN_mp_toradix_n #define mp_unsigned_bin_size TclBN_mp_unsigned_bin_size #define mp_xor TclBN_mp_xor #define mp_zero TclBN_mp_zero #define s_mp_add TclBN_s_mp_add #define s_mp_mul_digs TclBN_s_mp_mul_digs #define s_mp_sqr TclBN_s_mp_sqr #define s_mp_sub TclBN_s_mp_sub #endif 

Changes to generic/tommath.h.

 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 ... 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 ... 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 ... 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 ... 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 ... 595 596 597 598 599 600 601 602  #include #include #include #include #include #undef MIN #define MIN(x,y) ((x)<(y)?(x):(y)) #undef MAX #define MAX(x,y) ((x)>(y)?(x):(y)) #ifdef __cplusplus extern "C" { /* C++ compilers don't like assigning void * to mp_digit * */ #define OPT_CAST(x) (x *) ................................................................................ #define XMALLOC malloc #define XFREE free #define XREALLOC realloc #define XCALLOC calloc #else /* prototypes for our heap functions */ extern void *XMALLOC(size_t n); extern void *REALLOC(void *p, size_t n); extern void *XCALLOC(size_t n, size_t s); extern void XFREE(void *p); #endif #endif /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ ................................................................................ #define MP_YES 1 /* yes response */ #define MP_NO 0 /* no response */ /* Primality generation flags */ #define LTM_PRIME_BBS 0x0001 /* BBS style prime */ #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ #define LTM_PRIME_2MSB_OFF 0x0004 /* force 2nd MSB to 0 */ #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ typedef int mp_err; /* you'll have to tune these... */ extern int KARATSUBA_MUL_CUTOFF, KARATSUBA_SQR_CUTOFF, ................................................................................ /* define this to use lower memory usage routines (exptmods mostly) */ /* #define MP_LOW_MEM */ /* default precision */ #ifndef MP_PREC #ifndef MP_LOW_MEM #define MP_PREC 64 /* default digits of precision */ #else #define MP_PREC 8 /* default digits of precision */ #endif #endif /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1)) ................................................................................ */ TOMMATH_STORAGE_CLASS int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); /* ---> radix conversion <--- */ TOMMATH_STORAGE_CLASS int mp_count_bits(mp_int *a); TOMMATH_STORAGE_CLASS int mp_unsigned_bin_size(mp_int *a); TOMMATH_STORAGE_CLASS int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c); TOMMATH_STORAGE_CLASS int mp_to_unsigned_bin(mp_int *a, unsigned char *b); TOMMATH_STORAGE_CLASS int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); TOMMATH_STORAGE_CLASS int mp_signed_bin_size(mp_int *a); TOMMATH_STORAGE_CLASS int mp_read_signed_bin(mp_int *a, unsigned char *b, int c); TOMMATH_STORAGE_CLASS int mp_to_signed_bin(mp_int *a, unsigned char *b); TOMMATH_STORAGE_CLASS int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); TOMMATH_STORAGE_CLASS int mp_read_radix(mp_int *a, const char *str, int radix); TOMMATH_STORAGE_CLASS int mp_toradix(mp_int *a, char *str, int radix); TOMMATH_STORAGE_CLASS int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); TOMMATH_STORAGE_CLASS int mp_radix_size(mp_int *a, int radix, int *size); ................................................................................ #ifdef __cplusplus } #endif #endif   | | > > | | > | < | | | > > > >  26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 ... 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 ... 165 166 167 168 169 170 171 172 173 174 175 176 177 178 ... 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 ... 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 ... 597 598 599 600 601 602 603 604 605 606 607 608  #include #include #include #include #include #ifndef MIN #define MIN(x,y) ((x)<(y)?(x):(y)) #endif #ifndef MAX #define MAX(x,y) ((x)>(y)?(x):(y)) #endif #ifdef __cplusplus extern "C" { /* C++ compilers don't like assigning void * to mp_digit * */ #define OPT_CAST(x) (x *) ................................................................................ #define XMALLOC malloc #define XFREE free #define XREALLOC realloc #define XCALLOC calloc #else /* prototypes for our heap functions */ extern void *XMALLOC(size_t n); extern void *XREALLOC(void *p, size_t n); extern void *XCALLOC(size_t n, size_t s); extern void XFREE(void *p); #endif #endif /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ ................................................................................ #define MP_YES 1 /* yes response */ #define MP_NO 0 /* no response */ /* Primality generation flags */ #define LTM_PRIME_BBS 0x0001 /* BBS style prime */ #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ typedef int mp_err; /* you'll have to tune these... */ extern int KARATSUBA_MUL_CUTOFF, KARATSUBA_SQR_CUTOFF, ................................................................................ /* define this to use lower memory usage routines (exptmods mostly) */ /* #define MP_LOW_MEM */ /* default precision */ #ifndef MP_PREC #ifndef MP_LOW_MEM #define MP_PREC 32 /* default digits of precision */ #else #define MP_PREC 8 /* default digits of precision */ #endif #endif /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1)) ................................................................................ */ TOMMATH_STORAGE_CLASS int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); /* ---> radix conversion <--- */ TOMMATH_STORAGE_CLASS int mp_count_bits(mp_int *a); TOMMATH_STORAGE_CLASS int mp_unsigned_bin_size(mp_int *a); TOMMATH_STORAGE_CLASS int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); TOMMATH_STORAGE_CLASS int mp_to_unsigned_bin(mp_int *a, unsigned char *b); TOMMATH_STORAGE_CLASS int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); TOMMATH_STORAGE_CLASS int mp_signed_bin_size(mp_int *a); TOMMATH_STORAGE_CLASS int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); TOMMATH_STORAGE_CLASS int mp_to_signed_bin(mp_int *a, unsigned char *b); TOMMATH_STORAGE_CLASS int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); TOMMATH_STORAGE_CLASS int mp_read_radix(mp_int *a, const char *str, int radix); TOMMATH_STORAGE_CLASS int mp_toradix(mp_int *a, char *str, int radix); TOMMATH_STORAGE_CLASS int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); TOMMATH_STORAGE_CLASS int mp_radix_size(mp_int *a, int radix, int *size); ................................................................................ #ifdef __cplusplus } #endif #endif /* $Source: /root/tcl/repos-to-convert/tcl/generic/tommath.h,v$ */ /* $Revision: 1.1.2.4$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn.pdf.

cannot compute difference between binary files

Changes to libtommath/bn.tex.


     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47  #include #ifdef BN_ERROR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ static const struct { int code; char *msg; } msgs[] = { { MP_OKAY, "Successful" }, { MP_MEM, "Out of heap" }, { MP_VAL, "Value out of range" } }; /* return a char * string for a given code */ char *mp_error_to_string(int code) { int x; /* scan the lookup table for the given message */ for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) { if (msgs[x].code == code) { return msgs[x].msg; } } /* generic reply for invalid code */ return "Invalid error code"; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_error.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_fast_mp_invmod.c.

 138 139 140 141 142 143 144   c->sign = neg; res = MP_OKAY; LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); return res; } #endif   > > > >  138 139 140 141 142 143 144 145 146 147 148   c->sign = neg; res = MP_OKAY; LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_fast_mp_invmod.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_fast_mp_montgomery_reduce.c.

 162 163 164 165 166 167 168   /* if A >= m then A = A - m */ if (mp_cmp_mag (x, n) != MP_LT) { return s_mp_sub (x, n, x); } return MP_OKAY; } #endif   > > > >  162 163 164 165 166 167 168 169 170 171 172   /* if A >= m then A = A - m */ if (mp_cmp_mag (x, n) != MP_LT) { return s_mp_sub (x, n, x); } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_fast_mp_montgomery_reduce.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_fast_s_mp_mul_digs.c.

 66 67 68 69 70 71 72 73 74 75 76 77 78 79 .. 99 100 101 102 103 104 105   while (tx++ < a->used && ty-- >= 0) { ... } */ iy = MIN(a->used-tx, ty+1); /* execute loop */ for (iz = 0; iz < iy; ++iz) { _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); } /* store term */ W[ix] = ((mp_digit)_W) & MP_MASK; /* make next carry */ _W = _W >> ((mp_word)DIGIT_BIT); ................................................................................ *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } #endif   > > > > >  66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 ... 100 101 102 103 104 105 106 107 108 109 110   while (tx++ < a->used && ty-- >= 0) { ... } */ iy = MIN(a->used-tx, ty+1); /* execute loop */ for (iz = 0; iz < iy; ++iz) { _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); } /* store term */ W[ix] = ((mp_digit)_W) & MP_MASK; /* make next carry */ _W = _W >> ((mp_word)DIGIT_BIT); ................................................................................ *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_fast_s_mp_mul_digs.c,v$ */ /* $Revision: 1.1.1.1.2.3$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_fast_s_mp_mul_high_digs.c.

 91 92 93 94 95 96 97   *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } #endif   > > > >  91 92 93 94 95 96 97 98 99 100 101   *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_fast_s_mp_mul_high_digs.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_fast_s_mp_sqr.c.

 104 105 106 107 108 109 110   *tmpb++ = 0; } } mp_clamp (b); return MP_OKAY; } #endif   > > > >  104 105 106 107 108 109 110 111 112 113 114   *tmpb++ = 0; } } mp_clamp (b); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_fast_s_mp_sqr.c,v$ */ /* $Revision: 1.1.1.1.2.3$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48  #include #ifdef BN_MP_2EXPT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* computes a = 2**b * * Simple algorithm which zeroes the int, grows it then just sets one bit * as required. */ int mp_2expt (mp_int * a, int b) { int res; /* zero a as per default */ mp_zero (a); /* grow a to accomodate the single bit */ if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) { return res; } /* set the used count of where the bit will go */ a->used = b / DIGIT_BIT + 1; /* put the single bit in its place */ a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_2expt.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43  #include #ifdef BN_MP_ABS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* b = |a| * * Simple function copies the input and fixes the sign to positive */ int mp_abs (mp_int * a, mp_int * b) { int res; /* copy a to b */ if (a != b) { if ((res = mp_copy (a, b)) != MP_OKAY) { return res; } } /* force the sign of b to positive */ b->sign = MP_ZPOS; return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_abs.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53  #include #ifdef BN_MP_ADD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* high level addition (handles signs) */ int mp_add (mp_int * a, mp_int * b, mp_int * c) { int sa, sb, res; /* get sign of both inputs */ sa = a->sign; sb = b->sign; /* handle two cases, not four */ if (sa == sb) { /* both positive or both negative */ /* add their magnitudes, copy the sign */ c->sign = sa; res = s_mp_add (a, b, c); } else { /* one positive, the other negative */ /* subtract the one with the greater magnitude from */ /* the one of the lesser magnitude. The result gets */ /* the sign of the one with the greater magnitude. */ if (mp_cmp_mag (a, b) == MP_LT) { c->sign = sb; res = s_mp_sub (b, a, c); } else { c->sign = sa; res = s_mp_sub (a, b, c); } } return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_add.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

 100 101 102 103 104 105 106   } mp_clamp(c); return MP_OKAY; } #endif   > > > >  100 101 102 103 104 105 106 107 108 109 110   } mp_clamp(c); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_add_d.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41  #include #ifdef BN_MP_ADDMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* d = a + b (mod c) */ int mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) { int res; mp_int t; if ((res = mp_init (&t)) != MP_OKAY) { return res; } if ((res = mp_add (a, b, &t)) != MP_OKAY) { mp_clear (&t); return res; } res = mp_mod (&t, c, d); mp_clear (&t); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_addmod.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57  #include #ifdef BN_MP_AND_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* AND two ints together */ int mp_and (mp_int * a, mp_int * b, mp_int * c) { int res, ix, px; mp_int t, *x; if (a->used > b->used) { if ((res = mp_init_copy (&t, a)) != MP_OKAY) { return res; } px = b->used; x = b; } else { if ((res = mp_init_copy (&t, b)) != MP_OKAY) { return res; } px = a->used; x = a; } for (ix = 0; ix < px; ix++) { t.dp[ix] &= x->dp[ix]; } /* zero digits above the last from the smallest mp_int */ for (; ix < t.used; ix++) { t.dp[ix] = 0; } mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_and.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44  #include #ifdef BN_MP_CLAMP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* trim unused digits * * This is used to ensure that leading zero digits are * trimed and the leading "used" digit will be non-zero * Typically very fast. Also fixes the sign if there * are no more leading digits */ void mp_clamp (mp_int * a) { /* decrease used while the most significant digit is * zero. */ while (a->used > 0 && a->dp[a->used - 1] == 0) { --(a->used); } /* reset the sign flag if used == 0 */ if (a->used == 0) { a->sign = MP_ZPOS; } } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_clamp.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44  #include #ifdef BN_MP_CLEAR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* clear one (frees) */ void mp_clear (mp_int * a) { int i; /* only do anything if a hasn't been freed previously */ if (a->dp != NULL) { /* first zero the digits */ for (i = 0; i < a->used; i++) { a->dp[i] = 0; } /* free ram */ XFREE(a->dp); /* reset members to make debugging easier */ a->dp = NULL; a->alloc = a->used = 0; a->sign = MP_ZPOS; } } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_clear.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34  #include #ifdef BN_MP_CLEAR_MULTI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include void mp_clear_multi(mp_int *mp, ...) { mp_int* next_mp = mp; va_list args; va_start(args, mp); while (next_mp != NULL) { mp_clear(next_mp); next_mp = va_arg(args, mp_int*); } va_end(args); } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_clear_multi.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43  #include #ifdef BN_MP_CMP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* compare two ints (signed)*/ int mp_cmp (mp_int * a, mp_int * b) { /* compare based on sign */ if (a->sign != b->sign) { if (a->sign == MP_NEG) { return MP_LT; } else { return MP_GT; } } /* compare digits */ if (a->sign == MP_NEG) { /* if negative compare opposite direction */ return mp_cmp_mag(b, a); } else { return mp_cmp_mag(a, b); } } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_cmp.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44  #include #ifdef BN_MP_CMP_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* compare a digit */ int mp_cmp_d(mp_int * a, mp_digit b) { /* compare based on sign */ if (a->sign == MP_NEG) { return MP_LT; } /* compare based on magnitude */ if (a->used > 1) { return MP_GT; } /* compare the only digit of a to b */ if (a->dp[0] > b) { return MP_GT; } else if (a->dp[0] < b) { return MP_LT; } else { return MP_EQ; } } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_cmp_d.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55  #include #ifdef BN_MP_CMP_MAG_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* compare maginitude of two ints (unsigned) */ int mp_cmp_mag (mp_int * a, mp_int * b) { int n; mp_digit *tmpa, *tmpb; /* compare based on # of non-zero digits */ if (a->used > b->used) { return MP_GT; } if (a->used < b->used) { return MP_LT; } /* alias for a */ tmpa = a->dp + (a->used - 1); /* alias for b */ tmpb = b->dp + (a->used - 1); /* compare based on digits */ for (n = 0; n < a->used; ++n, --tmpa, --tmpb) { if (*tmpa > *tmpb) { return MP_GT; } if (*tmpa < *tmpb) { return MP_LT; } } return MP_EQ; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_cmp_mag.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53  #include #ifdef BN_MP_CNT_LSB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ static const int lnz[16] = { 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 }; /* Counts the number of lsbs which are zero before the first zero bit */ int mp_cnt_lsb(mp_int *a) { int x; mp_digit q, qq; /* easy out */ if (mp_iszero(a) == 1) { return 0; } /* scan lower digits until non-zero */ for (x = 0; x < a->used && a->dp[x] == 0; x++); q = a->dp[x]; x *= DIGIT_BIT; /* now scan this digit until a 1 is found */ if ((q & 1) == 0) { do { qq = q & 15; x += lnz[qq]; q >>= 4; } while (qq == 0); } return x; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_cnt_lsb.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68  #include #ifdef BN_MP_COPY_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* copy, b = a */ int mp_copy (mp_int * a, mp_int * b) { int res, n; /* if dst == src do nothing */ if (a == b) { return MP_OKAY; } /* grow dest */ if (b->alloc < a->used) { if ((res = mp_grow (b, a->used)) != MP_OKAY) { return res; } } /* zero b and copy the parameters over */ { register mp_digit *tmpa, *tmpb; /* pointer aliases */ /* source */ tmpa = a->dp; /* destination */ tmpb = b->dp; /* copy all the digits */ for (n = 0; n < a->used; n++) { *tmpb++ = *tmpa++; } /* clear high digits */ for (; n < b->used; n++) { *tmpb++ = 0; } } /* copy used count and sign */ b->used = a->used; b->sign = a->sign; return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_copy.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45  #include #ifdef BN_MP_COUNT_BITS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* returns the number of bits in an int */ int mp_count_bits (mp_int * a) { int r; mp_digit q; /* shortcut */ if (a->used == 0) { return 0; } /* get number of digits and add that */ r = (a->used - 1) * DIGIT_BIT; /* take the last digit and count the bits in it */ q = a->dp[a->used - 1]; while (q > ((mp_digit) 0)) { ++r; q >>= ((mp_digit) 1); } return r; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_count_bits.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292  #include #ifdef BN_MP_DIV_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #ifdef BN_MP_DIV_SMALL /* slower bit-bang division... also smaller */ int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d) { mp_int ta, tb, tq, q; int res, n, n2; /* is divisor zero ? */ if (mp_iszero (b) == 1) { return MP_VAL; } /* if a < b then q=0, r = a */ if (mp_cmp_mag (a, b) == MP_LT) { if (d != NULL) { res = mp_copy (a, d); } else { res = MP_OKAY; } if (c != NULL) { mp_zero (c); } return res; } /* init our temps */ if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) { return res; } mp_set(&tq, 1); n = mp_count_bits(a) - mp_count_bits(b); if (((res = mp_abs(a, &ta)) != MP_OKAY) || ((res = mp_abs(b, &tb)) != MP_OKAY) || ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) { goto LBL_ERR; } while (n-- >= 0) { if (mp_cmp(&tb, &ta) != MP_GT) { if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) { goto LBL_ERR; } } if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) || ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) { goto LBL_ERR; } } /* now q == quotient and ta == remainder */ n = a->sign; n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG); if (c != NULL) { mp_exch(c, &q); c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2; } if (d != NULL) { mp_exch(d, &ta); d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n; } LBL_ERR: mp_clear_multi(&ta, &tb, &tq, &q, NULL); return res; } #else /* integer signed division. * c*b + d == a [e.g. a/b, c=quotient, d=remainder] * HAC pp.598 Algorithm 14.20 * * Note that the description in HAC is horribly * incomplete. For example, it doesn't consider * the case where digits are removed from 'x' in * the inner loop. It also doesn't consider the * case that y has fewer than three digits, etc.. * * The overall algorithm is as described as * 14.20 from HAC but fixed to treat these cases. */ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d) { mp_int q, x, y, t1, t2; int res, n, t, i, norm, neg; /* is divisor zero ? */ if (mp_iszero (b) == 1) { return MP_VAL; } /* if a < b then q=0, r = a */ if (mp_cmp_mag (a, b) == MP_LT) { if (d != NULL) { res = mp_copy (a, d); } else { res = MP_OKAY; } if (c != NULL) { mp_zero (c); } return res; } if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) { return res; } q.used = a->used + 2; if ((res = mp_init (&t1)) != MP_OKAY) { goto LBL_Q; } if ((res = mp_init (&t2)) != MP_OKAY) { goto LBL_T1; } if ((res = mp_init_copy (&x, a)) != MP_OKAY) { goto LBL_T2; } if ((res = mp_init_copy (&y, b)) != MP_OKAY) { goto LBL_X; } /* fix the sign */ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; x.sign = y.sign = MP_ZPOS; /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */ norm = mp_count_bits(&y) % DIGIT_BIT; if (norm < (int)(DIGIT_BIT-1)) { norm = (DIGIT_BIT-1) - norm; if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) { goto LBL_Y; } if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) { goto LBL_Y; } } else { norm = 0; } /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */ n = x.used - 1; t = y.used - 1; /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */ if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */ goto LBL_Y; } while (mp_cmp (&x, &y) != MP_LT) { ++(q.dp[n - t]); if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) { goto LBL_Y; } } /* reset y by shifting it back down */ mp_rshd (&y, n - t); /* step 3. for i from n down to (t + 1) */ for (i = n; i >= (t + 1); i--) { if (i > x.used) { continue; } /* step 3.1 if xi == yt then set q{i-t-1} to b-1, * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */ if (x.dp[i] == y.dp[t]) { q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1); } else { mp_word tmp; tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT); tmp |= ((mp_word) x.dp[i - 1]); tmp /= ((mp_word) y.dp[t]); if (tmp > (mp_word) MP_MASK) tmp = MP_MASK; q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK)); } /* while (q{i-t-1} * (yt * b + y{t-1})) > xi * b**2 + xi-1 * b + xi-2 do q{i-t-1} -= 1; */ q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK; do { q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK; /* find left hand */ mp_zero (&t1); t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1]; t1.dp[1] = y.dp[t]; t1.used = 2; if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) { goto LBL_Y; } /* find right hand */ t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2]; t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1]; t2.dp[2] = x.dp[i]; t2.used = 3; } while (mp_cmp_mag(&t1, &t2) == MP_GT); /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */ if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) { goto LBL_Y; } if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { goto LBL_Y; } if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) { goto LBL_Y; } /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */ if (x.sign == MP_NEG) { if ((res = mp_copy (&y, &t1)) != MP_OKAY) { goto LBL_Y; } if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { goto LBL_Y; } if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) { goto LBL_Y; } q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK; } } /* now q is the quotient and x is the remainder * [which we have to normalize] */ /* get sign before writing to c */ x.sign = x.used == 0 ? MP_ZPOS : a->sign; if (c != NULL) { mp_clamp (&q); mp_exch (&q, c); c->sign = neg; } if (d != NULL) { mp_div_2d (&x, norm, &x, NULL); mp_exch (&x, d); } res = MP_OKAY; LBL_Y:mp_clear (&y); LBL_X:mp_clear (&x); LBL_T2:mp_clear (&t2); LBL_T1:mp_clear (&t1); LBL_Q:mp_clear (&q); return res; } #endif #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_div.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68  #include #ifdef BN_MP_DIV_2_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* b = a/2 */ int mp_div_2(mp_int * a, mp_int * b) { int x, res, oldused; /* copy */ if (b->alloc < a->used) { if ((res = mp_grow (b, a->used)) != MP_OKAY) { return res; } } oldused = b->used; b->used = a->used; { register mp_digit r, rr, *tmpa, *tmpb; /* source alias */ tmpa = a->dp + b->used - 1; /* dest alias */ tmpb = b->dp + b->used - 1; /* carry */ r = 0; for (x = b->used - 1; x >= 0; x--) { /* get the carry for the next iteration */ rr = *tmpa & 1; /* shift the current digit, add in carry and store */ *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1)); /* forward carry to next iteration */ r = rr; } /* zero excess digits */ tmpb = b->dp + b->used; for (x = b->used; x < oldused; x++) { *tmpb++ = 0; } } b->sign = a->sign; mp_clamp (b); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_div_2.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97  #include #ifdef BN_MP_DIV_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* shift right by a certain bit count (store quotient in c, optional remainder in d) */ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) { mp_digit D, r, rr; int x, res; mp_int t; /* if the shift count is <= 0 then we do no work */ if (b <= 0) { res = mp_copy (a, c); if (d != NULL) { mp_zero (d); } return res; } if ((res = mp_init (&t)) != MP_OKAY) { return res; } /* get the remainder */ if (d != NULL) { if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) { mp_clear (&t); return res; } } /* copy */ if ((res = mp_copy (a, c)) != MP_OKAY) { mp_clear (&t); return res; } /* shift by as many digits in the bit count */ if (b >= (int)DIGIT_BIT) { mp_rshd (c, b / DIGIT_BIT); } /* shift any bit count < DIGIT_BIT */ D = (mp_digit) (b % DIGIT_BIT); if (D != 0) { register mp_digit *tmpc, mask, shift; /* mask */ mask = (((mp_digit)1) << D) - 1; /* shift for lsb */ shift = DIGIT_BIT - D; /* alias */ tmpc = c->dp + (c->used - 1); /* carry */ r = 0; for (x = c->used - 1; x >= 0; x--) { /* get the lower bits of this word in a temp */ rr = *tmpc & mask; /* shift the current word and mix in the carry bits from the previous word */ *tmpc = (*tmpc >> D) | (r << shift); --tmpc; /* set the carry to the carry bits of the current word found above */ r = rr; } } mp_clamp (c); if (d != NULL) { mp_exch (&t, d); } mp_clear (&t); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_div_2d.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79  #include #ifdef BN_MP_DIV_3_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* divide by three (based on routine from MPI and the GMP manual) */ int mp_div_3 (mp_int * a, mp_int *c, mp_digit * d) { mp_int q; mp_word w, t; mp_digit b; int res, ix; /* b = 2**DIGIT_BIT / 3 */ b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3); if ((res = mp_init_size(&q, a->used)) != MP_OKAY) { return res; } q.used = a->used; q.sign = a->sign; w = 0; for (ix = a->used - 1; ix >= 0; ix--) { w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]); if (w >= 3) { /* multiply w by [1/3] */ t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT); /* now subtract 3 * [w/3] from w, to get the remainder */ w -= t+t+t; /* fixup the remainder as required since * the optimization is not exact. */ while (w >= 3) { t += 1; w -= 3; } } else { t = 0; } q.dp[ix] = (mp_digit)t; } /* [optional] store the remainder */ if (d != NULL) { *d = (mp_digit)w; } /* [optional] store the quotient */ if (c != NULL) { mp_clamp(&q); mp_exch(&q, c); } mp_clear(&q); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_div_3.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110  #include #ifdef BN_MP_DIV_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ static int s_is_power_of_two(mp_digit b, int *p) { int x; for (x = 1; x < DIGIT_BIT; x++) { if (b == (((mp_digit)1)<dp[0] & ((((mp_digit)1)<used)) != MP_OKAY) { return res; } q.used = a->used; q.sign = a->sign; w = 0; for (ix = a->used - 1; ix >= 0; ix--) { w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]); if (w >= b) { t = (mp_digit)(w / b); w -= ((mp_word)t) * ((mp_word)b); } else { t = 0; } q.dp[ix] = (mp_digit)t; } if (d != NULL) { *d = (mp_digit)w; } if (c != NULL) { mp_clamp(&q); mp_exch(&q, c); } mp_clear(&q); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_div_d.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43  #include #ifdef BN_MP_DR_IS_MODULUS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* determines if a number is a valid DR modulus */ int mp_dr_is_modulus(mp_int *a) { int ix; /* must be at least two digits */ if (a->used < 2) { return 0; } /* must be of the form b**k - a [a <= b] so all * but the first digit must be equal to -1 (mod b). */ for (ix = 1; ix < a->used; ix++) { if (a->dp[ix] != MP_MASK) { return 0; } } return 1; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_dr_is_modulus.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94  #include #ifdef BN_MP_DR_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* reduce "x" in place modulo "n" using the Diminished Radix algorithm. * * Based on algorithm from the paper * * "Generating Efficient Primes for Discrete Log Cryptosystems" * Chae Hoon Lim, Pil Joong Lee, * POSTECH Information Research Laboratories * * The modulus must be of a special format [see manual] * * Has been modified to use algorithm 7.10 from the LTM book instead * * Input x must be in the range 0 <= x <= (n-1)**2 */ int mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k) { int err, i, m; mp_word r; mp_digit mu, *tmpx1, *tmpx2; /* m = digits in modulus */ m = n->used; /* ensure that "x" has at least 2m digits */ if (x->alloc < m + m) { if ((err = mp_grow (x, m + m)) != MP_OKAY) { return err; } } /* top of loop, this is where the code resumes if * another reduction pass is required. */ top: /* aliases for digits */ /* alias for lower half of x */ tmpx1 = x->dp; /* alias for upper half of x, or x/B**m */ tmpx2 = x->dp + m; /* set carry to zero */ mu = 0; /* compute (x mod B**m) + k * [x/B**m] inline and inplace */ for (i = 0; i < m; i++) { r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu; *tmpx1++ = (mp_digit)(r & MP_MASK); mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT)); } /* set final carry */ *tmpx1++ = mu; /* zero words above m */ for (i = m + 1; i < x->used; i++) { *tmpx1++ = 0; } /* clamp, sub and return */ mp_clamp (x); /* if x >= n then subtract and reduce again * Each successive "recursion" makes the input smaller and smaller. */ if (mp_cmp_mag (x, n) != MP_LT) { s_mp_sub(x, n, x); goto top; } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_dr_reduce.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  #include #ifdef BN_MP_DR_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* determines the setup value */ void mp_dr_setup(mp_int *a, mp_digit *d) { /* the casts are required if DIGIT_BIT is one less than * the number of bits in a mp_digit [e.g. DIGIT_BIT==31] */ *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - ((mp_word)a->dp[0])); } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_dr_setup.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34  #include #ifdef BN_MP_EXCH_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* swap the elements of two integers, for cases where you can't simply swap the * mp_int pointers around */ void mp_exch (mp_int * a, mp_int * b) { mp_int t; t = *a; *a = *b; *b = t; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_exch.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57  #include #ifdef BN_MP_EXPT_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* calculate c = a**b using a square-multiply algorithm */ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) { int res, x; mp_int g; if ((res = mp_init_copy (&g, a)) != MP_OKAY) { return res; } /* set initial result */ mp_set (c, 1); for (x = 0; x < (int) DIGIT_BIT; x++) { /* square */ if ((res = mp_sqr (c, c)) != MP_OKAY) { mp_clear (&g); return res; } /* if the bit is set multiply */ if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) { if ((res = mp_mul (c, &g, c)) != MP_OKAY) { mp_clear (&g); return res; } } /* shift to next bit */ b <<= 1; } mp_clear (&g); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_expt_d.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_exptmod.c.

 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 ... 102 103 104 105 106 107 108  #else /* no invmod */ return MP_VAL; #endif } /* modified diminished radix reduction */ #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) if (mp_reduce_is_2k_l(P) == MP_YES) { return s_mp_exptmod(G, X, P, Y, 1); } #endif #ifdef BN_MP_DR_IS_MODULUS_C /* is it a DR modulus? */ ................................................................................ #endif #ifdef BN_MP_EXPTMOD_FAST_C } #endif } #endif   | > > > >  62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 ... 102 103 104 105 106 107 108 109 110 111 112  #else /* no invmod */ return MP_VAL; #endif } /* modified diminished radix reduction */ #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C) if (mp_reduce_is_2k_l(P) == MP_YES) { return s_mp_exptmod(G, X, P, Y, 1); } #endif #ifdef BN_MP_DR_IS_MODULUS_C /* is it a DR modulus? */ ................................................................................ #endif #ifdef BN_MP_EXPTMOD_FAST_C } #endif } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_exptmod.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_exptmod_fast.c.

 311 312 313 314 315 316 317   for (x = 1<<(winsize-1); x < (1 << winsize); x++) { mp_clear (&M[x]); } return err; } #endif   > > > >  311 312 313 314 315 316 317 318 319 320 321   for (x = 1<<(winsize-1); x < (1 << winsize); x++) { mp_clear (&M[x]); } return err; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_exptmod_fast.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_exteuclid.c.

 72 73 74 75 76 77 78   if (U3 != NULL) { mp_exch(U3, &u3); } err = MP_OKAY; _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); return err; } #endif   > > > >  72 73 74 75 76 77 78 79 80 81 82   if (U3 != NULL) { mp_exch(U3, &u3); } err = MP_OKAY; _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); return err; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_exteuclid.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67  #include #ifdef BN_MP_FREAD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* read a bigint from a file stream in ASCII */ int mp_fread(mp_int *a, int radix, FILE *stream) { int err, ch, neg, y; /* clear a */ mp_zero(a); /* if first digit is - then set negative */ ch = fgetc(stream); if (ch == '-') { neg = MP_NEG; ch = fgetc(stream); } else { neg = MP_ZPOS; } for (;;) { /* find y in the radix map */ for (y = 0; y < radix; y++) { if (mp_s_rmap[y] == ch) { break; } } if (y == radix) { break; } /* shift up and add */ if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) { return err; } if ((err = mp_add_d(a, y, a)) != MP_OKAY) { return err; } ch = fgetc(stream); } if (mp_cmp_d(a, 0) != MP_EQ) { a->sign = neg; } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_fread.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52  #include #ifdef BN_MP_FWRITE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ int mp_fwrite(mp_int *a, int radix, FILE *stream) { char *buf; int err, len, x; if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) { return err; } buf = OPT_CAST(char) XMALLOC (len); if (buf == NULL) { return MP_MEM; } if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) { XFREE (buf); return err; } for (x = 0; x < len; x++) { if (fputc(buf[x], stream) == EOF) { XFREE (buf); return MP_VAL; } } XFREE (buf); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_fwrite.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113  #include #ifdef BN_MP_GCD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* Greatest Common Divisor using the binary method */ int mp_gcd (mp_int * a, mp_int * b, mp_int * c) { mp_int u, v; int k, u_lsb, v_lsb, res; /* either zero than gcd is the largest */ if (mp_iszero (a) == 1 && mp_iszero (b) == 0) { return mp_abs (b, c); } if (mp_iszero (a) == 0 && mp_iszero (b) == 1) { return mp_abs (a, c); } /* optimized. At this point if a == 0 then * b must equal zero too */ if (mp_iszero (a) == 1) { mp_zero(c); return MP_OKAY; } /* get copies of a and b we can modify */ if ((res = mp_init_copy (&u, a)) != MP_OKAY) { return res; } if ((res = mp_init_copy (&v, b)) != MP_OKAY) { goto LBL_U; } /* must be positive for the remainder of the algorithm */ u.sign = v.sign = MP_ZPOS; /* B1. Find the common power of two for u and v */ u_lsb = mp_cnt_lsb(&u); v_lsb = mp_cnt_lsb(&v); k = MIN(u_lsb, v_lsb); if (k > 0) { /* divide the power of two out */ if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) { goto LBL_V; } if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) { goto LBL_V; } } /* divide any remaining factors of two out */ if (u_lsb != k) { if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) { goto LBL_V; } } if (v_lsb != k) { if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) { goto LBL_V; } } while (mp_iszero(&v) == 0) { /* make sure v is the largest */ if (mp_cmp_mag(&u, &v) == MP_GT) { /* swap u and v to make sure v is >= u */ mp_exch(&u, &v); } /* subtract smallest from largest */ if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) { goto LBL_V; } /* Divide out all factors of two */ if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) { goto LBL_V; } } /* multiply by 2**k which we divided out at the beginning */ if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) { goto LBL_V; } c->sign = MP_ZPOS; res = MP_OKAY; LBL_V:mp_clear (&u); LBL_U:mp_clear (&v); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_gcd.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45  #include #ifdef BN_MP_GET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* get the lower 32-bits of an mp_int */ unsigned long mp_get_int(mp_int * a) { int i; unsigned long res; if (a->used == 0) { return 0; } /* get number of digits of the lsb we have to read */ i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1; /* get most significant digit of result */ res = DIGIT(a,i); while (--i >= 0) { res = (res << DIGIT_BIT) | DIGIT(a,i); } /* force result to 32-bits always so it is consistent on non 32-bit platforms */ return res & 0xFFFFFFFFUL; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_get_int.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57  #include #ifdef BN_MP_GROW_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* grow as required */ int mp_grow (mp_int * a, int size) { int i; mp_digit *tmp; /* if the alloc size is smaller alloc more ram */ if (a->alloc < size) { /* ensure there are always at least MP_PREC digits extra on top */ size += (MP_PREC * 2) - (size % MP_PREC); /* reallocate the array a->dp * * We store the return in a temporary variable * in case the operation failed we don't want * to overwrite the dp member of a. */ tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size); if (tmp == NULL) { /* reallocation failed but "a" is still valid [can be freed] */ return MP_MEM; } /* reallocation succeeded so set a->dp */ a->dp = tmp; /* zero excess digits */ i = a->alloc; a->alloc = size; for (; i < a->alloc; i++) { a->dp[i] = 0; } } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_grow.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46  #include #ifdef BN_MP_INIT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* init a new mp_int */ int mp_init (mp_int * a) { int i; /* allocate memory required and clear it */ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC); if (a->dp == NULL) { return MP_MEM; } /* set the digits to zero */ for (i = 0; i < MP_PREC; i++) { a->dp[i] = 0; } /* set the used to zero, allocated digits to the default precision * and sign to positive */ a->used = 0; a->alloc = MP_PREC; a->sign = MP_ZPOS; return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_init.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  #include #ifdef BN_MP_INIT_COPY_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* creates "a" then copies b into it */ int mp_init_copy (mp_int * a, mp_int * b) { int res; if ((res = mp_init (a)) != MP_OKAY) { return res; } return mp_copy (b, a); } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_init_copy.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59  #include #ifdef BN_MP_INIT_MULTI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include int mp_init_multi(mp_int *mp, ...) { mp_err res = MP_OKAY; /* Assume ok until proven otherwise */ int n = 0; /* Number of ok inits */ mp_int* cur_arg = mp; va_list args; va_start(args, mp); /* init args to next argument from caller */ while (cur_arg != NULL) { if (mp_init(cur_arg) != MP_OKAY) { /* Oops - error! Back-track and mp_clear what we already succeeded in init-ing, then return error. */ va_list clean_args; /* end the current list */ va_end(args); /* now start cleaning up */ cur_arg = mp; va_start(clean_args, mp); while (n--) { mp_clear(cur_arg); cur_arg = va_arg(clean_args, mp_int*); } va_end(clean_args); res = MP_MEM; break; } n++; cur_arg = va_arg(args, mp_int*); } va_end(args); return res; /* Assumed ok, if error flagged above. */ } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_init_multi.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  #include #ifdef BN_MP_INIT_SET_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* initialize and set a digit */ int mp_init_set (mp_int * a, mp_digit b) { int err; if ((err = mp_init(a)) != MP_OKAY) { return err; } mp_set(a, b); return err; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_init_set.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31  #include #ifdef BN_MP_INIT_SET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* initialize and set a digit */ int mp_init_set_int (mp_int * a, unsigned long b) { int err; if ((err = mp_init(a)) != MP_OKAY) { return err; } return mp_set_int(a, b); } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_init_set_int.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48  #include #ifdef BN_MP_INIT_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* init an mp_init for a given size */ int mp_init_size (mp_int * a, int size) { int x; /* pad size so there are always extra digits */ size += (MP_PREC * 2) - (size % MP_PREC); /* alloc mem */ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size); if (a->dp == NULL) { return MP_MEM; } /* set the members */ a->used = 0; a->alloc = size; a->sign = MP_ZPOS; /* zero the digits */ for (x = 0; x < size; x++) { a->dp[x] = 0; } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_init_size.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43  #include #ifdef BN_MP_INVMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* hac 14.61, pp608 */ int mp_invmod (mp_int * a, mp_int * b, mp_int * c) { /* b cannot be negative */ if (b->sign == MP_NEG || mp_iszero(b) == 1) { return MP_VAL; } #ifdef BN_FAST_MP_INVMOD_C /* if the modulus is odd we can use a faster routine instead */ if (mp_isodd (b) == 1) { return fast_mp_invmod (a, b, c); } #endif #ifdef BN_MP_INVMOD_SLOW_C return mp_invmod_slow(a, b, c); #endif return MP_VAL; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_invmod.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_invmod_slow.c.

 165 166 167 168 169 170 171   /* C is now the inverse */ mp_exch (&C, c); res = MP_OKAY; LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); return res; } #endif   > > > >  165 166 167 168 169 170 171 172 173 174 175   /* C is now the inverse */ mp_exch (&C, c); res = MP_OKAY; LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_invmod_slow.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109  #include #ifdef BN_MP_IS_SQUARE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* Check if remainders are possible squares - fast exclude non-squares */ static const char rem_128[128] = { 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 }; static const char rem_105[105] = { 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1 }; /* Store non-zero to ret if arg is square, and zero if not */ int mp_is_square(mp_int *arg,int *ret) { int res; mp_digit c; mp_int t; unsigned long r; /* Default to Non-square :) */ *ret = MP_NO; if (arg->sign == MP_NEG) { return MP_VAL; } /* digits used? (TSD) */ if (arg->used == 0) { return MP_OKAY; } /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */ if (rem_128[127 & DIGIT(arg,0)] == 1) { return MP_OKAY; } /* Next check mod 105 (3*5*7) */ if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) { return res; } if (rem_105[c] == 1) { return MP_OKAY; } if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) { return res; } if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) { goto ERR; } r = mp_get_int(&t); /* Check for other prime modules, note it's not an ERROR but we must * free "t" so the easiest way is to goto ERR. We know that res * is already equal to MP_OKAY from the mp_mod call */ if ( (1L<<(r%11)) & 0x5C4L ) goto ERR; if ( (1L<<(r%13)) & 0x9E4L ) goto ERR; if ( (1L<<(r%17)) & 0x5CE8L ) goto ERR; if ( (1L<<(r%19)) & 0x4F50CL ) goto ERR; if ( (1L<<(r%23)) & 0x7ACCA0L ) goto ERR; if ( (1L<<(r%29)) & 0xC2EDD0CL ) goto ERR; if ( (1L<<(r%31)) & 0x6DE2B848L ) goto ERR; /* Final check - is sqr(sqrt(arg)) == arg ? */ if ((res = mp_sqrt(arg,&t)) != MP_OKAY) { goto ERR; } if ((res = mp_sqr(&t,&t)) != MP_OKAY) { goto ERR; } *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO; ERR:mp_clear(&t); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_is_square.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105  #include #ifdef BN_MP_JACOBI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* computes the jacobi c = (a | n) (or Legendre if n is prime) * HAC pp. 73 Algorithm 2.149 */ int mp_jacobi (mp_int * a, mp_int * p, int *c) { mp_int a1, p1; int k, s, r, res; mp_digit residue; /* if p <= 0 return MP_VAL */ if (mp_cmp_d(p, 0) != MP_GT) { return MP_VAL; } /* step 1. if a == 0, return 0 */ if (mp_iszero (a) == 1) { *c = 0; return MP_OKAY; } /* step 2. if a == 1, return 1 */ if (mp_cmp_d (a, 1) == MP_EQ) { *c = 1; return MP_OKAY; } /* default */ s = 0; /* step 3. write a = a1 * 2**k */ if ((res = mp_init_copy (&a1, a)) != MP_OKAY) { return res; } if ((res = mp_init (&p1)) != MP_OKAY) { goto LBL_A1; } /* divide out larger power of two */ k = mp_cnt_lsb(&a1); if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) { goto LBL_P1; } /* step 4. if e is even set s=1 */ if ((k & 1) == 0) { s = 1; } else { /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */ residue = p->dp[0] & 7; if (residue == 1 || residue == 7) { s = 1; } else if (residue == 3 || residue == 5) { s = -1; } } /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */ if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) { s = -s; } /* if a1 == 1 we're done */ if (mp_cmp_d (&a1, 1) == MP_EQ) { *c = s; } else { /* n1 = n mod a1 */ if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) { goto LBL_P1; } if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) { goto LBL_P1; } *c = s * r; } /* done */ res = MP_OKAY; LBL_P1:mp_clear (&p1); LBL_A1:mp_clear (&a1); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_jacobi.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167  #include #ifdef BN_MP_KARATSUBA_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* c = |a| * |b| using Karatsuba Multiplication using * three half size multiplications * * Let B represent the radix [e.g. 2**DIGIT_BIT] and * let n represent half of the number of digits in * the min(a,b) * * a = a1 * B**n + a0 * b = b1 * B**n + b0 * * Then, a * b => a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 * * Note that a1b1 and a0b0 are used twice and only need to be * computed once. So in total three half size (half # of * digit) multiplications are performed, a0b0, a1b1 and * (a1+b1)(a0+b0) * * Note that a multiplication of half the digits requires * 1/4th the number of single precision multiplications so in * total after one call 25% of the single precision multiplications * are saved. Note also that the call to mp_mul can end up back * in this function if the a0, a1, b0, or b1 are above the threshold. * This is known as divide-and-conquer and leads to the famous * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than * the standard O(N**2) that the baseline/comba methods use. * Generally though the overhead of this method doesn't pay off * until a certain size (N ~ 80) is reached. */ int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c) { mp_int x0, x1, y0, y1, t1, x0y0, x1y1; int B, err; /* default the return code to an error */ err = MP_MEM; /* min # of digits */ B = MIN (a->used, b->used); /* now divide in two */ B = B >> 1; /* init copy all the temps */ if (mp_init_size (&x0, B) != MP_OKAY) goto ERR; if (mp_init_size (&x1, a->used - B) != MP_OKAY) goto X0; if (mp_init_size (&y0, B) != MP_OKAY) goto X1; if (mp_init_size (&y1, b->used - B) != MP_OKAY) goto Y0; /* init temps */ if (mp_init_size (&t1, B * 2) != MP_OKAY) goto Y1; if (mp_init_size (&x0y0, B * 2) != MP_OKAY) goto T1; if (mp_init_size (&x1y1, B * 2) != MP_OKAY) goto X0Y0; /* now shift the digits */ x0.used = y0.used = B; x1.used = a->used - B; y1.used = b->used - B; { register int x; register mp_digit *tmpa, *tmpb, *tmpx, *tmpy; /* we copy the digits directly instead of using higher level functions * since we also need to shift the digits */ tmpa = a->dp; tmpb = b->dp; tmpx = x0.dp; tmpy = y0.dp; for (x = 0; x < B; x++) { *tmpx++ = *tmpa++; *tmpy++ = *tmpb++; } tmpx = x1.dp; for (x = B; x < a->used; x++) { *tmpx++ = *tmpa++; } tmpy = y1.dp; for (x = B; x < b->used; x++) { *tmpy++ = *tmpb++; } } /* only need to clamp the lower words since by definition the * upper words x1/y1 must have a known number of digits */ mp_clamp (&x0); mp_clamp (&y0); /* now calc the products x0y0 and x1y1 */ /* after this x0 is no longer required, free temp [x0==t2]! */ if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY) goto X1Y1; /* x0y0 = x0*y0 */ if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) goto X1Y1; /* x1y1 = x1*y1 */ /* now calc x1+x0 and y1+y0 */ if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = x1 - x0 */ if (s_mp_add (&y1, &y0, &x0) != MP_OKAY) goto X1Y1; /* t2 = y1 - y0 */ if (mp_mul (&t1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ /* add x0y0 */ if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) goto X1Y1; /* t2 = x0y0 + x1y1 */ if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121  #include #ifdef BN_MP_KARATSUBA_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* Karatsuba squaring, computes b = a*a using three * half size squarings * * See comments of karatsuba_mul for details. It * is essentially the same algorithm but merely * tuned to perform recursive squarings. */ int mp_karatsuba_sqr (mp_int * a, mp_int * b) { mp_int x0, x1, t1, t2, x0x0, x1x1; int B, err; err = MP_MEM; /* min # of digits */ B = a->used; /* now divide in two */ B = B >> 1; /* init copy all the temps */ if (mp_init_size (&x0, B) != MP_OKAY) goto ERR; if (mp_init_size (&x1, a->used - B) != MP_OKAY) goto X0; /* init temps */ if (mp_init_size (&t1, a->used * 2) != MP_OKAY) goto X1; if (mp_init_size (&t2, a->used * 2) != MP_OKAY) goto T1; if (mp_init_size (&x0x0, B * 2) != MP_OKAY) goto T2; if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY) goto X0X0; { register int x; register mp_digit *dst, *src; src = a->dp; /* now shift the digits */ dst = x0.dp; for (x = 0; x < B; x++) { *dst++ = *src++; } dst = x1.dp; for (x = B; x < a->used; x++) { *dst++ = *src++; } } x0.used = B; x1.used = a->used - B; mp_clamp (&x0); /* now calc the products x0*x0 and x1*x1 */ if (mp_sqr (&x0, &x0x0) != MP_OKAY) goto X1X1; /* x0x0 = x0*x0 */ if (mp_sqr (&x1, &x1x1) != MP_OKAY) goto X1X1; /* x1x1 = x1*x1 */ /* now calc (x1+x0)**2 */ if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) goto X1X1; /* t1 = x1 - x0 */ if (mp_sqr (&t1, &t1) != MP_OKAY) goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ /* add x0y0 */ if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY) goto X1X1; /* t2 = x0x0 + x1x1 */ if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY) goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60  #include #ifdef BN_MP_LCM_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* computes least common multiple as |a*b|/(a, b) */ int mp_lcm (mp_int * a, mp_int * b, mp_int * c) { int res; mp_int t1, t2; if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) { return res; } /* t1 = get the GCD of the two inputs */ if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) { goto LBL_T; } /* divide the smallest by the GCD */ if (mp_cmp_mag(a, b) == MP_LT) { /* store quotient in t2 such that t2 * b is the LCM */ if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) { goto LBL_T; } res = mp_mul(b, &t2, c); } else { /* store quotient in t2 such that t2 * a is the LCM */ if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) { goto LBL_T; } res = mp_mul(a, &t2, c); } /* fix the sign to positive */ c->sign = MP_ZPOS; LBL_T: mp_clear_multi (&t1, &t2, NULL); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_lcm.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67  #include #ifdef BN_MP_LSHD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* shift left a certain amount of digits */ int mp_lshd (mp_int * a, int b) { int x, res; /* if its less than zero return */ if (b <= 0) { return MP_OKAY; } /* grow to fit the new digits */ if (a->alloc < a->used + b) { if ((res = mp_grow (a, a->used + b)) != MP_OKAY) { return res; } } { register mp_digit *top, *bottom; /* increment the used by the shift amount then copy upwards */ a->used += b; /* top */ top = a->dp + a->used - 1; /* base */ bottom = a->dp + a->used - 1 - b; /* much like mp_rshd this is implemented using a sliding window * except the window goes the otherway around. Copying from * the bottom to the top. see bn_mp_rshd.c for more info. */ for (x = a->used - 1; x >= b; x--) { *top-- = *bottom--; } /* zero the lower digits */ top = a->dp; for (x = 0; x < b; x++) { *top++ = 0; } } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_lshd.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48  #include #ifdef BN_MP_MOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* c = a mod b, 0 <= c < b */ int mp_mod (mp_int * a, mp_int * b, mp_int * c) { mp_int t; int res; if ((res = mp_init (&t)) != MP_OKAY) { return res; } if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) { mp_clear (&t); return res; } if (t.sign != b->sign) { res = mp_add (b, &t, c); } else { res = MP_OKAY; mp_exch (&t, c); } mp_clear (&t); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_mod.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55  #include #ifdef BN_MP_MOD_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* calc a value mod 2**b */ int mp_mod_2d (mp_int * a, int b, mp_int * c) { int x, res; /* if b is <= 0 then zero the int */ if (b <= 0) { mp_zero (c); return MP_OKAY; } /* if the modulus is larger than the value than return */ if (b >= (int) (a->used * DIGIT_BIT)) { res = mp_copy (a, c); return res; } /* copy */ if ((res = mp_copy (a, c)) != MP_OKAY) { return res; } /* zero digits above the last digit of the modulus */ for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) { c->dp[x] = 0; } /* clear the digit that is not completely outside/inside the modulus */ c->dp[b / DIGIT_BIT] &= (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1)); mp_clamp (c); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_mod_2d.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  #include #ifdef BN_MP_MOD_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ int mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) { return mp_div_d(a, b, NULL, c); } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_mod_d.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_montgomery_calc_normalization.c.

 49 50 51 52 53 54 55   } } } return MP_OKAY; } #endif   > > > >  49 50 51 52 53 54 55 56 57 58 59   } } } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_montgomery_calc_normalization.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118  #include #ifdef BN_MP_MONTGOMERY_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* computes xR**-1 == x (mod N) via Montgomery Reduction */ int mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) { int ix, res, digs; mp_digit mu; /* can the fast reduction [comba] method be used? * * Note that unlike in mul you're safely allowed *less* * than the available columns [255 per default] since carries * are fixed up in the inner loop. */ digs = n->used * 2 + 1; if ((digs < MP_WARRAY) && n->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { return fast_mp_montgomery_reduce (x, n, rho); } /* grow the input as required */ if (x->alloc < digs) { if ((res = mp_grow (x, digs)) != MP_OKAY) { return res; } } x->used = digs; for (ix = 0; ix < n->used; ix++) { /* mu = ai * rho mod b * * The value of rho must be precalculated via * montgomery_setup() such that * it equals -1/n0 mod b this allows the * following inner loop to reduce the * input one digit at a time */ mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK); /* a = a + mu * m * b**i */ { register int iy; register mp_digit *tmpn, *tmpx, u; register mp_word r; /* alias for digits of the modulus */ tmpn = n->dp; /* alias for the digits of x [the input] */ tmpx = x->dp + ix; /* set the carry to zero */ u = 0; /* Multiply and add in place */ for (iy = 0; iy < n->used; iy++) { /* compute product and sum */ r = ((mp_word)mu) * ((mp_word)*tmpn++) + ((mp_word) u) + ((mp_word) * tmpx); /* get carry */ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); /* fix digit */ *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK)); } /* At this point the ix'th digit of x should be zero */ /* propagate carries upwards as required*/ while (u) { *tmpx += u; u = *tmpx >> DIGIT_BIT; *tmpx++ &= MP_MASK; } } } /* at this point the n.used'th least * significant digits of x are all zero * which means we can shift x to the * right by n.used digits and the * residue is unchanged. */ /* x = x/b**n.used */ mp_clamp(x); mp_rshd (x, n->used); /* if x >= n then x = x - n */ if (mp_cmp_mag (x, n) != MP_LT) { return s_mp_sub (x, n, x); } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_montgomery_reduce.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59  #include #ifdef BN_MP_MONTGOMERY_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* setups the montgomery reduction stuff */ int mp_montgomery_setup (mp_int * n, mp_digit * rho) { mp_digit x, b; /* fast inversion mod 2**k * * Based on the fact that * * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) * => 2*X*A - X*X*A*A = 1 * => 2*(1) - (1) = 1 */ b = n->dp[0]; if ((b & 1) == 0) { return MP_VAL; } x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */ x *= 2 - b * x; /* here x*a==1 mod 2**8 */ #if !defined(MP_8BIT) x *= 2 - b * x; /* here x*a==1 mod 2**16 */ #endif #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT)) x *= 2 - b * x; /* here x*a==1 mod 2**32 */ #endif #ifdef MP_64BIT x *= 2 - b * x; /* here x*a==1 mod 2**64 */ #endif /* rho = -1/m mod b */ *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_montgomery_setup.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66  #include #ifdef BN_MP_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* high level multiplication (handles sign) */ int mp_mul (mp_int * a, mp_int * b, mp_int * c) { int res, neg; neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; /* use Toom-Cook? */ #ifdef BN_MP_TOOM_MUL_C if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) { res = mp_toom_mul(a, b, c); } else #endif #ifdef BN_MP_KARATSUBA_MUL_C /* use Karatsuba? */ if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) { res = mp_karatsuba_mul (a, b, c); } else #endif { /* can we use the fast multiplier? * * The fast multiplier can be used if the output will * have less than MP_WARRAY digits and the number of * digits won't affect carry propagation */ int digs = a->used + b->used + 1; #ifdef BN_FAST_S_MP_MUL_DIGS_C if ((digs < MP_WARRAY) && MIN(a->used, b->used) <= (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { res = fast_s_mp_mul_digs (a, b, c, digs); } else #endif #ifdef BN_S_MP_MUL_DIGS_C res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */ #else res = MP_VAL; #endif } c->sign = (c->used > 0) ? neg : MP_ZPOS; return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_mul.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82  #include #ifdef BN_MP_MUL_2_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* b = a*2 */ int mp_mul_2(mp_int * a, mp_int * b) { int x, res, oldused; /* grow to accomodate result */ if (b->alloc < a->used + 1) { if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) { return res; } } oldused = b->used; b->used = a->used; { register mp_digit r, rr, *tmpa, *tmpb; /* alias for source */ tmpa = a->dp; /* alias for dest */ tmpb = b->dp; /* carry */ r = 0; for (x = 0; x < a->used; x++) { /* get what will be the *next* carry bit from the * MSB of the current digit */ rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1)); /* now shift up this digit, add in the carry [from the previous] */ *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK; /* copy the carry that would be from the source * digit into the next iteration */ r = rr; } /* new leading digit? */ if (r != 0) { /* add a MSB which is always 1 at this point */ *tmpb = 1; ++(b->used); } /* now zero any excess digits on the destination * that we didn't write to */ tmpb = b->dp + b->used; for (x = b->used; x < oldused; x++) { *tmpb++ = 0; } } b->sign = a->sign; return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_mul_2.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85  #include #ifdef BN_MP_MUL_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* shift left by a certain bit count */ int mp_mul_2d (mp_int * a, int b, mp_int * c) { mp_digit d; int res; /* copy */ if (a != c) { if ((res = mp_copy (a, c)) != MP_OKAY) { return res; } } if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) { if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) { return res; } } /* shift by as many digits in the bit count */ if (b >= (int)DIGIT_BIT) { if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) { return res; } } /* shift any bit count < DIGIT_BIT */ d = (mp_digit) (b % DIGIT_BIT); if (d != 0) { register mp_digit *tmpc, shift, mask, r, rr; register int x; /* bitmask for carries */ mask = (((mp_digit)1) << d) - 1; /* shift for msbs */ shift = DIGIT_BIT - d; /* alias */ tmpc = c->dp; /* carry */ r = 0; for (x = 0; x < c->used; x++) { /* get the higher bits of the current word */ rr = (*tmpc >> shift) & mask; /* shift the current word and OR in the carry */ *tmpc = ((*tmpc << d) | r) & MP_MASK; ++tmpc; /* set the carry to the carry bits of the current word */ r = rr; } /* set final carry */ if (r != 0) { c->dp[(c->used)++] = r; } } mp_clamp (c); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_mul_2d.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_mul_d.c.

 69 70 71 72 73 74 75   /* set used count */ c->used = a->used + 1; mp_clamp(c); return MP_OKAY; } #endif   > > > >  69 70 71 72 73 74 75 76 77 78 79   /* set used count */ c->used = a->used + 1; mp_clamp(c); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_mul_d.c,v$ */ /* $Revision: 1.1.1.1.2.3$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40  #include #ifdef BN_MP_MULMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* d = a * b (mod c) */ int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) { int res; mp_int t; if ((res = mp_init (&t)) != MP_OKAY) { return res; } if ((res = mp_mul (a, b, &t)) != MP_OKAY) { mp_clear (&t); return res; } res = mp_mod (&t, c, d); mp_clear (&t); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_mulmod.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132  #include #ifdef BN_MP_N_ROOT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* find the n'th root of an integer * * Result found such that (c)**b <= a and (c+1)**b > a * * This algorithm uses Newton's approximation * x[i+1] = x[i] - f(x[i])/f'(x[i]) * which will find the root in log(N) time where * each step involves a fair bit. This is not meant to * find huge roots [square and cube, etc]. */ int mp_n_root (mp_int * a, mp_digit b, mp_int * c) { mp_int t1, t2, t3; int res, neg; /* input must be positive if b is even */ if ((b & 1) == 0 && a->sign == MP_NEG) { return MP_VAL; } if ((res = mp_init (&t1)) != MP_OKAY) { return res; } if ((res = mp_init (&t2)) != MP_OKAY) { goto LBL_T1; } if ((res = mp_init (&t3)) != MP_OKAY) { goto LBL_T2; } /* if a is negative fudge the sign but keep track */ neg = a->sign; a->sign = MP_ZPOS; /* t2 = 2 */ mp_set (&t2, 2); do { /* t1 = t2 */ if ((res = mp_copy (&t2, &t1)) != MP_OKAY) { goto LBL_T3; } /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ /* t3 = t1**(b-1) */ if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) { goto LBL_T3; } /* numerator */ /* t2 = t1**b */ if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) { goto LBL_T3; } /* t2 = t1**b - a */ if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) { goto LBL_T3; } /* denominator */ /* t3 = t1**(b-1) * b */ if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) { goto LBL_T3; } /* t3 = (t1**b - a)/(b * t1**(b-1)) */ if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) { goto LBL_T3; } if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) { goto LBL_T3; } } while (mp_cmp (&t1, &t2) != MP_EQ); /* result can be off by a few so check */ for (;;) { if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) { goto LBL_T3; } if (mp_cmp (&t2, a) == MP_GT) { if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) { goto LBL_T3; } } else { break; } } /* reset the sign of a first */ a->sign = neg; /* set the result */ mp_exch (&t1, c); /* set the sign of the result */ c->sign = neg; res = MP_OKAY; LBL_T3:mp_clear (&t3); LBL_T2:mp_clear (&t2); LBL_T1:mp_clear (&t1); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_n_root.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_neg.c.

 30 31 32 33 34 35 36   } else { b->sign = MP_ZPOS; } return MP_OKAY; } #endif   > > > >  30 31 32 33 34 35 36 37 38 39 40   } else { b->sign = MP_ZPOS; } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_neg.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50  #include #ifdef BN_MP_OR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* OR two ints together */ int mp_or (mp_int * a, mp_int * b, mp_int * c) { int res, ix, px; mp_int t, *x; if (a->used > b->used) { if ((res = mp_init_copy (&t, a)) != MP_OKAY) { return res; } px = b->used; x = b; } else { if ((res = mp_init_copy (&t, b)) != MP_OKAY) { return res; } px = a->used; x = a; } for (ix = 0; ix < px; ix++) { t.dp[ix] |= x->dp[ix]; } mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_or.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62  #include #ifdef BN_MP_PRIME_FERMAT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* performs one Fermat test. * * If "a" were prime then b**a == b (mod a) since the order of * the multiplicative sub-group would be phi(a) = a-1. That means * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a). * * Sets result to 1 if the congruence holds, or zero otherwise. */ int mp_prime_fermat (mp_int * a, mp_int * b, int *result) { mp_int t; int err; /* default to composite */ *result = MP_NO; /* ensure b > 1 */ if (mp_cmp_d(b, 1) != MP_GT) { return MP_VAL; } /* init t */ if ((err = mp_init (&t)) != MP_OKAY) { return err; } /* compute t = b**a mod a */ if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) { goto LBL_T; } /* is it equal to b? */ if (mp_cmp (&t, b) == MP_EQ) { *result = MP_YES; } err = MP_OKAY; LBL_T:mp_clear (&t); return err; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_prime_fermat.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50  #include #ifdef BN_MP_PRIME_IS_DIVISIBLE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* determines if an integers is divisible by one * of the first PRIME_SIZE primes or not * * sets result to 0 if not, 1 if yes */ int mp_prime_is_divisible (mp_int * a, int *result) { int err, ix; mp_digit res; /* default to not */ *result = MP_NO; for (ix = 0; ix < PRIME_SIZE; ix++) { /* what is a mod LBL_prime_tab[ix] */ if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) { return err; } /* is the residue zero? */ if (res == 0) { *result = MP_YES; return MP_OKAY; } } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_prime_is_divisible.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83  #include #ifdef BN_MP_PRIME_IS_PRIME_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* performs a variable number of rounds of Miller-Rabin * * Probability of error after t rounds is no more than * * Sets result to 1 if probably prime, 0 otherwise */ int mp_prime_is_prime (mp_int * a, int t, int *result) { mp_int b; int ix, err, res; /* default to no */ *result = MP_NO; /* valid value of t? */ if (t <= 0 || t > PRIME_SIZE) { return MP_VAL; } /* is the input equal to one of the primes in the table? */ for (ix = 0; ix < PRIME_SIZE; ix++) { if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) { *result = 1; return MP_OKAY; } } /* first perform trial division */ if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) { return err; } /* return if it was trivially divisible */ if (res == MP_YES) { return MP_OKAY; } /* now perform the miller-rabin rounds */ if ((err = mp_init (&b)) != MP_OKAY) { return err; } for (ix = 0; ix < t; ix++) { /* set the prime */ mp_set (&b, ltm_prime_tab[ix]); if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) { goto LBL_B; } if (res == MP_NO) { goto LBL_B; } } /* passed the test */ *result = MP_YES; LBL_B:mp_clear (&b); return err; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_prime_is_prime.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103  #include #ifdef BN_MP_PRIME_MILLER_RABIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* Miller-Rabin test of "a" to the base of "b" as described in * HAC pp. 139 Algorithm 4.24 * * Sets result to 0 if definitely composite or 1 if probably prime. * Randomly the chance of error is no more than 1/4 and often * very much lower. */ int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result) { mp_int n1, y, r; int s, j, err; /* default */ *result = MP_NO; /* ensure b > 1 */ if (mp_cmp_d(b, 1) != MP_GT) { return MP_VAL; } /* get n1 = a - 1 */ if ((err = mp_init_copy (&n1, a)) != MP_OKAY) { return err; } if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) { goto LBL_N1; } /* set 2**s * r = n1 */ if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) { goto LBL_N1; } /* count the number of least significant bits * which are zero */ s = mp_cnt_lsb(&r); /* now divide n - 1 by 2**s */ if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) { goto LBL_R; } /* compute y = b**r mod a */ if ((err = mp_init (&y)) != MP_OKAY) { goto LBL_R; } if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) { goto LBL_Y; } /* if y != 1 and y != n1 do */ if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) { j = 1; /* while j <= s-1 and y != n1 */ while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) { if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) { goto LBL_Y; } /* if y == 1 then composite */ if (mp_cmp_d (&y, 1) == MP_EQ) { goto LBL_Y; } ++j; } /* if y != n1 then composite */ if (mp_cmp (&y, &n1) != MP_EQ) { goto LBL_Y; } } /* probably prime now */ *result = MP_YES; LBL_Y:mp_clear (&y); LBL_R:mp_clear (&r); LBL_N1:mp_clear (&n1); return err; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_prime_miller_rabin.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170  #include #ifdef BN_MP_PRIME_NEXT_PRIME_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* finds the next prime after the number "a" using "t" trials * of Miller-Rabin. * * bbs_style = 1 means the prime must be congruent to 3 mod 4 */ int mp_prime_next_prime(mp_int *a, int t, int bbs_style) { int err, res, x, y; mp_digit res_tab[PRIME_SIZE], step, kstep; mp_int b; /* ensure t is valid */ if (t <= 0 || t > PRIME_SIZE) { return MP_VAL; } /* force positive */ a->sign = MP_ZPOS; /* simple algo if a is less than the largest prime in the table */ if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) { /* find which prime it is bigger than */ for (x = PRIME_SIZE - 2; x >= 0; x--) { if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) { if (bbs_style == 1) { /* ok we found a prime smaller or * equal [so the next is larger] * * however, the prime must be * congruent to 3 mod 4 */ if ((ltm_prime_tab[x + 1] & 3) != 3) { /* scan upwards for a prime congruent to 3 mod 4 */ for (y = x + 1; y < PRIME_SIZE; y++) { if ((ltm_prime_tab[y] & 3) == 3) { mp_set(a, ltm_prime_tab[y]); return MP_OKAY; } } } } else { mp_set(a, ltm_prime_tab[x + 1]); return MP_OKAY; } } } /* at this point a maybe 1 */ if (mp_cmp_d(a, 1) == MP_EQ) { mp_set(a, 2); return MP_OKAY; } /* fall through to the sieve */ } /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */ if (bbs_style == 1) { kstep = 4; } else { kstep = 2; } /* at this point we will use a combination of a sieve and Miller-Rabin */ if (bbs_style == 1) { /* if a mod 4 != 3 subtract the correct value to make it so */ if ((a->dp[0] & 3) != 3) { if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; }; } } else { if (mp_iseven(a) == 1) { /* force odd */ if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { return err; } } } /* generate the restable */ for (x = 1; x < PRIME_SIZE; x++) { if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) { return err; } } /* init temp used for Miller-Rabin Testing */ if ((err = mp_init(&b)) != MP_OKAY) { return err; } for (;;) { /* skip to the next non-trivially divisible candidate */ step = 0; do { /* y == 1 if any residue was zero [e.g. cannot be prime] */ y = 0; /* increase step to next candidate */ step += kstep; /* compute the new residue without using division */ for (x = 1; x < PRIME_SIZE; x++) { /* add the step to each residue */ res_tab[x] += kstep; /* subtract the modulus [instead of using division] */ if (res_tab[x] >= ltm_prime_tab[x]) { res_tab[x] -= ltm_prime_tab[x]; } /* set flag if zero */ if (res_tab[x] == 0) { y = 1; } } } while (y == 1 && step < ((((mp_digit)1)<= ((((mp_digit)1)<

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52  #include #ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ static const struct { int k, t; } sizes[] = { { 128, 28 }, { 256, 16 }, { 384, 10 }, { 512, 7 }, { 640, 6 }, { 768, 5 }, { 896, 4 }, { 1024, 4 } }; /* returns # of RM trials required for a given bit size */ int mp_prime_rabin_miller_trials(int size) { int x; for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) { if (sizes[x].k == size) { return sizes[x].t; } else if (sizes[x].k > size) { return (x == 0) ? sizes[0].t : sizes[x - 1].t; } } return sizes[x-1].t + 1; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_prime_rabin_miller_trials.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_prime_random_ex.c.

 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 ... 117 118 119 120 121 122 123   /* calc the maskAND value for the MSbyte*/ maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7))); /* calc the maskOR_msb */ maskOR_msb = 0; maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; if (flags & LTM_PRIME_2MSB_ON) { maskOR_msb |= 1 << ((size - 2) & 7); } else if (flags & LTM_PRIME_2MSB_OFF) { maskAND &= ~(1 << ((size - 2) & 7)); } /* get the maskOR_lsb */ maskOR_lsb = 1; if (flags & LTM_PRIME_BBS) { maskOR_lsb |= 3; } ................................................................................ error: XFREE(tmp); return err; } #endif   | < < | > > > >  58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 ... 115 116 117 118 119 120 121 122 123 124 125   /* calc the maskAND value for the MSbyte*/ maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7))); /* calc the maskOR_msb */ maskOR_msb = 0; maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; if (flags & LTM_PRIME_2MSB_ON) { maskOR_msb |= 0x80 >> ((9 - size) & 7); } /* get the maskOR_lsb */ maskOR_lsb = 1; if (flags & LTM_PRIME_BBS) { maskOR_lsb |= 3; } ................................................................................ error: XFREE(tmp); return err; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_prime_random_ex.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

 77 78 79 80 81 82 83   } else { *size = 3; } return MP_OKAY; } #endif   > > > >  77 78 79 80 81 82 83 84 85 86 87   } else { *size = 3; } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_radix_size.c,v$ */ /* $Revision: 1.1.1.1.2.3$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  #include #ifdef BN_MP_RADIX_SMAP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* chars used in radix conversions */ const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_radix_smap.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_rand.c.

 45 46 47 48 49 50 51   return res; } } return MP_OKAY; } #endif   > > > >  45 46 47 48 49 50 51 52 53 54 55   return res; } } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_rand.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

 79 80 81 82 83 84 85   /* set the sign only if a != 0 */ if (mp_iszero(a) != 1) { a->sign = neg; } return MP_OKAY; } #endif   > > > >  79 80 81 82 83 84 85 86 87 88 89   /* set the sign only if a != 0 */ if (mp_iszero(a) != 1) { a->sign = neg; } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_read_radix.c,v$ */ /* $Revision: 1.1.1.1.2.3$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41  #include #ifdef BN_MP_READ_SIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* read signed bin, big endian, first byte is 0==positive or 1==negative */ int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c) { int res; /* read magnitude */ if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) { return res; } /* first byte is 0 for positive, non-zero for negative */ if (b[0] == 0) { a->sign = MP_ZPOS; } else { a->sign = MP_NEG; } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_read_signed_bin.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55  #include #ifdef BN_MP_READ_UNSIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* reads a unsigned char array, assumes the msb is stored first [big endian] */ int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c) { int res; /* make sure there are at least two digits */ if (a->alloc < 2) { if ((res = mp_grow(a, 2)) != MP_OKAY) { return res; } } /* zero the int */ mp_zero (a); /* read the bytes in */ while (c-- > 0) { if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) { return res; } #ifndef MP_8BIT a->dp[0] |= *b++; a->used += 1; #else a->dp[0] = (*b & MP_MASK); a->dp[1] |= ((*b++ >> 7U) & 1); a->used += 2; #endif } mp_clamp (a); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_read_unsigned_bin.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_reduce.c.

 90 91 92 93 94 95 96   CLEANUP: mp_clear (&q); return res; } #endif   > > > >  90 91 92 93 94 95 96 97 98 99 100   CLEANUP: mp_clear (&q); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_reduce.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_reduce_2k.c.

 51 52 53 54 55 56 57   ERR: mp_clear(&q); return res; } #endif   > > > >  51 52 53 54 55 56 57 58 59 60 61   ERR: mp_clear(&q); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_reduce_2k.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_reduce_2k_l.c.

 52 53 54 55 56 57 58   ERR: mp_clear(&q); return res; } #endif   > > > >  52 53 54 55 56 57 58 59 60 61 62   ERR: mp_clear(&q); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_reduce_2k_l.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_reduce_2k_setup.c.

 37 38 39 40 41 42 43   } *d = tmp.dp[0]; mp_clear(&tmp); return MP_OKAY; } #endif   > > > >  37 38 39 40 41 42 43 44 45 46 47   } *d = tmp.dp[0]; mp_clear(&tmp); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_reduce_2k_setup.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_reduce_2k_setup_l.c.

 34 35 36 37 38 39 40   } ERR: mp_clear(&tmp); return res; } #endif   > > > >  34 35 36 37 38 39 40 41 42 43 44   } ERR: mp_clear(&tmp); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_reduce_2k_setup_l.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_reduce_is_2k.c.

 42 43 44 45 46 47 48   } } } return MP_YES; } #endif   > > > >  42 43 44 45 46 47 48 49 50 51 52   } } } return MP_YES; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_reduce_is_2k.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

Changes to libtommath/bn_mp_reduce_is_2k_l.c.

 34 35 36 37 38 39 40   return (iy >= (a->used/2)) ? MP_YES : MP_NO; } return MP_NO; } #endif   > > > >  34 35 36 37 38 39 40 41 42 43 44   return (iy >= (a->used/2)) ? MP_YES : MP_NO; } return MP_NO; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_reduce_is_2k_l.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34  #include #ifdef BN_MP_REDUCE_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* pre-calculate the value required for Barrett reduction * For a given modulus "b" it calulates the value required in "a" */ int mp_reduce_setup (mp_int * a, mp_int * b) { int res; if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) { return res; } return mp_div (a, b, a, NULL); } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_reduce_setup.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72  #include #ifdef BN_MP_RSHD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* shift right a certain amount of digits */ void mp_rshd (mp_int * a, int b) { int x; /* if b <= 0 then ignore it */ if (b <= 0) { return; } /* if b > used then simply zero it and return */ if (a->used <= b) { mp_zero (a); return; } { register mp_digit *bottom, *top; /* shift the digits down */ /* bottom */ bottom = a->dp; /* top [offset into digits] */ top = a->dp + b; /* this is implemented as a sliding window where * the window is b-digits long and digits from * the top of the window are copied to the bottom * * e.g. b-2 | b-1 | b0 | b1 | b2 | ... | bb | ----> /\ | ----> \-------------------/ ----> */ for (x = 0; x < (a->used - b); x++) { *bottom++ = *top++; } /* zero the top digits */ for (; x < a->used; x++) { *bottom++ = 0; } } /* remove excess digits */ a->used -= b; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_rshd.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29  #include #ifdef BN_MP_SET_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* set to a digit */ void mp_set (mp_int * a, mp_digit b) { mp_zero (a); a->dp[0] = b & MP_MASK; a->used = (a->dp[0] != 0) ? 1 : 0; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_set.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48  #include #ifdef BN_MP_SET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* set a 32-bit const */ int mp_set_int (mp_int * a, unsigned long b) { int x, res; mp_zero (a); /* set four bits at a time */ for (x = 0; x < 8; x++) { /* shift the number up four bits */ if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) { return res; } /* OR in the top four bits of the source */ a->dp[0] |= (b >> 28) & 15; /* shift the source up to the next four bits */ b <<= 4; /* ensure that digits are not clamped off */ a->used += 1; } mp_clamp (a); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_set_int.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35  #include #ifdef BN_MP_SHRINK_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* shrink a bignum */ int mp_shrink (mp_int * a) { mp_digit *tmp; if (a->alloc != a->used && a->used > 0) { if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * a->used)) == NULL) { return MP_MEM; } a->dp = tmp; a->alloc = a->used; } return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_shrink.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  #include #ifdef BN_MP_SIGNED_BIN_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* get the size for an signed equivalent */ int mp_signed_bin_size (mp_int * a) { return 1 + mp_unsigned_bin_size (a); } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_signed_bin_size.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58  #include #ifdef BN_MP_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* computes b = a*a */ int mp_sqr (mp_int * a, mp_int * b) { int res; #ifdef BN_MP_TOOM_SQR_C /* use Toom-Cook? */ if (a->used >= TOOM_SQR_CUTOFF) { res = mp_toom_sqr(a, b); /* Karatsuba? */ } else #endif #ifdef BN_MP_KARATSUBA_SQR_C if (a->used >= KARATSUBA_SQR_CUTOFF) { res = mp_karatsuba_sqr (a, b); } else #endif { #ifdef BN_FAST_S_MP_SQR_C /* can we use the fast comba multiplier? */ if ((a->used * 2 + 1) < MP_WARRAY && a->used < (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) { res = fast_s_mp_sqr (a, b); } else #endif #ifdef BN_S_MP_SQR_C res = s_mp_sqr (a, b); #else res = MP_VAL; #endif } b->sign = MP_ZPOS; return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_sqr.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41  #include #ifdef BN_MP_SQRMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* c = a * a (mod b) */ int mp_sqrmod (mp_int * a, mp_int * b, mp_int * c) { int res; mp_int t; if ((res = mp_init (&t)) != MP_OKAY) { return res; } if ((res = mp_sqr (a, &t)) != MP_OKAY) { mp_clear (&t); return res; } res = mp_mod (&t, b, c); mp_clear (&t); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_sqrmod.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81  #include #ifdef BN_MP_SQRT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* this function is less generic than mp_n_root, simpler and faster */ int mp_sqrt(mp_int *arg, mp_int *ret) { int res; mp_int t1,t2; /* must be positive */ if (arg->sign == MP_NEG) { return MP_VAL; } /* easy out */ if (mp_iszero(arg) == MP_YES) { mp_zero(ret); return MP_OKAY; } if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) { return res; } if ((res = mp_init(&t2)) != MP_OKAY) { goto E2; } /* First approx. (not very bad for large arg) */ mp_rshd (&t1,t1.used/2); /* t1 > 0 */ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) { goto E1; } if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) { goto E1; } if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) { goto E1; } /* And now t1 > sqrt(arg) */ do { if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) { goto E1; } if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) { goto E1; } if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) { goto E1; } /* t1 >= sqrt(arg) >= t2 at this point */ } while (mp_cmp_mag(&t1,&t2) == MP_GT); mp_exch(&t1,ret); E1: mp_clear(&t2); E2: mp_clear(&t1); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_sqrt.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59  #include #ifdef BN_MP_SUB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* high level subtraction (handles signs) */ int mp_sub (mp_int * a, mp_int * b, mp_int * c) { int sa, sb, res; sa = a->sign; sb = b->sign; if (sa != sb) { /* subtract a negative from a positive, OR */ /* subtract a positive from a negative. */ /* In either case, ADD their magnitudes, */ /* and use the sign of the first number. */ c->sign = sa; res = s_mp_add (a, b, c); } else { /* subtract a positive from a positive, OR */ /* subtract a negative from a negative. */ /* First, take the difference between their */ /* magnitudes, then... */ if (mp_cmp_mag (a, b) != MP_LT) { /* Copy the sign from the first */ c->sign = sa; /* The first has a larger or equal magnitude */ res = s_mp_sub (a, b, c); } else { /* The result has the *opposite* sign from */ /* the first number. */ c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS; /* The second has a larger magnitude */ res = s_mp_sub (b, a, c); } } return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_sub.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  #include #ifdef BN_MP_SUB_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* single digit subtraction */ int mp_sub_d (mp_int * a, mp_digit b, mp_int * c) { mp_digit *tmpa, *tmpc, mu; int res, ix, oldused; /* grow c as required */ if (c->alloc < a->used + 1) { if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) { return res; } } /* if a is negative just do an unsigned * addition [with fudged signs] */ if (a->sign == MP_NEG) { a->sign = MP_ZPOS; res = mp_add_d(a, b, c); a->sign = c->sign = MP_NEG; return res; } /* setup regs */ oldused = c->used; tmpa = a->dp; tmpc = c->dp; /* if a <= b simply fix the single digit */ if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) { if (a->used == 1) { *tmpc++ = b - *tmpa; } else { *tmpc++ = b; } ix = 1; /* negative/1digit */ c->sign = MP_NEG; c->used = 1; } else { /* positive/size */ c->sign = MP_ZPOS; c->used = a->used; /* subtract first digit */ *tmpc = *tmpa++ - b; mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1); *tmpc++ &= MP_MASK; /* handle rest of the digits */ for (ix = 1; ix < a->used; ix++) { *tmpc = *tmpa++ - mu; mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1); *tmpc++ &= MP_MASK; } } /* zero excess digits */ while (ix++ < oldused) { *tmpc++ = 0; } mp_clamp(c); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_sub_d.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:53$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42  #include #ifdef BN_MP_SUBMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* d = a - b (mod c) */ int mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) { int res; mp_int t; if ((res = mp_init (&t)) != MP_OKAY) { return res; } if ((res = mp_sub (a, b, &t)) != MP_OKAY) { mp_clear (&t); return res; } res = mp_mod (&t, c, d); mp_clear (&t); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_submod.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_mp_to_signed_bin.c.

 23 24 25 26 27 28 29   if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) { return res; } b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1); return MP_OKAY; } #endif   > > > >  23 24 25 26 27 28 29 30 31 32 33   if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) { return res; } b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_to_signed_bin.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_mp_to_signed_bin_n.c.

 21 22 23 24 25 26 27   if (*outlen < (unsigned long)mp_signed_bin_size(a)) { return MP_VAL; } *outlen = mp_signed_bin_size(a); return mp_to_signed_bin(a, b); } #endif   > > > >  21 22 23 24 25 26 27 28 29 30 31   if (*outlen < (unsigned long)mp_signed_bin_size(a)) { return MP_VAL; } *outlen = mp_signed_bin_size(a); return mp_to_signed_bin(a, b); } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_to_signed_bin_n.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_mp_to_unsigned_bin.c.

 38 39 40 41 42 43 44   } } bn_reverse (b, x); mp_clear (&t); return MP_OKAY; } #endif   > > > >  38 39 40 41 42 43 44 45 46 47 48   } } bn_reverse (b, x); mp_clear (&t); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_to_unsigned_bin.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_mp_to_unsigned_bin_n.c.

 21 22 23 24 25 26 27   if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) { return MP_VAL; } *outlen = mp_unsigned_bin_size(a); return mp_to_unsigned_bin(a, b); } #endif   > > > >  21 22 23 24 25 26 27 28 29 30 31   if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) { return MP_VAL; } *outlen = mp_unsigned_bin_size(a); return mp_to_unsigned_bin(a, b); } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_to_unsigned_bin_n.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_mp_toom_mul.c.

 274 275 276 277 278 279 280   mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &b0, &b1, &b2, &tmp1, &tmp2, NULL); return res; } #endif   > > > >  274 275 276 277 278 279 280 281 282 283 284   mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &b0, &b1, &b2, &tmp1, &tmp2, NULL); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_toom_mul.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226  #include #ifdef BN_MP_TOOM_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* squaring using Toom-Cook 3-way algorithm */ int mp_toom_sqr(mp_int *a, mp_int *b) { mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2; int res, B; /* init temps */ if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) { return res; } /* B */ B = a->used / 3; /* a = a2 * B**2 + a1 * B + a0 */ if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) { goto ERR; } if ((res = mp_copy(a, &a1)) != MP_OKAY) { goto ERR; } mp_rshd(&a1, B); mp_mod_2d(&a1, DIGIT_BIT * B, &a1); if ((res = mp_copy(a, &a2)) != MP_OKAY) { goto ERR; } mp_rshd(&a2, B*2); /* w0 = a0*a0 */ if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) { goto ERR; } /* w4 = a2 * a2 */ if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) { goto ERR; } /* w1 = (a2 + 2(a1 + 2a0))**2 */ if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) { goto ERR; } /* w3 = (a0 + 2(a1 + 2a2))**2 */ if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) { goto ERR; } /* w2 = (a2 + a1 + a0)**2 */ if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) { goto ERR; } /* now solve the matrix 0 0 0 0 1 1 2 4 8 16 1 1 1 1 1 16 8 4 2 1 1 0 0 0 0 using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication. */ /* r1 - r4 */ if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) { goto ERR; } /* r3 - r0 */ if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) { goto ERR; } /* r1/2 */ if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) { goto ERR; } /* r3/2 */ if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) { goto ERR; } /* r2 - r0 - r4 */ if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) { goto ERR; } if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) { goto ERR; } /* r1 - r2 */ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { goto ERR; } /* r3 - r2 */ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { goto ERR; } /* r1 - 8r0 */ if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) { goto ERR; } /* r3 - 8r4 */ if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) { goto ERR; } /* 3r2 - r1 - r3 */ if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) { goto ERR; } if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) { goto ERR; } if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) { goto ERR; } /* r1 - r2 */ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { goto ERR; } /* r3 - r2 */ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { goto ERR; } /* r1/3 */ if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) { goto ERR; } /* r3/3 */ if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) { goto ERR; } /* at this point shift W[n] by B*n */ if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) { goto ERR; } if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) { goto ERR; } if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) { goto ERR; } if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) { goto ERR; } if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) { goto ERR; } if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) { goto ERR; } if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) { goto ERR; } ERR: mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL); return res; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_toom_sqr.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75  #include #ifdef BN_MP_TORADIX_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* stores a bignum as a ASCII string in a given radix (2..64) */ int mp_toradix (mp_int * a, char *str, int radix) { int res, digs; mp_int t; mp_digit d; char *_s = str; /* check range of the radix */ if (radix < 2 || radix > 64) { return MP_VAL; } /* quick out if its zero */ if (mp_iszero(a) == 1) { *str++ = '0'; *str = '\0'; return MP_OKAY; } if ((res = mp_init_copy (&t, a)) != MP_OKAY) { return res; } /* if it is negative output a - */ if (t.sign == MP_NEG) { ++_s; *str++ = '-'; t.sign = MP_ZPOS; } digs = 0; while (mp_iszero (&t) == 0) { if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { mp_clear (&t); return res; } *str++ = mp_s_rmap[d]; ++digs; } /* reverse the digits of the string. In this case _s points * to the first digit [exluding the sign] of the number] */ bn_reverse ((unsigned char *)_s, digs); /* append a NULL so the string is properly terminated */ *str = '\0'; mp_clear (&t); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_toradix.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  #include #ifdef BN_MP_TORADIX_N_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* stores a bignum as a ASCII string in a given radix (2..64) * * Stores upto maxlen-1 chars and always a NULL byte */ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen) { int res, digs; mp_int t; mp_digit d; char *_s = str; /* check range of the maxlen, radix */ if (maxlen < 3 || radix < 2 || radix > 64) { return MP_VAL; } /* quick out if its zero */ if (mp_iszero(a) == 1) { *str++ = '0'; *str = '\0'; return MP_OKAY; } if ((res = mp_init_copy (&t, a)) != MP_OKAY) { return res; } /* if it is negative output a - */ if (t.sign == MP_NEG) { /* we have to reverse our digits later... but not the - sign!! */ ++_s; /* store the flag and mark the number as positive */ *str++ = '-'; t.sign = MP_ZPOS; /* subtract a char */ --maxlen; } digs = 0; while (mp_iszero (&t) == 0) { if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { mp_clear (&t); return res; } *str++ = mp_s_rmap[d]; ++digs; if (--maxlen == 1) { /* no more room */ break; } } /* reverse the digits of the string. In this case _s points * to the first digit [exluding the sign] of the number] */ bn_reverse ((unsigned char *)_s, digs); /* append a NULL so the string is properly terminated */ *str = '\0'; mp_clear (&t); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_toradix_n.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_mp_unsigned_bin_size.c.

 18 19 20 21 22 23 24  /* get the size for an unsigned equivalent */ int mp_unsigned_bin_size (mp_int * a) { int size = mp_count_bits (a); return (size / 8 + ((size & 7) != 0 ? 1 : 0)); } #endif   > > > >  18 19 20 21 22 23 24 25 26 27 28  /* get the size for an unsigned equivalent */ int mp_unsigned_bin_size (mp_int * a) { int size = mp_count_bits (a); return (size / 8 + ((size & 7) != 0 ? 1 : 0)); } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_unsigned_bin_size.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_mp_xor.c.

 41 42 43 44 45 46 47   } mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } #endif   > > > >  41 42 43 44 45 46 47 48 49 50 51   } mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_xor.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_mp_zero.c.

 26 27 28 29 30 31 32   tmp = a->dp; for (n = 0; n < a->alloc; n++) { *tmp++ = 0; } } #endif   > > > >  26 27 28 29 30 31 32 33 34 35 36   tmp = a->dp; for (n = 0; n < a->alloc; n++) { *tmp++ = 0; } } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_mp_zero.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61  #include #ifdef BN_PRIME_TAB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ const mp_digit ltm_prime_tab[] = { 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, #ifndef MP_8BIT 0x0083, 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF, 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167, 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199, 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9, 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7, 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239, 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265, 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293, 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF, 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301, 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B, 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371, 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD, 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5, 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419, 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449, 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B, 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7, 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503, 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529, 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F, 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3, 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 #endif }; #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_prime_tab.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39  #include #ifdef BN_REVERSE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* reverse an array, used for radix code */ void bn_reverse (unsigned char *s, int len) { int ix, iy; unsigned char t; ix = 0; iy = len - 1; while (ix < iy) { t = s[ix]; s[ix] = s[iy]; s[iy] = t; ++ix; --iy; } } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_reverse.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109  #include #ifdef BN_S_MP_ADD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* low level addition, based on HAC pp.594, Algorithm 14.7 */ int s_mp_add (mp_int * a, mp_int * b, mp_int * c) { mp_int *x; int olduse, res, min, max; /* find sizes, we let |a| <= |b| which means we have to sort * them. "x" will point to the input with the most digits */ if (a->used > b->used) { min = b->used; max = a->used; x = a; } else { min = a->used; max = b->used; x = b; } /* init result */ if (c->alloc < max + 1) { if ((res = mp_grow (c, max + 1)) != MP_OKAY) { return res; } } /* get old used digit count and set new one */ olduse = c->used; c->used = max + 1; { register mp_digit u, *tmpa, *tmpb, *tmpc; register int i; /* alias for digit pointers */ /* first input */ tmpa = a->dp; /* second input */ tmpb = b->dp; /* destination */ tmpc = c->dp; /* zero the carry */ u = 0; for (i = 0; i < min; i++) { /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */ *tmpc = *tmpa++ + *tmpb++ + u; /* U = carry bit of T[i] */ u = *tmpc >> ((mp_digit)DIGIT_BIT); /* take away carry bit from T[i] */ *tmpc++ &= MP_MASK; } /* now copy higher words if any, that is in A+B * if A or B has more digits add those in */ if (min != max) { for (; i < max; i++) { /* T[i] = X[i] + U */ *tmpc = x->dp[i] + u; /* U = carry bit of T[i] */ u = *tmpc >> ((mp_digit)DIGIT_BIT); /* take away carry bit from T[i] */ *tmpc++ &= MP_MASK; } } /* add carry */ *tmpc++ = u; /* clear digits above oldused */ for (i = c->used; i < olduse; i++) { *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_s_mp_add.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_s_mp_exptmod.c.

 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ... 243 244 245 246 247 248 249   * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #ifdef MP_LOW_MEM #define TAB_SIZE 32 #else #define TAB_SIZE 256 #endif int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) ................................................................................ mp_clear(&M[1]); for (x = 1<<(winsize-1); x < (1 << winsize); x++) { mp_clear (&M[x]); } return err; } #endif   < > > > >  10 11 12 13 14 15 16 17 18 19 20 21 22 23 ... 242 243 244 245 246 247 248 249 250 251 252   * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #ifdef MP_LOW_MEM #define TAB_SIZE 32 #else #define TAB_SIZE 256 #endif int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) ................................................................................ mp_clear(&M[1]); for (x = 1<<(winsize-1); x < (1 << winsize); x++) { mp_clear (&M[x]); } return err; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_s_mp_exptmod.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_s_mp_mul_digs.c.

 80 81 82 83 84 85 86   mp_clamp (&t); mp_exch (&t, c); mp_clear (&t); return MP_OKAY; } #endif   > > > >  80 81 82 83 84 85 86 87 88 89 90   mp_clamp (&t); mp_exch (&t, c); mp_clear (&t); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_s_mp_mul_digs.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81  #include #ifdef BN_S_MP_MUL_HIGH_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* multiplies |a| * |b| and does not compute the lower digs digits * [meant to get the higher part of the product] */ int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { mp_int t; int res, pa, pb, ix, iy; mp_digit u; mp_word r; mp_digit tmpx, *tmpt, *tmpy; /* can we use the fast multiplier? */ #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C if (((a->used + b->used + 1) < MP_WARRAY) && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { return fast_s_mp_mul_high_digs (a, b, c, digs); } #endif if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) { return res; } t.used = a->used + b->used + 1; pa = a->used; pb = b->used; for (ix = 0; ix < pa; ix++) { /* clear the carry */ u = 0; /* left hand side of A[ix] * B[iy] */ tmpx = a->dp[ix]; /* alias to the address of where the digits will be stored */ tmpt = &(t.dp[digs]); /* alias for where to read the right hand side from */ tmpy = b->dp + (digs - ix); for (iy = digs - ix; iy < pb; iy++) { /* calculate the double precision result */ r = ((mp_word)*tmpt) + ((mp_word)tmpx) * ((mp_word)*tmpy++) + ((mp_word) u); /* get the lower part */ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); /* carry the carry */ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); } *tmpt = u; } mp_clamp (&t); mp_exch (&t, c); mp_clear (&t); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_s_mp_mul_high_digs.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bn_s_mp_sqr.c.

 74 75 76 77 78 79 80   mp_clamp (&t); mp_exch (&t, b); mp_clear (&t); return MP_OKAY; } #endif   > > > >  74 75 76 77 78 79 80 81 82 83 84   mp_clamp (&t); mp_exch (&t, b); mp_clear (&t); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_s_mp_sqr.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  #include #ifdef BN_S_MP_SUB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ int s_mp_sub (mp_int * a, mp_int * b, mp_int * c) { int olduse, res, min, max; /* find sizes */ min = b->used; max = a->used; /* init result */ if (c->alloc < max) { if ((res = mp_grow (c, max)) != MP_OKAY) { return res; } } olduse = c->used; c->used = max; { register mp_digit u, *tmpa, *tmpb, *tmpc; register int i; /* alias for digit pointers */ tmpa = a->dp; tmpb = b->dp; tmpc = c->dp; /* set carry to zero */ u = 0; for (i = 0; i < min; i++) { /* T[i] = A[i] - B[i] - U */ *tmpc = *tmpa++ - *tmpb++ - u; /* U = carry bit of T[i] * Note this saves performing an AND operation since * if a carry does occur it will propagate all the way to the * MSB. As a result a single shift is enough to get the carry */ u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1)); /* Clear carry from T[i] */ *tmpc++ &= MP_MASK; } /* now copy higher words if any, e.g. if A has more digits than B */ for (; i < max; i++) { /* T[i] = A[i] - U */ *tmpc = *tmpa++ - u; /* U = carry bit of T[i] */ u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1)); /* Clear carry from T[i] */ *tmpc++ &= MP_MASK; } /* clear digits above used (since we may not have grown result above) */ for (i = c->used; i < olduse; i++) { *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bn_s_mp_sub.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/bncore.c.

 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32   */ /* Known optimal configurations CPU /Compiler /MUL CUTOFF/SQR CUTOFF ------------------------------------------------------------- Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) AMD Athlon64 /GCC v3.4.4 / 74/ 124/LTM 0.34 */ int KARATSUBA_MUL_CUTOFF = 74, /* Min. number of digits before Karatsuba multiplication is used. */ KARATSUBA_SQR_CUTOFF = 124, /* Min. number of digits before Karatsuba squaring is used. */ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ TOOM_SQR_CUTOFF = 400; #endif   | | | > > > >  16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36   */ /* Known optimal configurations CPU /Compiler /MUL CUTOFF/SQR CUTOFF ------------------------------------------------------------- Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) AMD Athlon64 /GCC v3.4.4 / 80/ 120/LTM 0.35 */ int KARATSUBA_MUL_CUTOFF = 80, /* Min. number of digits before Karatsuba multiplication is used. */ KARATSUBA_SQR_CUTOFF = 120, /* Min. number of digits before Karatsuba squaring is used. */ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ TOOM_SQR_CUTOFF = 400; #endif /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/bncore.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265  #!/bin/perl # #Used to prepare the book "tommath.src" for LaTeX by pre-processing it into a .tex file # #Essentially you write the "tommath.src" as normal LaTex except where you want code snippets you put # #EXAM,file # #This preprocessor will then open "file" and insert it as a verbatim copy. # #Tom St Denis #get graphics type if (shift =~ /PDF/) { $graph = ""; } else {$graph = ".ps"; } open(IN,"tommath.tex") or die "Can't open destination file"; print "Scanning for sections\n"; $chapter =$section = $subsection = 0;$x = 0; while () { print "."; if (!(++$x % 80)) { print "\n"; } #update the headings if (~($_ =~ /\*/)) { if ($_ =~ /\\chapter{.+}/) { ++$chapter; $section =$subsection = 0; } elsif ($_ =~ /\\section{.+}/) { ++$section; $subsection = 0; } elsif ($_ =~ /\\subsection{.+}/) { ++$subsection; } } if ($_ =~ m/MARK/) { @m = split(",",$_); chomp(@m[1]);$index1{@m[1]} = $chapter;$index2{@m[1]} = $section;$index3{@m[1]} = $subsection; } } close(IN); open(IN,") { ++$readline; ++$srcline; if ($_ =~ m/MARK/) { } elsif ($_ =~ m/EXAM/ ||$_ =~ m/LIST/) { if ($_ =~ m/EXAM/) {$skipheader = 1; } else { $skipheader = 0; } # EXAM,file chomp($_); @m = split(",",$_); open(SRC,"<$m[1]") or die "Error:$srcline:Can't open source file$m[1]"; print "$srcline:Inserting$m[1]:"; $line = 0;$tmp = $m[1];$tmp =~ s/_/"\\_"/ge; print OUT "\\vspace{+3mm}\\begin{small}\n\\hspace{-5.1mm}{\\bf File}: $tmp\n\\vspace{-3mm}\n\\begin{alltt}\n";$wroteline += 5; if ($skipheader == 1) { # scan till next end of comment, e.g. skip license while () {$text[$line++] =$_; last if ($_ =~ /math\.libtomcrypt\.org/); } ; }$inline = 0; while () { next if ($_ =~ /\$Source/); next if ($_ =~ /\$Revision/); next if ($_ =~ /\$Date/); $text[$line++] = $_; ++$inline; chomp($_);$_ =~ s/\t/" "/ge; $_ =~ s/{/"^{"/ge;$_ =~ s/}/"^}"/ge; $_ =~ s/\\/'\symbol{92}'/ge;$_ =~ s/\^/"\\"/ge; printf OUT ("%03d ", $line); for ($x = 0; $x < length($_); $x++) { print OUT chr(vec($_, $x, 8)); if ($x == 75) { print OUT "\n "; ++$wroteline; } } print OUT "\n"; ++$wroteline; } $totlines =$line; print OUT "\\end{alltt}\n\\end{small}\n"; close(SRC); print "$inline lines\n";$wroteline += 2; } elsif ($_ =~ m/@\d+,.+@/) { # line contains [number,text] # e.g. @14,for (ix = 0)@$txt = $_; while ($txt =~ m/@\d+,.+@/) { @m = split("@",$txt); # splits into text, one, two @parms = split(",",$m[1]); # splits one,two into two elements # now search from $parms[0] down for$parms[1] $found1 = 0;$found2 = 0; for ($i =$parms[0]; $i <$totlines && $found1 == 0;$i++) { if ($text[$i] =~ m/\Q$parms[1]\E/) {$foundline1 = $i + 1;$found1 = 1; } } # now search backwards for ($i =$parms[0] - 1; $i >= 0 &&$found2 == 0; $i--) { if ($text[$i] =~ m/\Q$parms[1]\E/) { $foundline2 =$i + 1; $found2 = 1; } } # now use the closest match or the first if tied if ($found1 == 1 && $found2 == 0) {$found = 1; $foundline =$foundline1; } elsif ($found1 == 0 &&$found2 == 1) { $found = 1;$foundline = $foundline2; } elsif ($found1 == 1 && $found2 == 1) {$found = 1; if (($foundline1 -$parms[0]) <= ($parms[0] -$foundline2)) { $foundline =$foundline1; } else { $foundline =$foundline2; } } else { $found = 0; } # if found replace if ($found == 1) { $delta =$parms[0] - $foundline; print "Found replacement tag for \"$parms[1]\" on line $srcline which refers to line$foundline (delta $delta)\n";$_ =~ s/@\Q$m[1]\E@/$foundline/; } else { print "ERROR: The tag \"$parms[1]\" on line$srcline was not found in the most recently parsed source!\n"; } # remake the rest of the line $cnt = @m;$txt = ""; for ($i = 2;$i < $cnt;$i++) { $txt =$txt . $m[$i] . "@"; } } print OUT $_; ++$wroteline; } elsif ($_ =~ /~.+~/) { # line contains a ~text~ pair used to refer to indexing :-)$txt = $_; while ($txt =~ /~.+~/) { @m = split("~", $txt); # word is the second position$word = @m[1]; $a =$index1{$word};$b = $index2{$word}; $c =$index3{$word}; # if chapter (a) is zero it wasn't found if ($a == 0) { print "ERROR: the tag \"$word\" on line$srcline was not found previously marked.\n"; } else { # format the tag as x, x.y or x.y.z depending on the values $str =$a; $str =$str . ".$b" if ($b != 0); $str =$str . ".$c" if ($c != 0); if ($b == 0 &&$c == 0) { # its a chapter if ($a <= 10) { if ($a == 1) { $str = "chapter one"; } elsif ($a == 2) { $str = "chapter two"; } elsif ($a == 3) { $str = "chapter three"; } elsif ($a == 4) { $str = "chapter four"; } elsif ($a == 5) { $str = "chapter five"; } elsif ($a == 6) { $str = "chapter six"; } elsif ($a == 7) { $str = "chapter seven"; } elsif ($a == 8) { $str = "chapter eight"; } elsif ($a == 9) { $str = "chapter nine"; } elsif ($a == 2) { $str = "chapter ten"; } } else {$str = "chapter " . $str; } } else {$str = "section " . $str if ($b != 0 && $c == 0);$str = "sub-section " . $str if ($b != 0 && $c != 0); } #substitute$_ =~ s/~\Q$word\E~/$str/; print "Found replacement tag for marker \"$word\" on line$srcline which refers to $str\n"; } # remake rest of the line$cnt = @m; $txt = ""; for ($i = 2; $i <$cnt; $i++) {$txt = $txt .$m[$i] . "~"; } } print OUT$_; ++$wroteline; } elsif ($_ =~ m/FIGU/) { # FIGU,file,caption chomp($_); @m = split(",",$_); print OUT "\\begin{center}\n\\begin{figure}[here]\n\\includegraphics{pics/$m[1]$graph}\n"; print OUT "\\caption{$m[2]}\n\\label{pic:$m[1]}\n\\end{figure}\n\\end{center}\n"; $wroteline += 4; } else { print OUT$_; ++$wroteline; } } print "Read$readline lines, wrote $wroteline lines\n"; close (OUT); close (IN);  Changes to libtommath/changes.txt.   1 2 3 4 5 6 7   March 12th, 2005 v0.35 -- Stupid XOR function missing line again... oops. -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt] -- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ] -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns. ;-) -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly  > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  August 1st, 2005 v0.36 -- LTM_PRIME_2MSB_ON was fixed and the "OFF" flag was removed. -- [Peter LaDow] found a typo in the XREALLOC macro -- [Peter LaDow] pointed out that mp_read_(un)signed_bin should have "const" on the input -- Ported LTC patch to fix the prime_random_ex() function to get the bitsize correct [and the maskOR flags] -- Kevin Kenny pointed out a stray // -- David Hulton pointed out a typo in the textbook [mp_montgomery_setup() pseudo-code] -- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use unsigned operations in the routine. -- Paul Schmidt pointed out a linking error in mp_exptmod() when BN_S_MP_EXPTMOD_C is undefined (and another for read_radix) -- Updated makefiles to be way more flexible March 12th, 2005 v0.35 -- Stupid XOR function missing line again... oops. -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt] -- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ] -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns. ;-) -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly  Changes to libtommath/demo/demo.c.  385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 ... 730 731 732 733 734 735 736  #endif div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n = sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n = sub_d_n = 0; /* force KARA and TOOM to enable despite cutoffs */ KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 110; TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 150; for (;;) { /* randomly clear and re-init one variable, this has the affect of triming the alloc space */ switch (abs(rand()) % 7) { case 0: mp_clear(&a); mp_init(&a); ................................................................................ printf("d == %d\n", ix); return 0; } } } return 0; }   | | > > > >  385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 ... 730 731 732 733 734 735 736 737 738 739 740  #endif div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n = sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n = sub_d_n = 0; /* force KARA and TOOM to enable despite cutoffs */ KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8; TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16; for (;;) { /* randomly clear and re-init one variable, this has the affect of triming the alloc space */ switch (abs(rand()) % 7) { case 0: mp_clear(&a); mp_init(&a); ................................................................................ printf("d == %d\n", ix); return 0; } } } return 0; } /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/demo/demo.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Changes to libtommath/demo/timing.c.  309 310 311 312 313 314 315   mp_count_bits(&a), CLK_PER_SEC / tt, tt); fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt); } fclose(log); return 0; }   > > > >  309 310 311 312 313 314 315 316 317 318 319   mp_count_bits(&a), CLK_PER_SEC / tt, tt); fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt); } fclose(log); return 0; } /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/demo/timing.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Added libtommath/etc/2kprime.c.      > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84  /* Makes safe primes of a 2k nature */ #include #include int sizes[] = {256, 512, 768, 1024, 1536, 2048, 3072, 4096}; int main(void) { char buf[2000]; int x, y; mp_int q, p; FILE *out; clock_t t1; mp_digit z; mp_init_multi(&q, &p, NULL); out = fopen("2kprime.1", "w"); for (x = 0; x < (int)(sizeof(sizes) / sizeof(sizes[0])); x++) { top: mp_2expt(&q, sizes[x]); mp_add_d(&q, 3, &q); z = -3; t1 = clock(); for(;;) { mp_sub_d(&q, 4, &q); z += 4; if (z > MP_MASK) { printf("No primes of size %d found\n", sizes[x]); break; } if (clock() - t1 > CLOCKS_PER_SEC) { printf("."); fflush(stdout); // sleep((clock() - t1 + CLOCKS_PER_SEC/2)/CLOCKS_PER_SEC); t1 = clock(); } /* quick test on q */ mp_prime_is_prime(&q, 1, &y); if (y == 0) { continue; } /* find (q-1)/2 */ mp_sub_d(&q, 1, &p); mp_div_2(&p, &p); mp_prime_is_prime(&p, 3, &y); if (y == 0) { continue; } /* test on q */ mp_prime_is_prime(&q, 3, &y); if (y == 0) { continue; } break; } if (y == 0) { ++sizes[x]; goto top; } mp_toradix(&q, buf, 10); printf("\n\n%d-bits (k = %lu) = %s\n", sizes[x], z, buf); fprintf(out, "%d-bits (k = %lu) = %s\n", sizes[x], z, buf); fflush(out); } return 0; } /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/etc/2kprime.c,v $*/ /*$Revision: 1.1.1.1.2.1 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Added libtommath/etc/drprime.c.      > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64  /* Makes safe primes of a DR nature */ #include int sizes[] = { 1+256/DIGIT_BIT, 1+512/DIGIT_BIT, 1+768/DIGIT_BIT, 1+1024/DIGIT_BIT, 1+2048/DIGIT_BIT, 1+4096/DIGIT_BIT }; int main(void) { int res, x, y; char buf[4096]; FILE *out; mp_int a, b; mp_init(&a); mp_init(&b); out = fopen("drprimes.txt", "w"); for (x = 0; x < (int)(sizeof(sizes)/sizeof(sizes[0])); x++) { top: printf("Seeking a %d-bit safe prime\n", sizes[x] * DIGIT_BIT); mp_grow(&a, sizes[x]); mp_zero(&a); for (y = 1; y < sizes[x]; y++) { a.dp[y] = MP_MASK; } /* make a DR modulus */ a.dp[0] = -1; a.used = sizes[x]; /* now loop */ res = 0; for (;;) { a.dp[0] += 4; if (a.dp[0] >= MP_MASK) break; mp_prime_is_prime(&a, 1, &res); if (res == 0) continue; printf("."); fflush(stdout); mp_sub_d(&a, 1, &b); mp_div_2(&b, &b); mp_prime_is_prime(&b, 3, &res); if (res == 0) continue; mp_prime_is_prime(&a, 3, &res); if (res == 1) break; } if (res != 1) { printf("Error not DR modulus\n"); sizes[x] += 1; goto top; } else { mp_toradix(&a, buf, 10); printf("\n\np == %s\n\n", buf); fprintf(out, "%d-bit prime:\np == %s\n\n", mp_count_bits(&a), buf); fflush(out); } } fclose(out); mp_clear(&a); mp_clear(&b); return 0; } /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/etc/drprime.c,v $*/ /*$Revision: 1.1.1.1.2.1 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Added libtommath/etc/makefile.icc.      > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67  CC = icc CFLAGS += -I../ # optimize for SPEED # # -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4 # -ax? specifies make code specifically for ? but compatible with IA-32 # -x? specifies compile solely for ? [not specifically IA-32 compatible] # # where ? is # K - PIII # W - first P4 [Williamette] # N - P4 Northwood # P - P4 Prescott # B - Blend of P4 and PM [mobile] # # Default to just generic max opts CFLAGS += -O3 -xP -ip # default lib name (requires install with root) # LIBNAME=-ltommath # libname when you can't install the lib with install LIBNAME=../libtommath.a #provable primes pprime: pprime.o$(CC) pprime.o $(LIBNAME) -o pprime # portable [well requires clock()] tuning app tune: tune.o$(CC) tune.o $(LIBNAME) -o tune # same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp] tune86: tune.c nasm -f coff timer.asm$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o$(LIBNAME) -o tune86 # for cygwin tune86c: tune.c nasm -f gnuwin32 timer.asm $(CC) -DX86_TIMER$(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86 #make tune86 for linux or any ELF format tune86l: tune.c nasm -f elf -DUSE_ELF timer.asm$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o$(LIBNAME) -o tune86l # spits out mersenne primes mersenne: mersenne.o $(CC) mersenne.o$(LIBNAME) -o mersenne # fines DR safe primes for the given config drprime: drprime.o $(CC) drprime.o$(LIBNAME) -o drprime # fines 2k safe primes for the given config 2kprime: 2kprime.o $(CC) 2kprime.o$(LIBNAME) -o 2kprime mont: mont.o $(CC) mont.o$(LIBNAME) -o mont clean: rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat *.il 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144  /* Finds Mersenne primes using the Lucas-Lehmer test * * Tom St Denis, tomstdenis@iahu.ca */ #include #include int is_mersenne (long s, int *pp) { mp_int n, u; int res, k; *pp = 0; if ((res = mp_init (&n)) != MP_OKAY) { return res; } if ((res = mp_init (&u)) != MP_OKAY) { goto LBL_N; } /* n = 2^s - 1 */ if ((res = mp_2expt(&n, s)) != MP_OKAY) { goto LBL_MU; } if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) { goto LBL_MU; } /* set u=4 */ mp_set (&u, 4); /* for k=1 to s-2 do */ for (k = 1; k <= s - 2; k++) { /* u = u^2 - 2 mod n */ if ((res = mp_sqr (&u, &u)) != MP_OKAY) { goto LBL_MU; } if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) { goto LBL_MU; } /* make sure u is positive */ while (u.sign == MP_NEG) { if ((res = mp_add (&u, &n, &u)) != MP_OKAY) { goto LBL_MU; } } /* reduce */ if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) { goto LBL_MU; } } /* if u == 0 then its prime */ if (mp_iszero (&u) == 1) { mp_prime_is_prime(&n, 8, pp); if (*pp != 1) printf("FAILURE\n"); } res = MP_OKAY; LBL_MU:mp_clear (&u); LBL_N:mp_clear (&n); return res; } /* square root of a long < 65536 */ long i_sqrt (long x) { long x1, x2; x2 = 16; do { x1 = x2; x2 = x1 - ((x1 * x1) - x) / (2 * x1); } while (x1 != x2); if (x1 * x1 > x) { --x1; } return x1; } /* is the long prime by brute force */ int isprime (long k) { long y, z; y = i_sqrt (k); for (z = 2; z <= y; z++) { if ((k % z) == 0) return 0; } return 1; } int main (void) { int pp; long k; clock_t tt; k = 3; for (;;) { /* start time */ tt = clock (); /* test if 2^k - 1 is prime */ if (is_mersenne (k, &pp) != MP_OKAY) { printf ("Whoa error\n"); return -1; } if (pp == 1) { /* count time */ tt = clock () - tt; /* display if prime */ printf ("2^%-5ld - 1 is prime, test took %ld ticks\n", k, tt); } /* goto next odd exponent */ k += 2; /* but make sure its prime */ while (isprime (k) == 0) { k += 2; } } return 0; } /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/etc/mersenne.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50  /* tests the montgomery routines */ #include int main(void) { mp_int modulus, R, p, pp; mp_digit mp; long x, y; srand(time(NULL)); mp_init_multi(&modulus, &R, &p, &pp, NULL); /* loop through various sizes */ for (x = 4; x < 256; x++) { printf("DIGITS == %3ld...", x); fflush(stdout); /* make up the odd modulus */ mp_rand(&modulus, x); modulus.dp[0] |= 1; /* now find the R value */ mp_montgomery_calc_normalization(&R, &modulus); mp_montgomery_setup(&modulus, &mp); /* now run through a bunch tests */ for (y = 0; y < 1000; y++) { mp_rand(&p, x/2); /* p = random */ mp_mul(&p, &R, &pp); /* pp = R * p */ mp_montgomery_reduce(&pp, &modulus, mp); /* should be equal to p */ if (mp_cmp(&pp, &p) != MP_EQ) { printf("FAILURE!\n"); exit(-1); } } printf("PASSED\n"); } return 0; } /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/etc/mont.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

     > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400  /* Generates provable primes * * See http://iahu.ca:8080/papers/pp.pdf for more info. * * Tom St Denis, tomstdenis@iahu.ca, http://tom.iahu.ca */ #include #include "tommath.h" int n_prime; FILE *primes; /* fast square root */ static mp_digit i_sqrt (mp_word x) { mp_word x1, x2; x2 = x; do { x1 = x2; x2 = x1 - ((x1 * x1) - x) / (2 * x1); } while (x1 != x2); if (x1 * x1 > x) { --x1; } return x1; } /* generates a prime digit */ static void gen_prime (void) { mp_digit r, x, y, next; FILE *out; out = fopen("pprime.dat", "wb"); /* write first set of primes */ r = 3; fwrite(&r, 1, sizeof(mp_digit), out); r = 5; fwrite(&r, 1, sizeof(mp_digit), out); r = 7; fwrite(&r, 1, sizeof(mp_digit), out); r = 11; fwrite(&r, 1, sizeof(mp_digit), out); r = 13; fwrite(&r, 1, sizeof(mp_digit), out); r = 17; fwrite(&r, 1, sizeof(mp_digit), out); r = 19; fwrite(&r, 1, sizeof(mp_digit), out); r = 23; fwrite(&r, 1, sizeof(mp_digit), out); r = 29; fwrite(&r, 1, sizeof(mp_digit), out); r = 31; fwrite(&r, 1, sizeof(mp_digit), out); /* get square root, since if 'r' is composite its factors must be < than this */ y = i_sqrt (r); next = (y + 1) * (y + 1); for (;;) { do { r += 2; /* next candidate */ r &= MP_MASK; if (r < 31) break; /* update sqrt ? */ if (next <= r) { ++y; next = (y + 1) * (y + 1); } /* loop if divisible by 3,5,7,11,13,17,19,23,29 */ if ((r % 3) == 0) { x = 0; continue; } if ((r % 5) == 0) { x = 0; continue; } if ((r % 7) == 0) { x = 0; continue; } if ((r % 11) == 0) { x = 0; continue; } if ((r % 13) == 0) { x = 0; continue; } if ((r % 17) == 0) { x = 0; continue; } if ((r % 19) == 0) { x = 0; continue; } if ((r % 23) == 0) { x = 0; continue; } if ((r % 29) == 0) { x = 0; continue; } /* now check if r is divisible by x + k={1,7,11,13,17,19,23,29} */ for (x = 30; x <= y; x += 30) { if ((r % (x + 1)) == 0) { x = 0; break; } if ((r % (x + 7)) == 0) { x = 0; break; } if ((r % (x + 11)) == 0) { x = 0; break; } if ((r % (x + 13)) == 0) { x = 0; break; } if ((r % (x + 17)) == 0) { x = 0; break; } if ((r % (x + 19)) == 0) { x = 0; break; } if ((r % (x + 23)) == 0) { x = 0; break; } if ((r % (x + 29)) == 0) { x = 0; break; } } } while (x == 0); if (r > 31) { fwrite(&r, 1, sizeof(mp_digit), out); printf("%9d\r", r); fflush(stdout); } if (r < 31) break; } fclose(out); } void load_tab(void) { primes = fopen("pprime.dat", "rb"); if (primes == NULL) { gen_prime(); primes = fopen("pprime.dat", "rb"); } fseek(primes, 0, SEEK_END); n_prime = ftell(primes) / sizeof(mp_digit); } mp_digit prime_digit(void) { int n; mp_digit d; n = abs(rand()) % n_prime; fseek(primes, n * sizeof(mp_digit), SEEK_SET); fread(&d, 1, sizeof(mp_digit), primes); return d; } /* makes a prime of at least k bits */ int pprime (int k, int li, mp_int * p, mp_int * q) { mp_int a, b, c, n, x, y, z, v; int res, ii; static const mp_digit bases[] = { 2, 3, 5, 7, 11, 13, 17, 19 }; /* single digit ? */ if (k <= (int) DIGIT_BIT) { mp_set (p, prime_digit ()); return MP_OKAY; } if ((res = mp_init (&c)) != MP_OKAY) { return res; } if ((res = mp_init (&v)) != MP_OKAY) { goto LBL_C; } /* product of first 50 primes */ if ((res = mp_read_radix (&v, "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190", 10)) != MP_OKAY) { goto LBL_V; } if ((res = mp_init (&a)) != MP_OKAY) { goto LBL_V; } /* set the prime */ mp_set (&a, prime_digit ()); if ((res = mp_init (&b)) != MP_OKAY) { goto LBL_A; } if ((res = mp_init (&n)) != MP_OKAY) { goto LBL_B; } if ((res = mp_init (&x)) != MP_OKAY) { goto LBL_N; } if ((res = mp_init (&y)) != MP_OKAY) { goto LBL_X; } if ((res = mp_init (&z)) != MP_OKAY) { goto LBL_Y; } /* now loop making the single digit */ while (mp_count_bits (&a) < k) { fprintf (stderr, "prime has %4d bits left\r", k - mp_count_bits (&a)); fflush (stderr); top: mp_set (&b, prime_digit ()); /* now compute z = a * b * 2 */ if ((res = mp_mul (&a, &b, &z)) != MP_OKAY) { /* z = a * b */ goto LBL_Z; } if ((res = mp_copy (&z, &c)) != MP_OKAY) { /* c = a * b */ goto LBL_Z; } if ((res = mp_mul_2 (&z, &z)) != MP_OKAY) { /* z = 2 * a * b */ goto LBL_Z; } /* n = z + 1 */ if ((res = mp_add_d (&z, 1, &n)) != MP_OKAY) { /* n = z + 1 */ goto LBL_Z; } /* check (n, v) == 1 */ if ((res = mp_gcd (&n, &v, &y)) != MP_OKAY) { /* y = (n, v) */ goto LBL_Z; } if (mp_cmp_d (&y, 1) != MP_EQ) goto top; /* now try base x=bases[ii] */ for (ii = 0; ii < li; ii++) { mp_set (&x, bases[ii]); /* compute x^a mod n */ if ((res = mp_exptmod (&x, &a, &n, &y)) != MP_OKAY) { /* y = x^a mod n */ goto LBL_Z; } /* if y == 1 loop */ if (mp_cmp_d (&y, 1) == MP_EQ) continue; /* now x^2a mod n */ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2a mod n */ goto LBL_Z; } if (mp_cmp_d (&y, 1) == MP_EQ) continue; /* compute x^b mod n */ if ((res = mp_exptmod (&x, &b, &n, &y)) != MP_OKAY) { /* y = x^b mod n */ goto LBL_Z; } /* if y == 1 loop */ if (mp_cmp_d (&y, 1) == MP_EQ) continue; /* now x^2b mod n */ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2b mod n */ goto LBL_Z; } if (mp_cmp_d (&y, 1) == MP_EQ) continue; /* compute x^c mod n == x^ab mod n */ if ((res = mp_exptmod (&x, &c, &n, &y)) != MP_OKAY) { /* y = x^ab mod n */ goto LBL_Z; } /* if y == 1 loop */ if (mp_cmp_d (&y, 1) == MP_EQ) continue; /* now compute (x^c mod n)^2 */ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2ab mod n */ goto LBL_Z; } /* y should be 1 */ if (mp_cmp_d (&y, 1) != MP_EQ) continue; break; } /* no bases worked? */ if (ii == li) goto top; { char buf[4096]; mp_toradix(&n, buf, 10); printf("Certificate of primality for:\n%s\n\n", buf); mp_toradix(&a, buf, 10); printf("A == \n%s\n\n", buf); mp_toradix(&b, buf, 10); printf("B == \n%s\n\nG == %d\n", buf, bases[ii]); printf("----------------------------------------------------------------\n"); } /* a = n */ mp_copy (&n, &a); } /* get q to be the order of the large prime subgroup */ mp_sub_d (&n, 1, q); mp_div_2 (q, q); mp_div (q, &b, q, NULL); mp_exch (&n, p); res = MP_OKAY; LBL_Z:mp_clear (&z); LBL_Y:mp_clear (&y); LBL_X:mp_clear (&x); LBL_N:mp_clear (&n); LBL_B:mp_clear (&b); LBL_A:mp_clear (&a); LBL_V:mp_clear (&v); LBL_C:mp_clear (&c); return res; } int main (void) { mp_int p, q; char buf[4096]; int k, li; clock_t t1; srand (time (NULL)); load_tab(); printf ("Enter # of bits: \n"); fgets (buf, sizeof (buf), stdin); sscanf (buf, "%d", &k); printf ("Enter number of bases to try (1 to 8):\n"); fgets (buf, sizeof (buf), stdin); sscanf (buf, "%d", &li); mp_init (&p); mp_init (&q); t1 = clock (); pprime (k, li, &p, &q); t1 = clock () - t1; printf ("\n\nTook %ld ticks, %d bits\n", t1, mp_count_bits (&p)); mp_toradix (&p, buf, 10); printf ("P == %s\n", buf); mp_toradix (&q, buf, 10); printf ("Q == %s\n", buf); return 0; } /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/etc/pprime.c,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/etc/tune.c.

 132 133 134 135 136 137 138   if (t2 < t1) break; } printf("KARATSUBA_MUL_CUTOFF = %d\n", y); printf("KARATSUBA_SQR_CUTOFF = %d\n", x); return 0; }   > > > >  132 133 134 135 136 137 138 139 140 141 142   if (t2 < t1) break; } printf("KARATSUBA_MUL_CUTOFF = %d\n", y); printf("KARATSUBA_SQR_CUTOFF = %d\n", x); return 0; } /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/etc/tune.c,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/logs/expt.log.

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Changes to libtommath/logs/expt_2k.log.

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Changes to libtommath/logs/expt_2kl.log.

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Changes to libtommath/logs/expt_dr.log.

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     > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27   LibTomMath Log Plots

Multipliers

Exptmod

Modular Inverse

/* $Source: /root/tcl/repos-to-convert/tcl/libtommath/logs/index.html,v$ */ /* $Revision: 1.1.1.1.2.1$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/makefile.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 .. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 .. 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 ... 147 148 149 150 151 152 153 154 155 156 157 158 159  #Makefile for GCC # #Tom St Denis #version of library VERSION=0.35 CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare #for speed CFLAGS += -O3 -funroll-all-loops #for size #CFLAGS += -Os #x86 optimizations [should be valid for any GCC install though] CFLAGS += -fomit-frame-pointer #debug #CFLAGS += -g3 #install as this user USER=root GROUP=root default: libtommath.a #default files to install LIBNAME=libtommath.a HEADERS=tommath.h tommath_class.h tommath_superclass.h #LIBPATH-The directory for libtommath to be installed to. #INCPATH-The directory to install the header files for libtommath. #DATAPATH-The directory to install the pdf docs. DESTDIR= LIBPATH=/usr/lib ................................................................................ bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \ bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o libtommath.a: $(OBJECTS)$(AR) $(ARFLAGS) libtommath.a$(OBJECTS) ranlib libtommath.a #make a profiled library (takes a while!!!) # # This will build the library with profile generation # then run the test demo and rebuild the library. # # So far I've seen improvements in the MP math ................................................................................ profiled_single: perl gen.pl $(CC)$(CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o $(CC)$(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -o ltmtest ./ltmtest rm -f *.o ltmtest $(CC)$(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o $(AR)$(ARFLAGS) libtommath.a mpi.o ranlib libtommath.a install: libtommath.a install -d -g $(GROUP) -o$(USER) $(DESTDIR)$(LIBPATH) install -d -g $(GROUP) -o$(USER) $(DESTDIR)$(INCPATH) install -g $(GROUP) -o$(USER) $(LIBNAME)$(DESTDIR)$(LIBPATH) install -g$(GROUP) -o $(USER)$(HEADERS) $(DESTDIR)$(INCPATH) test: libtommath.a demo/demo.o $(CC)$(CFLAGS) demo/demo.o libtommath.a -o test mtest: test cd mtest ; $(CC)$(CFLAGS) mtest.c -o mtest timing: libtommath.a $(CC)$(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest # makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think] docdvi: tommath.src cd pics ; make echo "hello" > tommath.ind perl booker.pl latex tommath > /dev/null ................................................................................ clean: rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \ *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex find -type f | grep [~] | xargs *.lo *.la rm -rf .libs cd etc ; make clean cd pics ; make clean zipup: clean manual poster docs perl gen.pl ; mv mpi.c pre_gen/ ; \ cd .. ; rm -rf ltm* libtommath-$(VERSION) ; mkdir libtommath-$(VERSION) ; \ cp -R ./libtommath/* ./libtommath-$(VERSION)/ ; \ tar -c libtommath-$(VERSION)/* | bzip2 -9vvc > ltm-$(VERSION).tar.bz2 ; \ zip -9 -r ltm-$(VERSION).zip libtommath-$(VERSION)/*   | > > | > > > > > > > > > | < > > > > | > | | | | | | | | | | > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 .. 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 ... 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 ... 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180  #Makefile for GCC # #Tom St Denis #version of library VERSION=0.36 CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare ifndef IGNORE_SPEED #for speed CFLAGS += -O3 -funroll-loops #for size #CFLAGS += -Os #x86 optimizations [should be valid for any GCC install though] CFLAGS += -fomit-frame-pointer #debug #CFLAGS += -g3 endif #install as this user ifndef INSTALL_GROUP GROUP=wheel else GROUP=$(INSTALL_GROUP) endif ifndef INSTALL_USER USER=root else USER=$(INSTALL_USER) endif default: libtommath.a #default files to install ifndef LIBNAME LIBNAME=libtommath.a endif HEADERS=tommath.h tommath_class.h tommath_superclass.h #LIBPATH-The directory for libtommath to be installed to. #INCPATH-The directory to install the header files for libtommath. #DATAPATH-The directory to install the pdf docs. DESTDIR= LIBPATH=/usr/lib ................................................................................ bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \ bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o$(LIBNAME): $(OBJECTS)$(AR) $(ARFLAGS)$@ $(OBJECTS) ranlib$@ #make a profiled library (takes a while!!!) # # This will build the library with profile generation # then run the test demo and rebuild the library. # # So far I've seen improvements in the MP math ................................................................................ profiled_single: perl gen.pl $(CC)$(CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o $(CC)$(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -o ltmtest ./ltmtest rm -f *.o ltmtest $(CC)$(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o $(AR)$(ARFLAGS) $(LIBNAME) mpi.o ranlib$(LIBNAME) install: $(LIBNAME) install -d -g$(GROUP) -o $(USER)$(DESTDIR)$(LIBPATH) install -d -g$(GROUP) -o $(USER)$(DESTDIR)$(INCPATH) install -g$(GROUP) -o $(USER)$(LIBNAME) $(DESTDIR)$(LIBPATH) install -g $(GROUP) -o$(USER) $(HEADERS)$(DESTDIR)$(INCPATH) test:$(LIBNAME) demo/demo.o $(CC)$(CFLAGS) demo/demo.o $(LIBNAME) -o test mtest: test cd mtest ;$(CC) $(CFLAGS) mtest.c -o mtest timing:$(LIBNAME) $(CC)$(CFLAGS) -DTIMER demo/timing.c $(LIBNAME) -o ltmtest # makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think] docdvi: tommath.src cd pics ; make echo "hello" > tommath.ind perl booker.pl latex tommath > /dev/null ................................................................................ clean: rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \ *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex find -type f | grep [~] | xargs *.lo *.la rm -rf .libs cd etc ; make clean cd pics ; make clean #zipup the project (take that!) no_oops: clean cd .. ; cvs commit echo Scanning for scratch/dirty files find . -type f | grep -v CVS | xargs -n 1 bash mess.sh zipup: clean manual poster docs perl gen.pl ; mv mpi.c pre_gen/ ; \ cd .. ; rm -rf ltm* libtommath-$(VERSION) ; mkdir libtommath-$(VERSION) ; \ cp -R ./libtommath/* ./libtommath-$(VERSION)/ ; \ tar -c libtommath-$(VERSION)/* | bzip2 -9vvc > ltm-$(VERSION).tar.bz2 ; \ zip -9 -r ltm-$(VERSION).zip libtommath-$(VERSION)/* 

Changes to libtommath/makefile.cygwin_dll.

 45 46 47 48 49 50 51   gcc -mno-cygwin -mdll -o libtommath.dll -Wl,--out-implib=libtommath.dll.a -Wl,--export-all-symbols *.o ranlib libtommath.dll.a # build the test program using the windows DLL test: $(OBJECTS) windll gcc$(CFLAGS) demo/demo.c libtommath.dll.a -Wl,--enable-auto-import -o test -s cd mtest ; $(CC) -O3 -fomit-frame-pointer -funroll-loops mtest.c -o mtest -s   > > > >  45 46 47 48 49 50 51 52 53 54 55   gcc -mno-cygwin -mdll -o libtommath.dll -Wl,--out-implib=libtommath.dll.a -Wl,--export-all-symbols *.o ranlib libtommath.dll.a # build the test program using the windows DLL test:$(OBJECTS) windll gcc $(CFLAGS) demo/demo.c libtommath.dll.a -Wl,--enable-auto-import -o test -s cd mtest ;$(CC) -O3 -fomit-frame-pointer -funroll-loops mtest.c -o mtest -s /* $Source: /root/tcl/repos-to-convert/tcl/libtommath/makefile.cygwin_dll,v$ */ /* $Revision: 1.1.1.1.2.2$ */ /* $Date: 2005/09/26 20:16:54$ */ 

Changes to libtommath/makefile.icc.

 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29  # K - PIII # W - first P4 [Williamette] # N - P4 Northwood # P - P4 Prescott # B - Blend of P4 and PM [mobile] # # Default to just generic max opts CFLAGS += -O3 -xN #install as this user USER=root GROUP=root default: libtommath.a   |  15 16 17 18 19 20 21 22 23 24 25 26 27 28 29  # K - PIII # W - first P4 [Williamette] # N - P4 Northwood # P - P4 Prescott # B - Blend of P4 and PM [mobile] # # Default to just generic max opts CFLAGS += -O3 -xP -ip #install as this user USER=root GROUP=root default: libtommath.a 

Changes to libtommath/makefile.msvc.

 1 2 3 4 5 6 7 8 9 10 11 12 .. 29 30 31 32 33 34 35 36 37 38  #MSVC Makefile # #Tom St Denis CFLAGS = /I. /Ox /DWIN32 /W4 default: library OBJECTS=bncore.obj bn_mp_init.obj bn_mp_clear.obj bn_mp_exch.obj bn_mp_grow.obj bn_mp_shrink.obj \ bn_mp_clamp.obj bn_mp_zero.obj bn_mp_set.obj bn_mp_set_int.obj bn_mp_init_size.obj bn_mp_copy.obj \ bn_mp_init_copy.obj bn_mp_abs.obj bn_mp_neg.obj bn_mp_cmp_mag.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \ bn_mp_rshd.obj bn_mp_lshd.obj bn_mp_mod_2d.obj bn_mp_div_2d.obj bn_mp_mul_2d.obj bn_mp_div_2.obj \ ................................................................................ bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \ bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \ bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \ bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \ bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \ bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \ bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj library: $(OBJECTS) lib /out:tommath.lib$(OBJECTS)   | > >  1 2 3 4 5 6 7 8 9 10 11 12 .. 29 30 31 32 33 34 35 36 37 38 39 40  #MSVC Makefile # #Tom St Denis CFLAGS = /I. /Ox /DWIN32 /W3 /Fo$@ default: library OBJECTS=bncore.obj bn_mp_init.obj bn_mp_clear.obj bn_mp_exch.obj bn_mp_grow.obj bn_mp_shrink.obj \ bn_mp_clamp.obj bn_mp_zero.obj bn_mp_set.obj bn_mp_set_int.obj bn_mp_init_size.obj bn_mp_copy.obj \ bn_mp_init_copy.obj bn_mp_abs.obj bn_mp_neg.obj bn_mp_cmp_mag.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \ bn_mp_rshd.obj bn_mp_lshd.obj bn_mp_mod_2d.obj bn_mp_div_2d.obj bn_mp_mul_2d.obj bn_mp_div_2.obj \ ................................................................................ bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \ bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \ bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \ bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \ bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \ bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \ bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj HEADERS=tommath.h tommath_class.h tommath_superclass.h library:$(OBJECTS) lib /out:tommath.lib $(OBJECTS)  Changes to libtommath/makefile.shared.  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 .. 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80  #Makefile for GCC # #Tom St Denis VERSION=0:35 CC = libtool --mode=compile gcc CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare #for speed CFLAGS += -O3 -funroll-loops #for size #CFLAGS += -Os #x86 optimizations [should be valid for any GCC install though] CFLAGS += -fomit-frame-pointer #install as this user USER=root GROUP=root default: libtommath.la #default files to install LIBNAME=libtommath.la HEADERS=tommath.h tommath_class.h tommath_superclass.h #LIBPATH-The directory for libtommath to be installed to. #INCPATH-The directory to install the header files for libtommath. #DATAPATH-The directory to install the pdf docs. DESTDIR= LIBPATH=/usr/lib ................................................................................ bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \ bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o libtommath.la:$(OBJECTS) libtool --mode=link gcc *.lo -o libtommath.la -rpath $(LIBPATH) -version-info$(VERSION) libtool --mode=link gcc *.o -o libtommath.a libtool --mode=install install -c libtommath.la $(LIBPATH)/libtommath.la install -d -g$(GROUP) -o $(USER)$(DESTDIR)$(INCPATH) install -g$(GROUP) -o $(USER)$(HEADERS) $(DESTDIR)$(INCPATH) test: libtommath.a demo/demo.o gcc $(CFLAGS) -c demo/demo.c -o demo/demo.o libtool --mode=link gcc -o test demo/demo.o libtommath.la mtest: test cd mtest ; gcc$(CFLAGS) mtest.c -o mtest -s timing: libtommath.la gcc $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest -s   | > > > > > > > > > > > > | < > > > > | > > > > < | | | > | | | | | |  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 .. 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99  #Makefile for GCC # #Tom St Denis VERSION=0:36 CC = libtool --mode=compile gcc CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare ifndef IGNORE_SPEED #for speed CFLAGS += -O3 -funroll-loops #for size #CFLAGS += -Os #x86 optimizations [should be valid for any GCC install though] CFLAGS += -fomit-frame-pointer endif #install as this user ifndef INSTALL_GROUP GROUP=wheel else GROUP=$(INSTALL_GROUP) endif ifndef INSTALL_USER USER=root else USER=$(INSTALL_USER) endif default: libtommath.la #default files to install ifndef LIBNAME LIBNAME=libtommath.la endif ifndef LIBNAME_S LIBNAME_S=libtommath.a endif HEADERS=tommath.h tommath_class.h tommath_superclass.h #LIBPATH-The directory for libtommath to be installed to. #INCPATH-The directory to install the header files for libtommath. #DATAPATH-The directory to install the pdf docs. DESTDIR= LIBPATH=/usr/lib ................................................................................ bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \ bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o$(LIBNAME): $(OBJECTS) libtool --mode=link gcc *.lo -o$(LIBNAME) -rpath $(LIBPATH) -version-info$(VERSION) libtool --mode=link gcc *.o -o $(LIBNAME_S) ranlib$(LIBNAME_S) libtool --mode=install install -c $(LIBNAME)$(LIBPATH)/$@ install -d -g$(GROUP) -o $(USER)$(DESTDIR)$(INCPATH) install -g$(GROUP) -o $(USER)$(HEADERS) $(DESTDIR)$(INCPATH) test: $(LIBNAME) demo/demo.o gcc$(CFLAGS) -c demo/demo.c -o demo/demo.o libtool --mode=link gcc -o test demo/demo.o $(LIBNAME_S) mtest: test cd mtest ; gcc$(CFLAGS) mtest.c -o mtest timing: $(LIBNAME) gcc$(CFLAGS) -DTIMER demo/timing.c $(LIBNAME_S) -o ltmtest  Added libtommath/mess.sh.      > > > >  1 2 3 4  #!/bin/bash if cvs log$1 >/dev/null 2>/dev/null; then exit 0; else echo "$1 shouldn't be here" ; exit 1; fi  Added libtommath/mtest/logtab.h.      > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  const float s_logv_2[] = { 0.000000000, 0.000000000, 1.000000000, 0.630929754, /* 0 1 2 3 */ 0.500000000, 0.430676558, 0.386852807, 0.356207187, /* 4 5 6 7 */ 0.333333333, 0.315464877, 0.301029996, 0.289064826, /* 8 9 10 11 */ 0.278942946, 0.270238154, 0.262649535, 0.255958025, /* 12 13 14 15 */ 0.250000000, 0.244650542, 0.239812467, 0.235408913, /* 16 17 18 19 */ 0.231378213, 0.227670249, 0.224243824, 0.221064729, /* 20 21 22 23 */ 0.218104292, 0.215338279, 0.212746054, 0.210309918, /* 24 25 26 27 */ 0.208014598, 0.205846832, 0.203795047, 0.201849087, /* 28 29 30 31 */ 0.200000000, 0.198239863, 0.196561632, 0.194959022, /* 32 33 34 35 */ 0.193426404, 0.191958720, 0.190551412, 0.189200360, /* 36 37 38 39 */ 0.187901825, 0.186652411, 0.185449023, 0.184288833, /* 40 41 42 43 */ 0.183169251, 0.182087900, 0.181042597, 0.180031327, /* 44 45 46 47 */ 0.179052232, 0.178103594, 0.177183820, 0.176291434, /* 48 49 50 51 */ 0.175425064, 0.174583430, 0.173765343, 0.172969690, /* 52 53 54 55 */ 0.172195434, 0.171441601, 0.170707280, 0.169991616, /* 56 57 58 59 */ 0.169293808, 0.168613099, 0.167948779, 0.167300179, /* 60 61 62 63 */ 0.166666667 }; /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/mtest/logtab.h,v $*/ /*$Revision: 1.1.1.1.2.1 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Added libtommath/mtest/mpi-config.h.      > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90  /* Default configuration for MPI library */ /*$Id: mpi-config.h,v 1.1.1.1.2.1 2005/09/26 20:16:54 kennykb Exp $*/ #ifndef MPI_CONFIG_H_ #define MPI_CONFIG_H_ /* For boolean options, 0 = no 1 = yes Other options are documented individually. */ #ifndef MP_IOFUNC #define MP_IOFUNC 0 /* include mp_print() ? */ #endif #ifndef MP_MODARITH #define MP_MODARITH 1 /* include modular arithmetic ? */ #endif #ifndef MP_NUMTH #define MP_NUMTH 1 /* include number theoretic functions? */ #endif #ifndef MP_LOGTAB #define MP_LOGTAB 1 /* use table of logs instead of log()? */ #endif #ifndef MP_MEMSET #define MP_MEMSET 1 /* use memset() to zero buffers? */ #endif #ifndef MP_MEMCPY #define MP_MEMCPY 1 /* use memcpy() to copy buffers? */ #endif #ifndef MP_CRYPTO #define MP_CRYPTO 1 /* erase memory on free? */ #endif #ifndef MP_ARGCHK /* 0 = no parameter checks 1 = runtime checks, continue execution and return an error to caller 2 = assertions; dump core on parameter errors */ #define MP_ARGCHK 2 /* how to check input arguments */ #endif #ifndef MP_DEBUG #define MP_DEBUG 0 /* print diagnostic output? */ #endif #ifndef MP_DEFPREC #define MP_DEFPREC 64 /* default precision, in digits */ #endif #ifndef MP_MACRO #define MP_MACRO 1 /* use macros for frequent calls? */ #endif #ifndef MP_SQUARE #define MP_SQUARE 1 /* use separate squaring code? */ #endif #ifndef MP_PTAB_SIZE /* When building mpprime.c, we build in a table of small prime values to use for primality testing. The more you include, the more space they take up. See primes.c for the possible values (currently 16, 32, 64, 128, 256, and 6542) */ #define MP_PTAB_SIZE 128 /* how many built-in primes? */ #endif #ifndef MP_COMPAT_MACROS #define MP_COMPAT_MACROS 1 /* define compatibility macros? */ #endif #endif /* ifndef MPI_CONFIG_H_ */ /* crc==3287762869, version==2, Sat Feb 02 06:43:53 2002 */ /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/mtest/mpi-config.h,v $*/ /*$Revision: 1.1.1.1.2.1 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Added libtommath/mtest/mpi-types.h.      > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  /* Type definitions generated by 'types.pl' */ typedef char mp_sign; typedef unsigned short mp_digit; /* 2 byte type */ typedef unsigned int mp_word; /* 4 byte type */ typedef unsigned int mp_size; typedef int mp_err; #define MP_DIGIT_BIT (CHAR_BIT*sizeof(mp_digit)) #define MP_DIGIT_MAX USHRT_MAX #define MP_WORD_BIT (CHAR_BIT*sizeof(mp_word)) #define MP_WORD_MAX UINT_MAX #define MP_DIGIT_SIZE 2 #define DIGIT_FMT "%04X" #define RADIX (MP_DIGIT_MAX+1) /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/mtest/mpi-types.h,v $*/ /*$Revision: 1.1.1.1.2.1 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Added libtommath/mtest/mpi.c.      > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > 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3979 3980 3981 3982 3983 3984 3985  /* mpi.c by Michael J. Fromberger Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved Arbitrary precision integer arithmetic library$Id: mpi.c,v 1.1.1.1.2.1 2005/09/26 20:16:54 kennykb Exp $*/ #include "mpi.h" #include #include #include #if MP_DEBUG #include #define DIAG(T,V) {fprintf(stderr,T);mp_print(V,stderr);fputc('\n',stderr);} #else #define DIAG(T,V) #endif /* If MP_LOGTAB is not defined, use the math library to compute the logarithms on the fly. Otherwise, use the static table below. Pick which works best for your system. */ #if MP_LOGTAB /* {{{ s_logv_2[] - log table for 2 in various bases */ /* A table of the logs of 2 for various bases (the 0 and 1 entries of this table are meaningless and should not be referenced). This table is used to compute output lengths for the mp_toradix() function. Since a number n in radix r takes up about log_r(n) digits, we estimate the output size by taking the least integer greater than log_r(n), where: log_r(n) = log_2(n) * log_r(2) This table, therefore, is a table of log_r(2) for 2 <= r <= 36, which are the output bases supported. */ #include "logtab.h" /* }}} */ #define LOG_V_2(R) s_logv_2[(R)] #else #include #define LOG_V_2(R) (log(2.0)/log(R)) #endif /* Default precision for newly created mp_int's */ static unsigned int s_mp_defprec = MP_DEFPREC; /* {{{ Digit arithmetic macros */ /* When adding and multiplying digits, the results can be larger than can be contained in an mp_digit. Thus, an mp_word is used. These macros mask off the upper and lower digits of the mp_word (the mp_word may be more than 2 mp_digits wide, but we only concern ourselves with the low-order 2 mp_digits) If your mp_word DOES have more than 2 mp_digits, you need to uncomment the first line, and comment out the second. */ /* #define CARRYOUT(W) (((W)>>DIGIT_BIT)&MP_DIGIT_MAX) */ #define CARRYOUT(W) ((W)>>DIGIT_BIT) #define ACCUM(W) ((W)&MP_DIGIT_MAX) /* }}} */ /* {{{ Comparison constants */ #define MP_LT -1 #define MP_EQ 0 #define MP_GT 1 /* }}} */ /* {{{ Constant strings */ /* Constant strings returned by mp_strerror() */ static const char *mp_err_string[] = { "unknown result code", /* say what? */ "boolean true", /* MP_OKAY, MP_YES */ "boolean false", /* MP_NO */ "out of memory", /* MP_MEM */ "argument out of range", /* MP_RANGE */ "invalid input parameter", /* MP_BADARG */ "result is undefined" /* MP_UNDEF */ }; /* Value to digit maps for radix conversion */ /* s_dmap_1 - standard digits and letters */ static const char *s_dmap_1 = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; #if 0 /* s_dmap_2 - base64 ordering for digits */ static const char *s_dmap_2 = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"; #endif /* }}} */ /* {{{ Static function declarations */ /* If MP_MACRO is false, these will be defined as actual functions; otherwise, suitable macro definitions will be used. This works around the fact that ANSI C89 doesn't support an 'inline' keyword (although I hear C9x will ... about bloody time). At present, the macro definitions are identical to the function bodies, but they'll expand in place, instead of generating a function call. I chose these particular functions to be made into macros because some profiling showed they are called a lot on a typical workload, and yet they are primarily housekeeping. */ #if MP_MACRO == 0 void s_mp_setz(mp_digit *dp, mp_size count); /* zero digits */ void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count); /* copy */ void *s_mp_alloc(size_t nb, size_t ni); /* general allocator */ void s_mp_free(void *ptr); /* general free function */ #else /* Even if these are defined as macros, we need to respect the settings of the MP_MEMSET and MP_MEMCPY configuration options... */ #if MP_MEMSET == 0 #define s_mp_setz(dp, count) \ {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=0;} #else #define s_mp_setz(dp, count) memset(dp, 0, (count) * sizeof(mp_digit)) #endif /* MP_MEMSET */ #if MP_MEMCPY == 0 #define s_mp_copy(sp, dp, count) \ {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=(sp)[ix];} #else #define s_mp_copy(sp, dp, count) memcpy(dp, sp, (count) * sizeof(mp_digit)) #endif /* MP_MEMCPY */ #define s_mp_alloc(nb, ni) calloc(nb, ni) #define s_mp_free(ptr) {if(ptr) free(ptr);} #endif /* MP_MACRO */ mp_err s_mp_grow(mp_int *mp, mp_size min); /* increase allocated size */ mp_err s_mp_pad(mp_int *mp, mp_size min); /* left pad with zeroes */ void s_mp_clamp(mp_int *mp); /* clip leading zeroes */ void s_mp_exch(mp_int *a, mp_int *b); /* swap a and b in place */ mp_err s_mp_lshd(mp_int *mp, mp_size p); /* left-shift by p digits */ void s_mp_rshd(mp_int *mp, mp_size p); /* right-shift by p digits */ void s_mp_div_2d(mp_int *mp, mp_digit d); /* divide by 2^d in place */ void s_mp_mod_2d(mp_int *mp, mp_digit d); /* modulo 2^d in place */ mp_err s_mp_mul_2d(mp_int *mp, mp_digit d); /* multiply by 2^d in place*/ void s_mp_div_2(mp_int *mp); /* divide by 2 in place */ mp_err s_mp_mul_2(mp_int *mp); /* multiply by 2 in place */ mp_digit s_mp_norm(mp_int *a, mp_int *b); /* normalize for division */ mp_err s_mp_add_d(mp_int *mp, mp_digit d); /* unsigned digit addition */ mp_err s_mp_sub_d(mp_int *mp, mp_digit d); /* unsigned digit subtract */ mp_err s_mp_mul_d(mp_int *mp, mp_digit d); /* unsigned digit multiply */ mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r); /* unsigned digit divide */ mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu); /* Barrett reduction */ mp_err s_mp_add(mp_int *a, mp_int *b); /* magnitude addition */ mp_err s_mp_sub(mp_int *a, mp_int *b); /* magnitude subtract */ mp_err s_mp_mul(mp_int *a, mp_int *b); /* magnitude multiply */ #if 0 void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len); /* multiply buffers in place */ #endif #if MP_SQUARE mp_err s_mp_sqr(mp_int *a); /* magnitude square */ #else #define s_mp_sqr(a) s_mp_mul(a, a) #endif mp_err s_mp_div(mp_int *a, mp_int *b); /* magnitude divide */ mp_err s_mp_2expt(mp_int *a, mp_digit k); /* a = 2^k */ int s_mp_cmp(mp_int *a, mp_int *b); /* magnitude comparison */ int s_mp_cmp_d(mp_int *a, mp_digit d); /* magnitude digit compare */ int s_mp_ispow2(mp_int *v); /* is v a power of 2? */ int s_mp_ispow2d(mp_digit d); /* is d a power of 2? */ int s_mp_tovalue(char ch, int r); /* convert ch to value */ char s_mp_todigit(int val, int r, int low); /* convert val to digit */ int s_mp_outlen(int bits, int r); /* output length in bytes */ /* }}} */ /* {{{ Default precision manipulation */ unsigned int mp_get_prec(void) { return s_mp_defprec; } /* end mp_get_prec() */ void mp_set_prec(unsigned int prec) { if(prec == 0) s_mp_defprec = MP_DEFPREC; else s_mp_defprec = prec; } /* end mp_set_prec() */ /* }}} */ /*------------------------------------------------------------------------*/ /* {{{ mp_init(mp) */ /* mp_init(mp) Initialize a new zero-valued mp_int. Returns MP_OKAY if successful, MP_MEM if memory could not be allocated for the structure. */ mp_err mp_init(mp_int *mp) { return mp_init_size(mp, s_mp_defprec); } /* end mp_init() */ /* }}} */ /* {{{ mp_init_array(mp[], count) */ mp_err mp_init_array(mp_int mp[], int count) { mp_err res; int pos; ARGCHK(mp !=NULL && count > 0, MP_BADARG); for(pos = 0; pos < count; ++pos) { if((res = mp_init(&mp[pos])) != MP_OKAY) goto CLEANUP; } return MP_OKAY; CLEANUP: while(--pos >= 0) mp_clear(&mp[pos]); return res; } /* end mp_init_array() */ /* }}} */ /* {{{ mp_init_size(mp, prec) */ /* mp_init_size(mp, prec) Initialize a new zero-valued mp_int with at least the given precision; returns MP_OKAY if successful, or MP_MEM if memory could not be allocated for the structure. */ mp_err mp_init_size(mp_int *mp, mp_size prec) { ARGCHK(mp != NULL && prec > 0, MP_BADARG); if((DIGITS(mp) = s_mp_alloc(prec, sizeof(mp_digit))) == NULL) return MP_MEM; SIGN(mp) = MP_ZPOS; USED(mp) = 1; ALLOC(mp) = prec; return MP_OKAY; } /* end mp_init_size() */ /* }}} */ /* {{{ mp_init_copy(mp, from) */ /* mp_init_copy(mp, from) Initialize mp as an exact copy of from. Returns MP_OKAY if successful, MP_MEM if memory could not be allocated for the new structure. */ mp_err mp_init_copy(mp_int *mp, mp_int *from) { ARGCHK(mp != NULL && from != NULL, MP_BADARG); if(mp == from) return MP_OKAY; if((DIGITS(mp) = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL) return MP_MEM; s_mp_copy(DIGITS(from), DIGITS(mp), USED(from)); USED(mp) = USED(from); ALLOC(mp) = USED(from); SIGN(mp) = SIGN(from); return MP_OKAY; } /* end mp_init_copy() */ /* }}} */ /* {{{ mp_copy(from, to) */ /* mp_copy(from, to) Copies the mp_int 'from' to the mp_int 'to'. It is presumed that 'to' has already been initialized (if not, use mp_init_copy() instead). If 'from' and 'to' are identical, nothing happens. */ mp_err mp_copy(mp_int *from, mp_int *to) { ARGCHK(from != NULL && to != NULL, MP_BADARG); if(from == to) return MP_OKAY; { /* copy */ mp_digit *tmp; /* If the allocated buffer in 'to' already has enough space to hold all the used digits of 'from', we'll re-use it to avoid hitting the memory allocater more than necessary; otherwise, we'd have to grow anyway, so we just allocate a hunk and make the copy as usual */ if(ALLOC(to) >= USED(from)) { s_mp_setz(DIGITS(to) + USED(from), ALLOC(to) - USED(from)); s_mp_copy(DIGITS(from), DIGITS(to), USED(from)); } else { if((tmp = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL) return MP_MEM; s_mp_copy(DIGITS(from), tmp, USED(from)); if(DIGITS(to) != NULL) { #if MP_CRYPTO s_mp_setz(DIGITS(to), ALLOC(to)); #endif s_mp_free(DIGITS(to)); } DIGITS(to) = tmp; ALLOC(to) = USED(from); } /* Copy the precision and sign from the original */ USED(to) = USED(from); SIGN(to) = SIGN(from); } /* end copy */ return MP_OKAY; } /* end mp_copy() */ /* }}} */ /* {{{ mp_exch(mp1, mp2) */ /* mp_exch(mp1, mp2) Exchange mp1 and mp2 without allocating any intermediate memory (well, unless you count the stack space needed for this call and the locals it creates...). This cannot fail. */ void mp_exch(mp_int *mp1, mp_int *mp2) { #if MP_ARGCHK == 2 assert(mp1 != NULL && mp2 != NULL); #else if(mp1 == NULL || mp2 == NULL) return; #endif s_mp_exch(mp1, mp2); } /* end mp_exch() */ /* }}} */ /* {{{ mp_clear(mp) */ /* mp_clear(mp) Release the storage used by an mp_int, and void its fields so that if someone calls mp_clear() again for the same int later, we won't get tollchocked. */ void mp_clear(mp_int *mp) { if(mp == NULL) return; if(DIGITS(mp) != NULL) { #if MP_CRYPTO s_mp_setz(DIGITS(mp), ALLOC(mp)); #endif s_mp_free(DIGITS(mp)); DIGITS(mp) = NULL; } USED(mp) = 0; ALLOC(mp) = 0; } /* end mp_clear() */ /* }}} */ /* {{{ mp_clear_array(mp[], count) */ void mp_clear_array(mp_int mp[], int count) { ARGCHK(mp != NULL && count > 0, MP_BADARG); while(--count >= 0) mp_clear(&mp[count]); } /* end mp_clear_array() */ /* }}} */ /* {{{ mp_zero(mp) */ /* mp_zero(mp) Set mp to zero. Does not change the allocated size of the structure, and therefore cannot fail (except on a bad argument, which we ignore) */ void mp_zero(mp_int *mp) { if(mp == NULL) return; s_mp_setz(DIGITS(mp), ALLOC(mp)); USED(mp) = 1; SIGN(mp) = MP_ZPOS; } /* end mp_zero() */ /* }}} */ /* {{{ mp_set(mp, d) */ void mp_set(mp_int *mp, mp_digit d) { if(mp == NULL) return; mp_zero(mp); DIGIT(mp, 0) = d; } /* end mp_set() */ /* }}} */ /* {{{ mp_set_int(mp, z) */ mp_err mp_set_int(mp_int *mp, long z) { int ix; unsigned long v = abs(z); mp_err res; ARGCHK(mp != NULL, MP_BADARG); mp_zero(mp); if(z == 0) return MP_OKAY; /* shortcut for zero */ for(ix = sizeof(long) - 1; ix >= 0; ix--) { if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY) return res; res = s_mp_add_d(mp, (mp_digit)((v >> (ix * CHAR_BIT)) & UCHAR_MAX)); if(res != MP_OKAY) return res; } if(z < 0) SIGN(mp) = MP_NEG; return MP_OKAY; } /* end mp_set_int() */ /* }}} */ /*------------------------------------------------------------------------*/ /* {{{ Digit arithmetic */ /* {{{ mp_add_d(a, d, b) */ /* mp_add_d(a, d, b) Compute the sum b = a + d, for a single digit d. Respects the sign of its primary addend (single digits are unsigned anyway). */ mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b) { mp_err res = MP_OKAY; ARGCHK(a != NULL && b != NULL, MP_BADARG); if((res = mp_copy(a, b)) != MP_OKAY) return res; if(SIGN(b) == MP_ZPOS) { res = s_mp_add_d(b, d); } else if(s_mp_cmp_d(b, d) >= 0) { res = s_mp_sub_d(b, d); } else { SIGN(b) = MP_ZPOS; DIGIT(b, 0) = d - DIGIT(b, 0); } return res; } /* end mp_add_d() */ /* }}} */ /* {{{ mp_sub_d(a, d, b) */ /* mp_sub_d(a, d, b) Compute the difference b = a - d, for a single digit d. Respects the sign of its subtrahend (single digits are unsigned anyway). */ mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b) { mp_err res; ARGCHK(a != NULL && b != NULL, MP_BADARG); if((res = mp_copy(a, b)) != MP_OKAY) return res; if(SIGN(b) == MP_NEG) { if((res = s_mp_add_d(b, d)) != MP_OKAY) return res; } else if(s_mp_cmp_d(b, d) >= 0) { if((res = s_mp_sub_d(b, d)) != MP_OKAY) return res; } else { mp_neg(b, b); DIGIT(b, 0) = d - DIGIT(b, 0); SIGN(b) = MP_NEG; } if(s_mp_cmp_d(b, 0) == 0) SIGN(b) = MP_ZPOS; return MP_OKAY; } /* end mp_sub_d() */ /* }}} */ /* {{{ mp_mul_d(a, d, b) */ /* mp_mul_d(a, d, b) Compute the product b = a * d, for a single digit d. Respects the sign of its multiplicand (single digits are unsigned anyway) */ mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b) { mp_err res; ARGCHK(a != NULL && b != NULL, MP_BADARG); if(d == 0) { mp_zero(b); return MP_OKAY; } if((res = mp_copy(a, b)) != MP_OKAY) return res; res = s_mp_mul_d(b, d); return res; } /* end mp_mul_d() */ /* }}} */ /* {{{ mp_mul_2(a, c) */ mp_err mp_mul_2(mp_int *a, mp_int *c) { mp_err res; ARGCHK(a != NULL && c != NULL, MP_BADARG); if((res = mp_copy(a, c)) != MP_OKAY) return res; return s_mp_mul_2(c); } /* end mp_mul_2() */ /* }}} */ /* {{{ mp_div_d(a, d, q, r) */ /* mp_div_d(a, d, q, r) Compute the quotient q = a / d and remainder r = a mod d, for a single digit d. Respects the sign of its divisor (single digits are unsigned anyway). */ mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r) { mp_err res; mp_digit rem; int pow; ARGCHK(a != NULL, MP_BADARG); if(d == 0) return MP_RANGE; /* Shortcut for powers of two ... */ if((pow = s_mp_ispow2d(d)) >= 0) { mp_digit mask; mask = (1 << pow) - 1; rem = DIGIT(a, 0) & mask; if(q) { mp_copy(a, q); s_mp_div_2d(q, pow); } if(r) *r = rem; return MP_OKAY; } /* If the quotient is actually going to be returned, we'll try to avoid hitting the memory allocator by copying the dividend into it and doing the division there. This can't be any _worse_ than always copying, and will sometimes be better (since it won't make another copy) If it's not going to be returned, we need to allocate a temporary to hold the quotient, which will just be discarded. */ if(q) { if((res = mp_copy(a, q)) != MP_OKAY) return res; res = s_mp_div_d(q, d, &rem); if(s_mp_cmp_d(q, 0) == MP_EQ) SIGN(q) = MP_ZPOS; } else { mp_int qp; if((res = mp_init_copy(&qp, a)) != MP_OKAY) return res; res = s_mp_div_d(&qp, d, &rem); if(s_mp_cmp_d(&qp, 0) == 0) SIGN(&qp) = MP_ZPOS; mp_clear(&qp); } if(r) *r = rem; return res; } /* end mp_div_d() */ /* }}} */ /* {{{ mp_div_2(a, c) */ /* mp_div_2(a, c) Compute c = a / 2, disregarding the remainder. */ mp_err mp_div_2(mp_int *a, mp_int *c) { mp_err res; ARGCHK(a != NULL && c != NULL, MP_BADARG); if((res = mp_copy(a, c)) != MP_OKAY) return res; s_mp_div_2(c); return MP_OKAY; } /* end mp_div_2() */ /* }}} */ /* {{{ mp_expt_d(a, d, b) */ mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c) { mp_int s, x; mp_err res; ARGCHK(a != NULL && c != NULL, MP_BADARG); if((res = mp_init(&s)) != MP_OKAY) return res; if((res = mp_init_copy(&x, a)) != MP_OKAY) goto X; DIGIT(&s, 0) = 1; while(d != 0) { if(d & 1) { if((res = s_mp_mul(&s, &x)) != MP_OKAY) goto CLEANUP; } d >>= 1; if((res = s_mp_sqr(&x)) != MP_OKAY) goto CLEANUP; } s_mp_exch(&s, c); CLEANUP: mp_clear(&x); X: mp_clear(&s); return res; } /* end mp_expt_d() */ /* }}} */ /* }}} */ /*------------------------------------------------------------------------*/ /* {{{ Full arithmetic */ /* {{{ mp_abs(a, b) */ /* mp_abs(a, b) Compute b = |a|. 'a' and 'b' may be identical. */ mp_err mp_abs(mp_int *a, mp_int *b) { mp_err res; ARGCHK(a != NULL && b != NULL, MP_BADARG); if((res = mp_copy(a, b)) != MP_OKAY) return res; SIGN(b) = MP_ZPOS; return MP_OKAY; } /* end mp_abs() */ /* }}} */ /* {{{ mp_neg(a, b) */ /* mp_neg(a, b) Compute b = -a. 'a' and 'b' may be identical. */ mp_err mp_neg(mp_int *a, mp_int *b) { mp_err res; ARGCHK(a != NULL && b != NULL, MP_BADARG); if((res = mp_copy(a, b)) != MP_OKAY) return res; if(s_mp_cmp_d(b, 0) == MP_EQ) SIGN(b) = MP_ZPOS; else SIGN(b) = (SIGN(b) == MP_NEG) ? MP_ZPOS : MP_NEG; return MP_OKAY; } /* end mp_neg() */ /* }}} */ /* {{{ mp_add(a, b, c) */ /* mp_add(a, b, c) Compute c = a + b. All parameters may be identical. */ mp_err mp_add(mp_int *a, mp_int *b, mp_int *c) { mp_err res; int cmp; ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); if(SIGN(a) == SIGN(b)) { /* same sign: add values, keep sign */ /* Commutativity of addition lets us do this in either order, so we avoid having to use a temporary even if the result is supposed to replace the output */ if(c == b) { if((res = s_mp_add(c, a)) != MP_OKAY) return res; } else { if(c != a && (res = mp_copy(a, c)) != MP_OKAY) return res; if((res = s_mp_add(c, b)) != MP_OKAY) return res; } } else if((cmp = s_mp_cmp(a, b)) > 0) { /* different sign: a > b */ /* If the output is going to be clobbered, we will use a temporary variable; otherwise, we'll do it without touching the memory allocator at all, if possible */ if(c == b) { mp_int tmp; if((res = mp_init_copy(&tmp, a)) != MP_OKAY) return res; if((res = s_mp_sub(&tmp, b)) != MP_OKAY) { mp_clear(&tmp); return res; } s_mp_exch(&tmp, c); mp_clear(&tmp); } else { if(c != a && (res = mp_copy(a, c)) != MP_OKAY) return res; if((res = s_mp_sub(c, b)) != MP_OKAY) return res; } } else if(cmp == 0) { /* different sign, a == b */ mp_zero(c); return MP_OKAY; } else { /* different sign: a < b */ /* See above... */ if(c == a) { mp_int tmp; if((res = mp_init_copy(&tmp, b)) != MP_OKAY) return res; if((res = s_mp_sub(&tmp, a)) != MP_OKAY) { mp_clear(&tmp); return res; } s_mp_exch(&tmp, c); mp_clear(&tmp); } else { if(c != b && (res = mp_copy(b, c)) != MP_OKAY) return res; if((res = s_mp_sub(c, a)) != MP_OKAY) return res; } } if(USED(c) == 1 && DIGIT(c, 0) == 0) SIGN(c) = MP_ZPOS; return MP_OKAY; } /* end mp_add() */ /* }}} */ /* {{{ mp_sub(a, b, c) */ /* mp_sub(a, b, c) Compute c = a - b. All parameters may be identical. */ mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c) { mp_err res; int cmp; ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); if(SIGN(a) != SIGN(b)) { if(c == a) { if((res = s_mp_add(c, b)) != MP_OKAY) return res; } else { if(c != b && ((res = mp_copy(b, c)) != MP_OKAY)) return res; if((res = s_mp_add(c, a)) != MP_OKAY) return res; SIGN(c) = SIGN(a); } } else if((cmp = s_mp_cmp(a, b)) > 0) { /* Same sign, a > b */ if(c == b) { mp_int tmp; if((res = mp_init_copy(&tmp, a)) != MP_OKAY) return res; if((res = s_mp_sub(&tmp, b)) != MP_OKAY) { mp_clear(&tmp); return res; } s_mp_exch(&tmp, c); mp_clear(&tmp); } else { if(c != a && ((res = mp_copy(a, c)) != MP_OKAY)) return res; if((res = s_mp_sub(c, b)) != MP_OKAY) return res; } } else if(cmp == 0) { /* Same sign, equal magnitude */ mp_zero(c); return MP_OKAY; } else { /* Same sign, b > a */ if(c == a) { mp_int tmp; if((res = mp_init_copy(&tmp, b)) != MP_OKAY) return res; if((res = s_mp_sub(&tmp, a)) != MP_OKAY) { mp_clear(&tmp); return res; } s_mp_exch(&tmp, c); mp_clear(&tmp); } else { if(c != b && ((res = mp_copy(b, c)) != MP_OKAY)) return res; if((res = s_mp_sub(c, a)) != MP_OKAY) return res; } SIGN(c) = !SIGN(b); } if(USED(c) == 1 && DIGIT(c, 0) == 0) SIGN(c) = MP_ZPOS; return MP_OKAY; } /* end mp_sub() */ /* }}} */ /* {{{ mp_mul(a, b, c) */ /* mp_mul(a, b, c) Compute c = a * b. All parameters may be identical. */ mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c) { mp_err res; mp_sign sgn; ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); sgn = (SIGN(a) == SIGN(b)) ? MP_ZPOS : MP_NEG; if(c == b) { if((res = s_mp_mul(c, a)) != MP_OKAY) return res; } else { if((res = mp_copy(a, c)) != MP_OKAY) return res; if((res = s_mp_mul(c, b)) != MP_OKAY) return res; } if(sgn == MP_ZPOS || s_mp_cmp_d(c, 0) == MP_EQ) SIGN(c) = MP_ZPOS; else SIGN(c) = sgn; return MP_OKAY; } /* end mp_mul() */ /* }}} */ /* {{{ mp_mul_2d(a, d, c) */ /* mp_mul_2d(a, d, c) Compute c = a * 2^d. a may be the same as c. */ mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c) { mp_err res; ARGCHK(a != NULL && c != NULL, MP_BADARG); if((res = mp_copy(a, c)) != MP_OKAY) return res; if(d == 0) return MP_OKAY; return s_mp_mul_2d(c, d); } /* end mp_mul() */ /* }}} */ /* {{{ mp_sqr(a, b) */ #if MP_SQUARE mp_err mp_sqr(mp_int *a, mp_int *b) { mp_err res; ARGCHK(a != NULL && b != NULL, MP_BADARG); if((res = mp_copy(a, b)) != MP_OKAY) return res; if((res = s_mp_sqr(b)) != MP_OKAY) return res; SIGN(b) = MP_ZPOS; return MP_OKAY; } /* end mp_sqr() */ #endif /* }}} */ /* {{{ mp_div(a, b, q, r) */ /* mp_div(a, b, q, r) Compute q = a / b and r = a mod b. Input parameters may be re-used as output parameters. If q or r is NULL, that portion of the computation will be discarded (although it will still be computed) Pay no attention to the hacker behind the curtain. */ mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r) { mp_err res; mp_int qtmp, rtmp; int cmp; ARGCHK(a != NULL && b != NULL, MP_BADARG); if(mp_cmp_z(b) == MP_EQ) return MP_RANGE; /* If a <= b, we can compute the solution without division, and avoid any memory allocation */ if((cmp = s_mp_cmp(a, b)) < 0) { if(r) { if((res = mp_copy(a, r)) != MP_OKAY) return res; } if(q) mp_zero(q); return MP_OKAY; } else if(cmp == 0) { /* Set quotient to 1, with appropriate sign */ if(q) { int qneg = (SIGN(a) != SIGN(b)); mp_set(q, 1); if(qneg) SIGN(q) = MP_NEG; } if(r) mp_zero(r); return MP_OKAY; } /* If we get here, it means we actually have to do some division */ /* Set up some temporaries... */ if((res = mp_init_copy(&qtmp, a)) != MP_OKAY) return res; if((res = mp_init_copy(&rtmp, b)) != MP_OKAY) goto CLEANUP; if((res = s_mp_div(&qtmp, &rtmp)) != MP_OKAY) goto CLEANUP; /* Compute the signs for the output */ SIGN(&rtmp) = SIGN(a); /* Sr = Sa */ if(SIGN(a) == SIGN(b)) SIGN(&qtmp) = MP_ZPOS; /* Sq = MP_ZPOS if Sa = Sb */ else SIGN(&qtmp) = MP_NEG; /* Sq = MP_NEG if Sa != Sb */ if(s_mp_cmp_d(&qtmp, 0) == MP_EQ) SIGN(&qtmp) = MP_ZPOS; if(s_mp_cmp_d(&rtmp, 0) == MP_EQ) SIGN(&rtmp) = MP_ZPOS; /* Copy output, if it is needed */ if(q) s_mp_exch(&qtmp, q); if(r) s_mp_exch(&rtmp, r); CLEANUP: mp_clear(&rtmp); mp_clear(&qtmp); return res; } /* end mp_div() */ /* }}} */ /* {{{ mp_div_2d(a, d, q, r) */ mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r) { mp_err res; ARGCHK(a != NULL, MP_BADARG); if(q) { if((res = mp_copy(a, q)) != MP_OKAY) return res; s_mp_div_2d(q, d); } if(r) { if((res = mp_copy(a, r)) != MP_OKAY) return res; s_mp_mod_2d(r, d); } return MP_OKAY; } /* end mp_div_2d() */ /* }}} */ /* {{{ mp_expt(a, b, c) */ /* mp_expt(a, b, c) Compute c = a ** b, that is, raise a to the b power. Uses a standard iterative square-and-multiply technique. */ mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c) { mp_int s, x; mp_err res; mp_digit d; int dig, bit; ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); if(mp_cmp_z(b) < 0) return MP_RANGE; if((res = mp_init(&s)) != MP_OKAY) return res; mp_set(&s, 1); if((res = mp_init_copy(&x, a)) != MP_OKAY) goto X; /* Loop over low-order digits in ascending order */ for(dig = 0; dig < (USED(b) - 1); dig++) { d = DIGIT(b, dig); /* Loop over bits of each non-maximal digit */ for(bit = 0; bit < DIGIT_BIT; bit++) { if(d & 1) { if((res = s_mp_mul(&s, &x)) != MP_OKAY) goto CLEANUP; } d >>= 1; if((res = s_mp_sqr(&x)) != MP_OKAY) goto CLEANUP; } } /* Consider now the last digit... */ d = DIGIT(b, dig); while(d) { if(d & 1) { if((res = s_mp_mul(&s, &x)) != MP_OKAY) goto CLEANUP; } d >>= 1; if((res = s_mp_sqr(&x)) != MP_OKAY) goto CLEANUP; } if(mp_iseven(b)) SIGN(&s) = SIGN(a); res = mp_copy(&s, c); CLEANUP: mp_clear(&x); X: mp_clear(&s); return res; } /* end mp_expt() */ /* }}} */ /* {{{ mp_2expt(a, k) */ /* Compute a = 2^k */ mp_err mp_2expt(mp_int *a, mp_digit k) { ARGCHK(a != NULL, MP_BADARG); return s_mp_2expt(a, k); } /* end mp_2expt() */ /* }}} */ /* {{{ mp_mod(a, m, c) */ /* mp_mod(a, m, c) Compute c = a (mod m). Result will always be 0 <= c < m. */ mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c) { mp_err res; int mag; ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG); if(SIGN(m) == MP_NEG) return MP_RANGE; /* If |a| > m, we need to divide to get the remainder and take the absolute value. If |a| < m, we don't need to do any division, just copy and adjust the sign (if a is negative). If |a| == m, we can simply set the result to zero. This order is intended to minimize the average path length of the comparison chain on common workloads -- the most frequent cases are that |a| != m, so we do those first. */ if((mag = s_mp_cmp(a, m)) > 0) { if((res = mp_div(a, m, NULL, c)) != MP_OKAY) return res; if(SIGN(c) == MP_NEG) { if((res = mp_add(c, m, c)) != MP_OKAY) return res; } } else if(mag < 0) { if((res = mp_copy(a, c)) != MP_OKAY) return res; if(mp_cmp_z(a) < 0) { if((res = mp_add(c, m, c)) != MP_OKAY) return res; } } else { mp_zero(c); } return MP_OKAY; } /* end mp_mod() */ /* }}} */ /* {{{ mp_mod_d(a, d, c) */ /* mp_mod_d(a, d, c) Compute c = a (mod d). Result will always be 0 <= c < d */ mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c) { mp_err res; mp_digit rem; ARGCHK(a != NULL && c != NULL, MP_BADARG); if(s_mp_cmp_d(a, d) > 0) { if((res = mp_div_d(a, d, NULL, &rem)) != MP_OKAY) return res; } else { if(SIGN(a) == MP_NEG) rem = d - DIGIT(a, 0); else rem = DIGIT(a, 0); } if(c) *c = rem; return MP_OKAY; } /* end mp_mod_d() */ /* }}} */ /* {{{ mp_sqrt(a, b) */ /* mp_sqrt(a, b) Compute the integer square root of a, and store the result in b. Uses an integer-arithmetic version of Newton's iterative linear approximation technique to determine this value; the result has the following two properties: b^2 <= a (b+1)^2 >= a It is a range error to pass a negative value. */ mp_err mp_sqrt(mp_int *a, mp_int *b) { mp_int x, t; mp_err res; ARGCHK(a != NULL && b != NULL, MP_BADARG); /* Cannot take square root of a negative value */ if(SIGN(a) == MP_NEG) return MP_RANGE; /* Special cases for zero and one, trivial */ if(mp_cmp_d(a, 0) == MP_EQ || mp_cmp_d(a, 1) == MP_EQ) return mp_copy(a, b); /* Initialize the temporaries we'll use below */ if((res = mp_init_size(&t, USED(a))) != MP_OKAY) return res; /* Compute an initial guess for the iteration as a itself */ if((res = mp_init_copy(&x, a)) != MP_OKAY) goto X; s_mp_rshd(&x, (USED(&x)/2)+1); mp_add_d(&x, 1, &x); for(;;) { /* t = (x * x) - a */ mp_copy(&x, &t); /* can't fail, t is big enough for original x */ if((res = mp_sqr(&t, &t)) != MP_OKAY || (res = mp_sub(&t, a, &t)) != MP_OKAY) goto CLEANUP; /* t = t / 2x */ s_mp_mul_2(&x); if((res = mp_div(&t, &x, &t, NULL)) != MP_OKAY) goto CLEANUP; s_mp_div_2(&x); /* Terminate the loop, if the quotient is zero */ if(mp_cmp_z(&t) == MP_EQ) break; /* x = x - t */ if((res = mp_sub(&x, &t, &x)) != MP_OKAY) goto CLEANUP; } /* Copy result to output parameter */ mp_sub_d(&x, 1, &x); s_mp_exch(&x, b); CLEANUP: mp_clear(&x); X: mp_clear(&t); return res; } /* end mp_sqrt() */ /* }}} */ /* }}} */ /*------------------------------------------------------------------------*/ /* {{{ Modular arithmetic */ #if MP_MODARITH /* {{{ mp_addmod(a, b, m, c) */ /* mp_addmod(a, b, m, c) Compute c = (a + b) mod m */ mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) { mp_err res; ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG); if((res = mp_add(a, b, c)) != MP_OKAY) return res; if((res = mp_mod(c, m, c)) != MP_OKAY) return res; return MP_OKAY; } /* }}} */ /* {{{ mp_submod(a, b, m, c) */ /* mp_submod(a, b, m, c) Compute c = (a - b) mod m */ mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) { mp_err res; ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG); if((res = mp_sub(a, b, c)) != MP_OKAY) return res; if((res = mp_mod(c, m, c)) != MP_OKAY) return res; return MP_OKAY; } /* }}} */ /* {{{ mp_mulmod(a, b, m, c) */ /* mp_mulmod(a, b, m, c) Compute c = (a * b) mod m */ mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) { mp_err res; ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG); if((res = mp_mul(a, b, c)) != MP_OKAY) return res; if((res = mp_mod(c, m, c)) != MP_OKAY) return res; return MP_OKAY; } /* }}} */ /* {{{ mp_sqrmod(a, m, c) */ #if MP_SQUARE mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c) { mp_err res; ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG); if((res = mp_sqr(a, c)) != MP_OKAY) return res; if((res = mp_mod(c, m, c)) != MP_OKAY) return res; return MP_OKAY; } /* end mp_sqrmod() */ #endif /* }}} */ /* {{{ mp_exptmod(a, b, m, c) */ /* mp_exptmod(a, b, m, c) Compute c = (a ** b) mod m. Uses a standard square-and-multiply method with modular reductions at each step. (This is basically the same code as mp_expt(), except for the addition of the reductions) The modular reductions are done using Barrett's algorithm (see s_mp_reduce() below for details) */ mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) { mp_int s, x, mu; mp_err res; mp_digit d, *db = DIGITS(b); mp_size ub = USED(b); int dig, bit; ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); if(mp_cmp_z(b) < 0 || mp_cmp_z(m) <= 0) return MP_RANGE; if((res = mp_init(&s)) != MP_OKAY) return res; if((res = mp_init_copy(&x, a)) != MP_OKAY) goto X; if((res = mp_mod(&x, m, &x)) != MP_OKAY || (res = mp_init(&mu)) != MP_OKAY) goto MU; mp_set(&s, 1); /* mu = b^2k / m */ s_mp_add_d(&mu, 1); s_mp_lshd(&mu, 2 * USED(m)); if((res = mp_div(&mu, m, &mu, NULL)) != MP_OKAY) goto CLEANUP; /* Loop over digits of b in ascending order, except highest order */ for(dig = 0; dig < (ub - 1); dig++) { d = *db++; /* Loop over the bits of the lower-order digits */ for(bit = 0; bit < DIGIT_BIT; bit++) { if(d & 1) { if((res = s_mp_mul(&s, &x)) != MP_OKAY) goto CLEANUP; if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY) goto CLEANUP; } d >>= 1; if((res = s_mp_sqr(&x)) != MP_OKAY) goto CLEANUP; if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY) goto CLEANUP; } } /* Now do the last digit... */ d = *db; while(d) { if(d & 1) { if((res = s_mp_mul(&s, &x)) != MP_OKAY) goto CLEANUP; if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY) goto CLEANUP; } d >>= 1; if((res = s_mp_sqr(&x)) != MP_OKAY) goto CLEANUP; if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY) goto CLEANUP; } s_mp_exch(&s, c); CLEANUP: mp_clear(&mu); MU: mp_clear(&x); X: mp_clear(&s); return res; } /* end mp_exptmod() */ /* }}} */ /* {{{ mp_exptmod_d(a, d, m, c) */ mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c) { mp_int s, x; mp_err res; ARGCHK(a != NULL && c != NULL, MP_BADARG); if((res = mp_init(&s)) != MP_OKAY) return res; if((res = mp_init_copy(&x, a)) != MP_OKAY) goto X; mp_set(&s, 1); while(d != 0) { if(d & 1) { if((res = s_mp_mul(&s, &x)) != MP_OKAY || (res = mp_mod(&s, m, &s)) != MP_OKAY) goto CLEANUP; } d /= 2; if((res = s_mp_sqr(&x)) != MP_OKAY || (res = mp_mod(&x, m, &x)) != MP_OKAY) goto CLEANUP; } s_mp_exch(&s, c); CLEANUP: mp_clear(&x); X: mp_clear(&s); return res; } /* end mp_exptmod_d() */ /* }}} */ #endif /* if MP_MODARITH */ /* }}} */ /*------------------------------------------------------------------------*/ /* {{{ Comparison functions */ /* {{{ mp_cmp_z(a) */ /* mp_cmp_z(a) Compare a <=> 0. Returns <0 if a<0, 0 if a=0, >0 if a>0. */ int mp_cmp_z(mp_int *a) { if(SIGN(a) == MP_NEG) return MP_LT; else if(USED(a) == 1 && DIGIT(a, 0) == 0) return MP_EQ; else return MP_GT; } /* end mp_cmp_z() */ /* }}} */ /* {{{ mp_cmp_d(a, d) */ /* mp_cmp_d(a, d) Compare a <=> d. Returns <0 if a0 if a>d */ int mp_cmp_d(mp_int *a, mp_digit d) { ARGCHK(a != NULL, MP_EQ); if(SIGN(a) == MP_NEG) return MP_LT; return s_mp_cmp_d(a, d); } /* end mp_cmp_d() */ /* }}} */ /* {{{ mp_cmp(a, b) */ int mp_cmp(mp_int *a, mp_int *b) { ARGCHK(a != NULL && b != NULL, MP_EQ); if(SIGN(a) == SIGN(b)) { int mag; if((mag = s_mp_cmp(a, b)) == MP_EQ) return MP_EQ; if(SIGN(a) == MP_ZPOS) return mag; else return -mag; } else if(SIGN(a) == MP_ZPOS) { return MP_GT; } else { return MP_LT; } } /* end mp_cmp() */ /* }}} */ /* {{{ mp_cmp_mag(a, b) */ /* mp_cmp_mag(a, b) Compares |a| <=> |b|, and returns an appropriate comparison result */ int mp_cmp_mag(mp_int *a, mp_int *b) { ARGCHK(a != NULL && b != NULL, MP_EQ); return s_mp_cmp(a, b); } /* end mp_cmp_mag() */ /* }}} */ /* {{{ mp_cmp_int(a, z) */ /* This just converts z to an mp_int, and uses the existing comparison routines. This is sort of inefficient, but it's not clear to me how frequently this wil get used anyway. For small positive constants, you can always use mp_cmp_d(), and for zero, there is mp_cmp_z(). */ int mp_cmp_int(mp_int *a, long z) { mp_int tmp; int out; ARGCHK(a != NULL, MP_EQ); mp_init(&tmp); mp_set_int(&tmp, z); out = mp_cmp(a, &tmp); mp_clear(&tmp); return out; } /* end mp_cmp_int() */ /* }}} */ /* {{{ mp_isodd(a) */ /* mp_isodd(a) Returns a true (non-zero) value if a is odd, false (zero) otherwise. */ int mp_isodd(mp_int *a) { ARGCHK(a != NULL, 0); return (DIGIT(a, 0) & 1); } /* end mp_isodd() */ /* }}} */ /* {{{ mp_iseven(a) */ int mp_iseven(mp_int *a) { return !mp_isodd(a); } /* end mp_iseven() */ /* }}} */ /* }}} */ /*------------------------------------------------------------------------*/ /* {{{ Number theoretic functions */ #if MP_NUMTH /* {{{ mp_gcd(a, b, c) */ /* Like the old mp_gcd() function, except computes the GCD using the binary algorithm due to Josef Stein in 1961 (via Knuth). */ mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c) { mp_err res; mp_int u, v, t; mp_size k = 0; ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); if(mp_cmp_z(a) == MP_EQ && mp_cmp_z(b) == MP_EQ) return MP_RANGE; if(mp_cmp_z(a) == MP_EQ) { return mp_copy(b, c); } else if(mp_cmp_z(b) == MP_EQ) { return mp_copy(a, c); } if((res = mp_init(&t)) != MP_OKAY) return res; if((res = mp_init_copy(&u, a)) != MP_OKAY) goto U; if((res = mp_init_copy(&v, b)) != MP_OKAY) goto V; SIGN(&u) = MP_ZPOS; SIGN(&v) = MP_ZPOS; /* Divide out common factors of 2 until at least 1 of a, b is even */ while(mp_iseven(&u) && mp_iseven(&v)) { s_mp_div_2(&u); s_mp_div_2(&v); ++k; } /* Initialize t */ if(mp_isodd(&u)) { if((res = mp_copy(&v, &t)) != MP_OKAY) goto CLEANUP; /* t = -v */ if(SIGN(&v) == MP_ZPOS) SIGN(&t) = MP_NEG; else SIGN(&t) = MP_ZPOS; } else { if((res = mp_copy(&u, &t)) != MP_OKAY) goto CLEANUP; } for(;;) { while(mp_iseven(&t)) { s_mp_div_2(&t); } if(mp_cmp_z(&t) == MP_GT) { if((res = mp_copy(&t, &u)) != MP_OKAY) goto CLEANUP; } else { if((res = mp_copy(&t, &v)) != MP_OKAY) goto CLEANUP; /* v = -t */ if(SIGN(&t) == MP_ZPOS) SIGN(&v) = MP_NEG; else SIGN(&v) = MP_ZPOS; } if((res = mp_sub(&u, &v, &t)) != MP_OKAY) goto CLEANUP; if(s_mp_cmp_d(&t, 0) == MP_EQ) break; } s_mp_2expt(&v, k); /* v = 2^k */ res = mp_mul(&u, &v, c); /* c = u * v */ CLEANUP: mp_clear(&v); V: mp_clear(&u); U: mp_clear(&t); return res; } /* end mp_bgcd() */ /* }}} */ /* {{{ mp_lcm(a, b, c) */ /* We compute the least common multiple using the rule: ab = [a, b](a, b) ... by computing the product, and dividing out the gcd. */ mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c) { mp_int gcd, prod; mp_err res; ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); /* Set up temporaries */ if((res = mp_init(&gcd)) != MP_OKAY) return res; if((res = mp_init(&prod)) != MP_OKAY) goto GCD; if((res = mp_mul(a, b, &prod)) != MP_OKAY) goto CLEANUP; if((res = mp_gcd(a, b, &gcd)) != MP_OKAY) goto CLEANUP; res = mp_div(&prod, &gcd, c, NULL); CLEANUP: mp_clear(&prod); GCD: mp_clear(&gcd); return res; } /* end mp_lcm() */ /* }}} */ /* {{{ mp_xgcd(a, b, g, x, y) */ /* mp_xgcd(a, b, g, x, y) Compute g = (a, b) and values x and y satisfying Bezout's identity (that is, ax + by = g). This uses the extended binary GCD algorithm based on the Stein algorithm used for mp_gcd() */ mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y) { mp_int gx, xc, yc, u, v, A, B, C, D; mp_int *clean[9]; mp_err res; int last = -1; if(mp_cmp_z(b) == 0) return MP_RANGE; /* Initialize all these variables we need */ if((res = mp_init(&u)) != MP_OKAY) goto CLEANUP; clean[++last] = &u; if((res = mp_init(&v)) != MP_OKAY) goto CLEANUP; clean[++last] = &v; if((res = mp_init(&gx)) != MP_OKAY) goto CLEANUP; clean[++last] = &gx; if((res = mp_init(&A)) != MP_OKAY) goto CLEANUP; clean[++last] = &A; if((res = mp_init(&B)) != MP_OKAY) goto CLEANUP; clean[++last] = &B; if((res = mp_init(&C)) != MP_OKAY) goto CLEANUP; clean[++last] = &C; if((res = mp_init(&D)) != MP_OKAY) goto CLEANUP; clean[++last] = &D; if((res = mp_init_copy(&xc, a)) != MP_OKAY) goto CLEANUP; clean[++last] = &xc; mp_abs(&xc, &xc); if((res = mp_init_copy(&yc, b)) != MP_OKAY) goto CLEANUP; clean[++last] = &yc; mp_abs(&yc, &yc); mp_set(&gx, 1); /* Divide by two until at least one of them is even */ while(mp_iseven(&xc) && mp_iseven(&yc)) { s_mp_div_2(&xc); s_mp_div_2(&yc); if((res = s_mp_mul_2(&gx)) != MP_OKAY) goto CLEANUP; } mp_copy(&xc, &u); mp_copy(&yc, &v); mp_set(&A, 1); mp_set(&D, 1); /* Loop through binary GCD algorithm */ for(;;) { while(mp_iseven(&u)) { s_mp_div_2(&u); if(mp_iseven(&A) && mp_iseven(&B)) { s_mp_div_2(&A); s_mp_div_2(&B); } else { if((res = mp_add(&A, &yc, &A)) != MP_OKAY) goto CLEANUP; s_mp_div_2(&A); if((res = mp_sub(&B, &xc, &B)) != MP_OKAY) goto CLEANUP; s_mp_div_2(&B); } } while(mp_iseven(&v)) { s_mp_div_2(&v); if(mp_iseven(&C) && mp_iseven(&D)) { s_mp_div_2(&C); s_mp_div_2(&D); } else { if((res = mp_add(&C, &yc, &C)) != MP_OKAY) goto CLEANUP; s_mp_div_2(&C); if((res = mp_sub(&D, &xc, &D)) != MP_OKAY) goto CLEANUP; s_mp_div_2(&D); } } if(mp_cmp(&u, &v) >= 0) { if((res = mp_sub(&u, &v, &u)) != MP_OKAY) goto CLEANUP; if((res = mp_sub(&A, &C, &A)) != MP_OKAY) goto CLEANUP; if((res = mp_sub(&B, &D, &B)) != MP_OKAY) goto CLEANUP; } else { if((res = mp_sub(&v, &u, &v)) != MP_OKAY) goto CLEANUP; if((res = mp_sub(&C, &A, &C)) != MP_OKAY) goto CLEANUP; if((res = mp_sub(&D, &B, &D)) != MP_OKAY) goto CLEANUP; } /* If we're done, copy results to output */ if(mp_cmp_z(&u) == 0) { if(x) if((res = mp_copy(&C, x)) != MP_OKAY) goto CLEANUP; if(y) if((res = mp_copy(&D, y)) != MP_OKAY) goto CLEANUP; if(g) if((res = mp_mul(&gx, &v, g)) != MP_OKAY) goto CLEANUP; break; } } CLEANUP: while(last >= 0) mp_clear(clean[last--]); return res; } /* end mp_xgcd() */ /* }}} */ /* {{{ mp_invmod(a, m, c) */ /* mp_invmod(a, m, c) Compute c = a^-1 (mod m), if there is an inverse for a (mod m). This is equivalent to the question of whether (a, m) = 1. If not, MP_UNDEF is returned, and there is no inverse. */ mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c) { mp_int g, x; mp_err res; ARGCHK(a && m && c, MP_BADARG); if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0) return MP_RANGE; if((res = mp_init(&g)) != MP_OKAY) return res; if((res = mp_init(&x)) != MP_OKAY) goto X; if((res = mp_xgcd(a, m, &g, &x, NULL)) != MP_OKAY) goto CLEANUP; if(mp_cmp_d(&g, 1) != MP_EQ) { res = MP_UNDEF; goto CLEANUP; } res = mp_mod(&x, m, c); SIGN(c) = SIGN(a); CLEANUP: mp_clear(&x); X: mp_clear(&g); return res; } /* end mp_invmod() */ /* }}} */ #endif /* if MP_NUMTH */ /* }}} */ /*------------------------------------------------------------------------*/ /* {{{ mp_print(mp, ofp) */ #if MP_IOFUNC /* mp_print(mp, ofp) Print a textual representation of the given mp_int on the output stream 'ofp'. Output is generated using the internal radix. */ void mp_print(mp_int *mp, FILE *ofp) { int ix; if(mp == NULL || ofp == NULL) return; fputc((SIGN(mp) == MP_NEG) ? '-' : '+', ofp); for(ix = USED(mp) - 1; ix >= 0; ix--) { fprintf(ofp, DIGIT_FMT, DIGIT(mp, ix)); } } /* end mp_print() */ #endif /* if MP_IOFUNC */ /* }}} */ /*------------------------------------------------------------------------*/ /* {{{ More I/O Functions */ /* {{{ mp_read_signed_bin(mp, str, len) */ /* mp_read_signed_bin(mp, str, len) Read in a raw value (base 256) into the given mp_int */ mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len) { mp_err res; ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG); if((res = mp_read_unsigned_bin(mp, str + 1, len - 1)) == MP_OKAY) { /* Get sign from first byte */ if(str[0]) SIGN(mp) = MP_NEG; else SIGN(mp) = MP_ZPOS; } return res; } /* end mp_read_signed_bin() */ /* }}} */ /* {{{ mp_signed_bin_size(mp) */ int mp_signed_bin_size(mp_int *mp) { ARGCHK(mp != NULL, 0); return mp_unsigned_bin_size(mp) + 1; } /* end mp_signed_bin_size() */ /* }}} */ /* {{{ mp_to_signed_bin(mp, str) */ mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str) { ARGCHK(mp != NULL && str != NULL, MP_BADARG); /* Caller responsible for allocating enough memory (use mp_raw_size(mp)) */ str[0] = (char)SIGN(mp); return mp_to_unsigned_bin(mp, str + 1); } /* end mp_to_signed_bin() */ /* }}} */ /* {{{ mp_read_unsigned_bin(mp, str, len) */ /* mp_read_unsigned_bin(mp, str, len) Read in an unsigned value (base 256) into the given mp_int */ mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len) { int ix; mp_err res; ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG); mp_zero(mp); for(ix = 0; ix < len; ix++) { if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY) return res; if((res = mp_add_d(mp, str[ix], mp)) != MP_OKAY) return res; } return MP_OKAY; } /* end mp_read_unsigned_bin() */ /* }}} */ /* {{{ mp_unsigned_bin_size(mp) */ int mp_unsigned_bin_size(mp_int *mp) { mp_digit topdig; int count; ARGCHK(mp != NULL, 0); /* Special case for the value zero */ if(USED(mp) == 1 && DIGIT(mp, 0) == 0) return 1; count = (USED(mp) - 1) * sizeof(mp_digit); topdig = DIGIT(mp, USED(mp) - 1); while(topdig != 0) { ++count; topdig >>= CHAR_BIT; } return count; } /* end mp_unsigned_bin_size() */ /* }}} */ /* {{{ mp_to_unsigned_bin(mp, str) */ mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str) { mp_digit *dp, *end, d; unsigned char *spos; ARGCHK(mp != NULL && str != NULL, MP_BADARG); dp = DIGITS(mp); end = dp + USED(mp) - 1; spos = str; /* Special case for zero, quick test */ if(dp == end && *dp == 0) { *str = '\0'; return MP_OKAY; } /* Generate digits in reverse order */ while(dp < end) { int ix; d = *dp; for(ix = 0; ix < sizeof(mp_digit); ++ix) { *spos = d & UCHAR_MAX; d >>= CHAR_BIT; ++spos; } ++dp; } /* Now handle last digit specially, high order zeroes are not written */ d = *end; while(d != 0) { *spos = d & UCHAR_MAX; d >>= CHAR_BIT; ++spos; } /* Reverse everything to get digits in the correct order */ while(--spos > str) { unsigned char t = *str; *str = *spos; *spos = t; ++str; } return MP_OKAY; } /* end mp_to_unsigned_bin() */ /* }}} */ /* {{{ mp_count_bits(mp) */ int mp_count_bits(mp_int *mp) { int len; mp_digit d; ARGCHK(mp != NULL, MP_BADARG); len = DIGIT_BIT * (USED(mp) - 1); d = DIGIT(mp, USED(mp) - 1); while(d != 0) { ++len; d >>= 1; } return len; } /* end mp_count_bits() */ /* }}} */ /* {{{ mp_read_radix(mp, str, radix) */ /* mp_read_radix(mp, str, radix) Read an integer from the given string, and set mp to the resulting value. The input is presumed to be in base 10. Leading non-digit characters are ignored, and the function reads until a non-digit character or the end of the string. */ mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix) { int ix = 0, val = 0; mp_err res; mp_sign sig = MP_ZPOS; ARGCHK(mp != NULL && str != NULL && radix >= 2 && radix <= MAX_RADIX, MP_BADARG); mp_zero(mp); /* Skip leading non-digit characters until a digit or '-' or '+' */ while(str[ix] && (s_mp_tovalue(str[ix], radix) < 0) && str[ix] != '-' && str[ix] != '+') { ++ix; } if(str[ix] == '-') { sig = MP_NEG; ++ix; } else if(str[ix] == '+') { sig = MP_ZPOS; /* this is the default anyway... */ ++ix; } while((val = s_mp_tovalue(str[ix], radix)) >= 0) { if((res = s_mp_mul_d(mp, radix)) != MP_OKAY) return res; if((res = s_mp_add_d(mp, val)) != MP_OKAY) return res; ++ix; } if(s_mp_cmp_d(mp, 0) == MP_EQ) SIGN(mp) = MP_ZPOS; else SIGN(mp) = sig; return MP_OKAY; } /* end mp_read_radix() */ /* }}} */ /* {{{ mp_radix_size(mp, radix) */ int mp_radix_size(mp_int *mp, int radix) { int len; ARGCHK(mp != NULL, 0); len = s_mp_outlen(mp_count_bits(mp), radix) + 1; /* for NUL terminator */ if(mp_cmp_z(mp) < 0) ++len; /* for sign */ return len; } /* end mp_radix_size() */ /* }}} */ /* {{{ mp_value_radix_size(num, qty, radix) */ /* num = number of digits qty = number of bits per digit radix = target base Return the number of digits in the specified radix that would be needed to express 'num' digits of 'qty' bits each. */ int mp_value_radix_size(int num, int qty, int radix) { ARGCHK(num >= 0 && qty > 0 && radix >= 2 && radix <= MAX_RADIX, 0); return s_mp_outlen(num * qty, radix); } /* end mp_value_radix_size() */ /* }}} */ /* {{{ mp_toradix(mp, str, radix) */ mp_err mp_toradix(mp_int *mp, unsigned char *str, int radix) { int ix, pos = 0; ARGCHK(mp != NULL && str != NULL, MP_BADARG); ARGCHK(radix > 1 && radix <= MAX_RADIX, MP_RANGE); if(mp_cmp_z(mp) == MP_EQ) { str[0] = '0'; str[1] = '\0'; } else { mp_err res; mp_int tmp; mp_sign sgn; mp_digit rem, rdx = (mp_digit)radix; char ch; if((res = mp_init_copy(&tmp, mp)) != MP_OKAY) return res; /* Save sign for later, and take absolute value */ sgn = SIGN(&tmp); SIGN(&tmp) = MP_ZPOS; /* Generate output digits in reverse order */ while(mp_cmp_z(&tmp) != 0) { if((res = s_mp_div_d(&tmp, rdx, &rem)) != MP_OKAY) { mp_clear(&tmp); return res; } /* Generate digits, use capital letters */ ch = s_mp_todigit(rem, radix, 0); str[pos++] = ch; } /* Add - sign if original value was negative */ if(sgn == MP_NEG) str[pos++] = '-'; /* Add trailing NUL to end the string */ str[pos--] = '\0'; /* Reverse the digits and sign indicator */ ix = 0; while(ix < pos) { char tmp = str[ix]; str[ix] = str[pos]; str[pos] = tmp; ++ix; --pos; } mp_clear(&tmp); } return MP_OKAY; } /* end mp_toradix() */ /* }}} */ /* {{{ mp_char2value(ch, r) */ int mp_char2value(char ch, int r) { return s_mp_tovalue(ch, r); } /* end mp_tovalue() */ /* }}} */ /* }}} */ /* {{{ mp_strerror(ec) */ /* mp_strerror(ec) Return a string describing the meaning of error code 'ec'. The string returned is allocated in static memory, so the caller should not attempt to modify or free the memory associated with this string. */ const char *mp_strerror(mp_err ec) { int aec = (ec < 0) ? -ec : ec; /* Code values are negative, so the senses of these comparisons are accurate */ if(ec < MP_LAST_CODE || ec > MP_OKAY) { return mp_err_string[0]; /* unknown error code */ } else { return mp_err_string[aec + 1]; } } /* end mp_strerror() */ /* }}} */ /*========================================================================*/ /*------------------------------------------------------------------------*/ /* Static function definitions (internal use only) */ /* {{{ Memory management */ /* {{{ s_mp_grow(mp, min) */ /* Make sure there are at least 'min' digits allocated to mp */ mp_err s_mp_grow(mp_int *mp, mp_size min) { if(min > ALLOC(mp)) { mp_digit *tmp; /* Set min to next nearest default precision block size */ min = ((min + (s_mp_defprec - 1)) / s_mp_defprec) * s_mp_defprec; if((tmp = s_mp_alloc(min, sizeof(mp_digit))) == NULL) return MP_MEM; s_mp_copy(DIGITS(mp), tmp, USED(mp)); #if MP_CRYPTO s_mp_setz(DIGITS(mp), ALLOC(mp)); #endif s_mp_free(DIGITS(mp)); DIGITS(mp) = tmp; ALLOC(mp) = min; } return MP_OKAY; } /* end s_mp_grow() */ /* }}} */ /* {{{ s_mp_pad(mp, min) */ /* Make sure the used size of mp is at least 'min', growing if needed */ mp_err s_mp_pad(mp_int *mp, mp_size min) { if(min > USED(mp)) { mp_err res; /* Make sure there is room to increase precision */ if(min > ALLOC(mp) && (res = s_mp_grow(mp, min)) != MP_OKAY) return res; /* Increase precision; should already be 0-filled */ USED(mp) = min; } return MP_OKAY; } /* end s_mp_pad() */ /* }}} */ /* {{{ s_mp_setz(dp, count) */ #if MP_MACRO == 0 /* Set 'count' digits pointed to by dp to be zeroes */ void s_mp_setz(mp_digit *dp, mp_size count) { #if MP_MEMSET == 0 int ix; for(ix = 0; ix < count; ix++) dp[ix] = 0; #else memset(dp, 0, count * sizeof(mp_digit)); #endif } /* end s_mp_setz() */ #endif /* }}} */ /* {{{ s_mp_copy(sp, dp, count) */ #if MP_MACRO == 0 /* Copy 'count' digits from sp to dp */ void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count) { #if MP_MEMCPY == 0 int ix; for(ix = 0; ix < count; ix++) dp[ix] = sp[ix]; #else memcpy(dp, sp, count * sizeof(mp_digit)); #endif } /* end s_mp_copy() */ #endif /* }}} */ /* {{{ s_mp_alloc(nb, ni) */ #if MP_MACRO == 0 /* Allocate ni records of nb bytes each, and return a pointer to that */ void *s_mp_alloc(size_t nb, size_t ni) { return calloc(nb, ni); } /* end s_mp_alloc() */ #endif /* }}} */ /* {{{ s_mp_free(ptr) */ #if MP_MACRO == 0 /* Free the memory pointed to by ptr */ void s_mp_free(void *ptr) { if(ptr) free(ptr); } /* end s_mp_free() */ #endif /* }}} */ /* {{{ s_mp_clamp(mp) */ /* Remove leading zeroes from the given value */ void s_mp_clamp(mp_int *mp) { mp_size du = USED(mp); mp_digit *zp = DIGITS(mp) + du - 1; while(du > 1 && !*zp--) --du; USED(mp) = du; } /* end s_mp_clamp() */ /* }}} */ /* {{{ s_mp_exch(a, b) */ /* Exchange the data for a and b; (b, a) = (a, b) */ void s_mp_exch(mp_int *a, mp_int *b) { mp_int tmp; tmp = *a; *a = *b; *b = tmp; } /* end s_mp_exch() */ /* }}} */ /* }}} */ /* {{{ Arithmetic helpers */ /* {{{ s_mp_lshd(mp, p) */ /* Shift mp leftward by p digits, growing if needed, and zero-filling the in-shifted digits at the right end. This is a convenient alternative to multiplication by powers of the radix */ mp_err s_mp_lshd(mp_int *mp, mp_size p) { mp_err res; mp_size pos; mp_digit *dp; int ix; if(p == 0) return MP_OKAY; if((res = s_mp_pad(mp, USED(mp) + p)) != MP_OKAY) return res; pos = USED(mp) - 1; dp = DIGITS(mp); /* Shift all the significant figures over as needed */ for(ix = pos - p; ix >= 0; ix--) dp[ix + p] = dp[ix]; /* Fill the bottom digits with zeroes */ for(ix = 0; ix < p; ix++) dp[ix] = 0; return MP_OKAY; } /* end s_mp_lshd() */ /* }}} */ /* {{{ s_mp_rshd(mp, p) */ /* Shift mp rightward by p digits. Maintains the invariant that digits above the precision are all zero. Digits shifted off the end are lost. Cannot fail. */ void s_mp_rshd(mp_int *mp, mp_size p) { mp_size ix; mp_digit *dp; if(p == 0) return; /* Shortcut when all digits are to be shifted off */ if(p >= USED(mp)) { s_mp_setz(DIGITS(mp), ALLOC(mp)); USED(mp) = 1; SIGN(mp) = MP_ZPOS; return; } /* Shift all the significant figures over as needed */ dp = DIGITS(mp); for(ix = p; ix < USED(mp); ix++) dp[ix - p] = dp[ix]; /* Fill the top digits with zeroes */ ix -= p; while(ix < USED(mp)) dp[ix++] = 0; /* Strip off any leading zeroes */ s_mp_clamp(mp); } /* end s_mp_rshd() */ /* }}} */ /* {{{ s_mp_div_2(mp) */ /* Divide by two -- take advantage of radix properties to do it fast */ void s_mp_div_2(mp_int *mp) { s_mp_div_2d(mp, 1); } /* end s_mp_div_2() */ /* }}} */ /* {{{ s_mp_mul_2(mp) */ mp_err s_mp_mul_2(mp_int *mp) { int ix; mp_digit kin = 0, kout, *dp = DIGITS(mp); mp_err res; /* Shift digits leftward by 1 bit */ for(ix = 0; ix < USED(mp); ix++) { kout = (dp[ix] >> (DIGIT_BIT - 1)) & 1; dp[ix] = (dp[ix] << 1) | kin; kin = kout; } /* Deal with rollover from last digit */ if(kin) { if(ix >= ALLOC(mp)) { if((res = s_mp_grow(mp, ALLOC(mp) + 1)) != MP_OKAY) return res; dp = DIGITS(mp); } dp[ix] = kin; USED(mp) += 1; } return MP_OKAY; } /* end s_mp_mul_2() */ /* }}} */ /* {{{ s_mp_mod_2d(mp, d) */ /* Remainder the integer by 2^d, where d is a number of bits. This amounts to a bitwise AND of the value, and does not require the full division code */ void s_mp_mod_2d(mp_int *mp, mp_digit d) { unsigned int ndig = (d / DIGIT_BIT), nbit = (d % DIGIT_BIT); unsigned int ix; mp_digit dmask, *dp = DIGITS(mp); if(ndig >= USED(mp)) return; /* Flush all the bits above 2^d in its digit */ dmask = (1 << nbit) - 1; dp[ndig] &= dmask; /* Flush all digits above the one with 2^d in it */ for(ix = ndig + 1; ix < USED(mp); ix++) dp[ix] = 0; s_mp_clamp(mp); } /* end s_mp_mod_2d() */ /* }}} */ /* {{{ s_mp_mul_2d(mp, d) */ /* Multiply by the integer 2^d, where d is a number of bits. This amounts to a bitwise shift of the value, and does not require the full multiplication code. */ mp_err s_mp_mul_2d(mp_int *mp, mp_digit d) { mp_err res; mp_digit save, next, mask, *dp; mp_size used; int ix; if((res = s_mp_lshd(mp, d / DIGIT_BIT)) != MP_OKAY) return res; dp = DIGITS(mp); used = USED(mp); d %= DIGIT_BIT; mask = (1 << d) - 1; /* If the shift requires another digit, make sure we've got one to work with */ if((dp[used - 1] >> (DIGIT_BIT - d)) & mask) { if((res = s_mp_grow(mp, used + 1)) != MP_OKAY) return res; dp = DIGITS(mp); } /* Do the shifting... */ save = 0; for(ix = 0; ix < used; ix++) { next = (dp[ix] >> (DIGIT_BIT - d)) & mask; dp[ix] = (dp[ix] << d) | save; save = next; } /* If, at this point, we have a nonzero carryout into the next digit, we'll increase the size by one digit, and store it... */ if(save) { dp[used] = save; USED(mp) += 1; } s_mp_clamp(mp); return MP_OKAY; } /* end s_mp_mul_2d() */ /* }}} */ /* {{{ s_mp_div_2d(mp, d) */ /* Divide the integer by 2^d, where d is a number of bits. This amounts to a bitwise shift of the value, and does not require the full division code (used in Barrett reduction, see below) */ void s_mp_div_2d(mp_int *mp, mp_digit d) { int ix; mp_digit save, next, mask, *dp = DIGITS(mp); s_mp_rshd(mp, d / DIGIT_BIT); d %= DIGIT_BIT; mask = (1 << d) - 1; save = 0; for(ix = USED(mp) - 1; ix >= 0; ix--) { next = dp[ix] & mask; dp[ix] = (dp[ix] >> d) | (save << (DIGIT_BIT - d)); save = next; } s_mp_clamp(mp); } /* end s_mp_div_2d() */ /* }}} */ /* {{{ s_mp_norm(a, b) */ /* s_mp_norm(a, b) Normalize a and b for division, where b is the divisor. In order that we might make good guesses for quotient digits, we want the leading digit of b to be at least half the radix, which we accomplish by multiplying a and b by a constant. This constant is returned (so that it can be divided back out of the remainder at the end of the division process). We multiply by the smallest power of 2 that gives us a leading digit at least half the radix. By choosing a power of 2, we simplify the multiplication and division steps to simple shifts. */ mp_digit s_mp_norm(mp_int *a, mp_int *b) { mp_digit t, d = 0; t = DIGIT(b, USED(b) - 1); while(t < (RADIX / 2)) { t <<= 1; ++d; } if(d != 0) { s_mp_mul_2d(a, d); s_mp_mul_2d(b, d); } return d; } /* end s_mp_norm() */ /* }}} */ /* }}} */ /* {{{ Primitive digit arithmetic */ /* {{{ s_mp_add_d(mp, d) */ /* Add d to |mp| in place */ mp_err s_mp_add_d(mp_int *mp, mp_digit d) /* unsigned digit addition */ { mp_word w, k = 0; mp_size ix = 1, used = USED(mp); mp_digit *dp = DIGITS(mp); w = dp[0] + d; dp[0] = ACCUM(w); k = CARRYOUT(w); while(ix < used && k) { w = dp[ix] + k; dp[ix] = ACCUM(w); k = CARRYOUT(w); ++ix; } if(k != 0) { mp_err res; if((res = s_mp_pad(mp, USED(mp) + 1)) != MP_OKAY) return res; DIGIT(mp, ix) = k; } return MP_OKAY; } /* end s_mp_add_d() */ /* }}} */ /* {{{ s_mp_sub_d(mp, d) */ /* Subtract d from |mp| in place, assumes |mp| > d */ mp_err s_mp_sub_d(mp_int *mp, mp_digit d) /* unsigned digit subtract */ { mp_word w, b = 0; mp_size ix = 1, used = USED(mp); mp_digit *dp = DIGITS(mp); /* Compute initial subtraction */ w = (RADIX + dp[0]) - d; b = CARRYOUT(w) ? 0 : 1; dp[0] = ACCUM(w); /* Propagate borrows leftward */ while(b && ix < used) { w = (RADIX + dp[ix]) - b; b = CARRYOUT(w) ? 0 : 1; dp[ix] = ACCUM(w); ++ix; } /* Remove leading zeroes */ s_mp_clamp(mp); /* If we have a borrow out, it's a violation of the input invariant */ if(b) return MP_RANGE; else return MP_OKAY; } /* end s_mp_sub_d() */ /* }}} */ /* {{{ s_mp_mul_d(a, d) */ /* Compute a = a * d, single digit multiplication */ mp_err s_mp_mul_d(mp_int *a, mp_digit d) { mp_word w, k = 0; mp_size ix, max; mp_err res; mp_digit *dp = DIGITS(a); /* Single-digit multiplication will increase the precision of the output by at most one digit. However, we can detect when this will happen -- if the high-order digit of a, times d, gives a two-digit result, then the precision of the result will increase; otherwise it won't. We use this fact to avoid calling s_mp_pad() unless absolutely necessary. */ max = USED(a); w = dp[max - 1] * d; if(CARRYOUT(w) != 0) { if((res = s_mp_pad(a, max + 1)) != MP_OKAY) return res; dp = DIGITS(a); } for(ix = 0; ix < max; ix++) { w = (dp[ix] * d) + k; dp[ix] = ACCUM(w); k = CARRYOUT(w); } /* If there is a precision increase, take care of it here; the above test guarantees we have enough storage to do this safely. */ if(k) { dp[max] = k; USED(a) = max + 1; } s_mp_clamp(a); return MP_OKAY; } /* end s_mp_mul_d() */ /* }}} */ /* {{{ s_mp_div_d(mp, d, r) */ /* s_mp_div_d(mp, d, r) Compute the quotient mp = mp / d and remainder r = mp mod d, for a single digit d. If r is null, the remainder will be discarded. */ mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r) { mp_word w = 0, t; mp_int quot; mp_err res; mp_digit *dp = DIGITS(mp), *qp; int ix; if(d == 0) return MP_RANGE; /* Make room for the quotient */ if((res = mp_init_size(", USED(mp))) != MP_OKAY) return res; USED(") = USED(mp); /* so clamping will work below */ qp = DIGITS("); /* Divide without subtraction */ for(ix = USED(mp) - 1; ix >= 0; ix--) { w = (w << DIGIT_BIT) | dp[ix]; if(w >= d) { t = w / d; w = w % d; } else { t = 0; } qp[ix] = t; } /* Deliver the remainder, if desired */ if(r) *r = w; s_mp_clamp("); mp_exch(", mp); mp_clear("); return MP_OKAY; } /* end s_mp_div_d() */ /* }}} */ /* }}} */ /* {{{ Primitive full arithmetic */ /* {{{ s_mp_add(a, b) */ /* Compute a = |a| + |b| */ mp_err s_mp_add(mp_int *a, mp_int *b) /* magnitude addition */ { mp_word w = 0; mp_digit *pa, *pb; mp_size ix, used = USED(b); mp_err res; /* Make sure a has enough precision for the output value */ if((used > USED(a)) && (res = s_mp_pad(a, used)) != MP_OKAY) return res; /* Add up all digits up to the precision of b. If b had initially the same precision as a, or greater, we took care of it by the padding step above, so there is no problem. If b had initially less precision, we'll have to make sure the carry out is duly propagated upward among the higher-order digits of the sum. */ pa = DIGITS(a); pb = DIGITS(b); for(ix = 0; ix < used; ++ix) { w += *pa + *pb++; *pa++ = ACCUM(w); w = CARRYOUT(w); } /* If we run out of 'b' digits before we're actually done, make sure the carries get propagated upward... */ used = USED(a); while(w && ix < used) { w += *pa; *pa++ = ACCUM(w); w = CARRYOUT(w); ++ix; } /* If there's an overall carry out, increase precision and include it. We could have done this initially, but why touch the memory allocator unless we're sure we have to? */ if(w) { if((res = s_mp_pad(a, used + 1)) != MP_OKAY) return res; DIGIT(a, ix) = w; /* pa may not be valid after s_mp_pad() call */ } return MP_OKAY; } /* end s_mp_add() */ /* }}} */ /* {{{ s_mp_sub(a, b) */ /* Compute a = |a| - |b|, assumes |a| >= |b| */ mp_err s_mp_sub(mp_int *a, mp_int *b) /* magnitude subtract */ { mp_word w = 0; mp_digit *pa, *pb; mp_size ix, used = USED(b); /* Subtract and propagate borrow. Up to the precision of b, this accounts for the digits of b; after that, we just make sure the carries get to the right place. This saves having to pad b out to the precision of a just to make the loops work right... */ pa = DIGITS(a); pb = DIGITS(b); for(ix = 0; ix < used; ++ix) { w = (RADIX + *pa) - w - *pb++; *pa++ = ACCUM(w); w = CARRYOUT(w) ? 0 : 1; } used = USED(a); while(ix < used) { w = RADIX + *pa - w; *pa++ = ACCUM(w); w = CARRYOUT(w) ? 0 : 1; ++ix; } /* Clobber any leading zeroes we created */ s_mp_clamp(a); /* If there was a borrow out, then |b| > |a| in violation of our input invariant. We've already done the work, but we'll at least complain about it... */ if(w) return MP_RANGE; else return MP_OKAY; } /* end s_mp_sub() */ /* }}} */ mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu) { mp_int q; mp_err res; mp_size um = USED(m); if((res = mp_init_copy(&q, x)) != MP_OKAY) return res; s_mp_rshd(&q, um - 1); /* q1 = x / b^(k-1) */ s_mp_mul(&q, mu); /* q2 = q1 * mu */ s_mp_rshd(&q, um + 1); /* q3 = q2 / b^(k+1) */ /* x = x mod b^(k+1), quick (no division) */ s_mp_mod_2d(x, (mp_digit)(DIGIT_BIT * (um + 1))); /* q = q * m mod b^(k+1), quick (no division), uses the short multiplier */ #ifndef SHRT_MUL s_mp_mul(&q, m); s_mp_mod_2d(&q, (mp_digit)(DIGIT_BIT * (um + 1))); #else s_mp_mul_dig(&q, m, um + 1); #endif /* x = x - q */ if((res = mp_sub(x, &q, x)) != MP_OKAY) goto CLEANUP; /* If x < 0, add b^(k+1) to it */ if(mp_cmp_z(x) < 0) { mp_set(&q, 1); if((res = s_mp_lshd(&q, um + 1)) != MP_OKAY) goto CLEANUP; if((res = mp_add(x, &q, x)) != MP_OKAY) goto CLEANUP; } /* Back off if it's too big */ while(mp_cmp(x, m) >= 0) { if((res = s_mp_sub(x, m)) != MP_OKAY) break; } CLEANUP: mp_clear(&q); return res; } /* end s_mp_reduce() */ /* {{{ s_mp_mul(a, b) */ /* Compute a = |a| * |b| */ mp_err s_mp_mul(mp_int *a, mp_int *b) { mp_word w, k = 0; mp_int tmp; mp_err res; mp_size ix, jx, ua = USED(a), ub = USED(b); mp_digit *pa, *pb, *pt, *pbt; if((res = mp_init_size(&tmp, ua + ub)) != MP_OKAY) return res; /* This has the effect of left-padding with zeroes... */ USED(&tmp) = ua + ub; /* We're going to need the base value each iteration */ pbt = DIGITS(&tmp); /* Outer loop: Digits of b */ pb = DIGITS(b); for(ix = 0; ix < ub; ++ix, ++pb) { if(*pb == 0) continue; /* Inner product: Digits of a */ pa = DIGITS(a); for(jx = 0; jx < ua; ++jx, ++pa) { pt = pbt + ix + jx; w = *pb * *pa + k + *pt; *pt = ACCUM(w); k = CARRYOUT(w); } pbt[ix + jx] = k; k = 0; } s_mp_clamp(&tmp); s_mp_exch(&tmp, a); mp_clear(&tmp); return MP_OKAY; } /* end s_mp_mul() */ /* }}} */ /* {{{ s_mp_kmul(a, b, out, len) */ #if 0 void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len) { mp_word w, k = 0; mp_size ix, jx; mp_digit *pa, *pt; for(ix = 0; ix < len; ++ix, ++b) { if(*b == 0) continue; pa = a; for(jx = 0; jx < len; ++jx, ++pa) { pt = out + ix + jx; w = *b * *pa + k + *pt; *pt = ACCUM(w); k = CARRYOUT(w); } out[ix + jx] = k; k = 0; } } /* end s_mp_kmul() */ #endif /* }}} */ /* {{{ s_mp_sqr(a) */ /* Computes the square of a, in place. This can be done more efficiently than a general multiplication, because many of the computation steps are redundant when squaring. The inner product step is a bit more complicated, but we save a fair number of iterations of the multiplication loop. */ #if MP_SQUARE mp_err s_mp_sqr(mp_int *a) { mp_word w, k = 0; mp_int tmp; mp_err res; mp_size ix, jx, kx, used = USED(a); mp_digit *pa1, *pa2, *pt, *pbt; if((res = mp_init_size(&tmp, 2 * used)) != MP_OKAY) return res; /* Left-pad with zeroes */ USED(&tmp) = 2 * used; /* We need the base value each time through the loop */ pbt = DIGITS(&tmp); pa1 = DIGITS(a); for(ix = 0; ix < used; ++ix, ++pa1) { if(*pa1 == 0) continue; w = DIGIT(&tmp, ix + ix) + (*pa1 * *pa1); pbt[ix + ix] = ACCUM(w); k = CARRYOUT(w); /* The inner product is computed as: (C, S) = t[i,j] + 2 a[i] a[j] + C This can overflow what can be represented in an mp_word, and since C arithmetic does not provide any way to check for overflow, we have to check explicitly for overflow conditions before they happen. */ for(jx = ix + 1, pa2 = DIGITS(a) + jx; jx < used; ++jx, ++pa2) { mp_word u = 0, v; /* Store this in a temporary to avoid indirections later */ pt = pbt + ix + jx; /* Compute the multiplicative step */ w = *pa1 * *pa2; /* If w is more than half MP_WORD_MAX, the doubling will overflow, and we need to record a carry out into the next word */ u = (w >> (MP_WORD_BIT - 1)) & 1; /* Double what we've got, overflow will be ignored as defined for C arithmetic (we've already noted if it is to occur) */ w *= 2; /* Compute the additive step */ v = *pt + k; /* If we do not already have an overflow carry, check to see if the addition will cause one, and set the carry out if so */ u |= ((MP_WORD_MAX - v) < w); /* Add in the rest, again ignoring overflow */ w += v; /* Set the i,j digit of the output */ *pt = ACCUM(w); /* Save carry information for the next iteration of the loop. This is why k must be an mp_word, instead of an mp_digit */ k = CARRYOUT(w) | (u << DIGIT_BIT); } /* for(jx ...) */ /* Set the last digit in the cycle and reset the carry */ k = DIGIT(&tmp, ix + jx) + k; pbt[ix + jx] = ACCUM(k); k = CARRYOUT(k); /* If we are carrying out, propagate the carry to the next digit in the output. This may cascade, so we have to be somewhat circumspect -- but we will have enough precision in the output that we won't overflow */ kx = 1; while(k) { k = pbt[ix + jx + kx] + 1; pbt[ix + jx + kx] = ACCUM(k); k = CARRYOUT(k); ++kx; } } /* for(ix ...) */ s_mp_clamp(&tmp); s_mp_exch(&tmp, a); mp_clear(&tmp); return MP_OKAY; } /* end s_mp_sqr() */ #endif /* }}} */ /* {{{ s_mp_div(a, b) */ /* s_mp_div(a, b) Compute a = a / b and b = a mod b. Assumes b > a. */ mp_err s_mp_div(mp_int *a, mp_int *b) { mp_int quot, rem, t; mp_word q; mp_err res; mp_digit d; int ix; if(mp_cmp_z(b) == 0) return MP_RANGE; /* Shortcut if b is power of two */ if((ix = s_mp_ispow2(b)) >= 0) { mp_copy(a, b); /* need this for remainder */ s_mp_div_2d(a, (mp_digit)ix); s_mp_mod_2d(b, (mp_digit)ix); return MP_OKAY; } /* Allocate space to store the quotient */ if((res = mp_init_size(", USED(a))) != MP_OKAY) return res; /* A working temporary for division */ if((res = mp_init_size(&t, USED(a))) != MP_OKAY) goto T; /* Allocate space for the remainder */ if((res = mp_init_size(&rem, USED(a))) != MP_OKAY) goto REM; /* Normalize to optimize guessing */ d = s_mp_norm(a, b); /* Perform the division itself...woo! */ ix = USED(a) - 1; while(ix >= 0) { /* Find a partial substring of a which is at least b */ while(s_mp_cmp(&rem, b) < 0 && ix >= 0) { if((res = s_mp_lshd(&rem, 1)) != MP_OKAY) goto CLEANUP; if((res = s_mp_lshd(", 1)) != MP_OKAY) goto CLEANUP; DIGIT(&rem, 0) = DIGIT(a, ix); s_mp_clamp(&rem); --ix; } /* If we didn't find one, we're finished dividing */ if(s_mp_cmp(&rem, b) < 0) break; /* Compute a guess for the next quotient digit */ q = DIGIT(&rem, USED(&rem) - 1); if(q <= DIGIT(b, USED(b) - 1) && USED(&rem) > 1) q = (q << DIGIT_BIT) | DIGIT(&rem, USED(&rem) - 2); q /= DIGIT(b, USED(b) - 1); /* The guess can be as much as RADIX + 1 */ if(q >= RADIX) q = RADIX - 1; /* See what that multiplies out to */ mp_copy(b, &t); if((res = s_mp_mul_d(&t, q)) != MP_OKAY) goto CLEANUP; /* If it's too big, back it off. We should not have to do this more than once, or, in rare cases, twice. Knuth describes a method by which this could be reduced to a maximum of once, but I didn't implement that here. */ while(s_mp_cmp(&t, &rem) > 0) { --q; s_mp_sub(&t, b); } /* At this point, q should be the right next digit */ if((res = s_mp_sub(&rem, &t)) != MP_OKAY) goto CLEANUP; /* Include the digit in the quotient. We allocated enough memory for any quotient we could ever possibly get, so we should not have to check for failures here */ DIGIT(", 0) = q; } /* Denormalize remainder */ if(d != 0) s_mp_div_2d(&rem, d); s_mp_clamp("); s_mp_clamp(&rem); /* Copy quotient back to output */ s_mp_exch(", a); /* Copy remainder back to output */ s_mp_exch(&rem, b); CLEANUP: mp_clear(&rem); REM: mp_clear(&t); T: mp_clear("); return res; } /* end s_mp_div() */ /* }}} */ /* {{{ s_mp_2expt(a, k) */ mp_err s_mp_2expt(mp_int *a, mp_digit k) { mp_err res; mp_size dig, bit; dig = k / DIGIT_BIT; bit = k % DIGIT_BIT; mp_zero(a); if((res = s_mp_pad(a, dig + 1)) != MP_OKAY) return res; DIGIT(a, dig) |= (1 << bit); return MP_OKAY; } /* end s_mp_2expt() */ /* }}} */ /* }}} */ /* }}} */ /* {{{ Primitive comparisons */ /* {{{ s_mp_cmp(a, b) */ /* Compare |a| <=> |b|, return 0 if equal, <0 if a0 if a>b */ int s_mp_cmp(mp_int *a, mp_int *b) { mp_size ua = USED(a), ub = USED(b); if(ua > ub) return MP_GT; else if(ua < ub) return MP_LT; else { int ix = ua - 1; mp_digit *ap = DIGITS(a) + ix, *bp = DIGITS(b) + ix; while(ix >= 0) { if(*ap > *bp) return MP_GT; else if(*ap < *bp) return MP_LT; --ap; --bp; --ix; } return MP_EQ; } } /* end s_mp_cmp() */ /* }}} */ /* {{{ s_mp_cmp_d(a, d) */ /* Compare |a| <=> d, return 0 if equal, <0 if a0 if a>d */ int s_mp_cmp_d(mp_int *a, mp_digit d) { mp_size ua = USED(a); mp_digit *ap = DIGITS(a); if(ua > 1) return MP_GT; if(*ap < d) return MP_LT; else if(*ap > d) return MP_GT; else return MP_EQ; } /* end s_mp_cmp_d() */ /* }}} */ /* {{{ s_mp_ispow2(v) */ /* Returns -1 if the value is not a power of two; otherwise, it returns k such that v = 2^k, i.e. lg(v). */ int s_mp_ispow2(mp_int *v) { mp_digit d, *dp; mp_size uv = USED(v); int extra = 0, ix; d = DIGIT(v, uv - 1); /* most significant digit of v */ while(d && ((d & 1) == 0)) { d >>= 1; ++extra; } if(d == 1) { ix = uv - 2; dp = DIGITS(v) + ix; while(ix >= 0) { if(*dp) return -1; /* not a power of two */ --dp; --ix; } return ((uv - 1) * DIGIT_BIT) + extra; } return -1; } /* end s_mp_ispow2() */ /* }}} */ /* {{{ s_mp_ispow2d(d) */ int s_mp_ispow2d(mp_digit d) { int pow = 0; while((d & 1) == 0) { ++pow; d >>= 1; } if(d == 1) return pow; return -1; } /* end s_mp_ispow2d() */ /* }}} */ /* }}} */ /* {{{ Primitive I/O helpers */ /* {{{ s_mp_tovalue(ch, r) */ /* Convert the given character to its digit value, in the given radix. If the given character is not understood in the given radix, -1 is returned. Otherwise the digit's numeric value is returned. The results will be odd if you use a radix < 2 or > 62, you are expected to know what you're up to. */ int s_mp_tovalue(char ch, int r) { int val, xch; if(r > 36) xch = ch; else xch = toupper(ch); if(isdigit(xch)) val = xch - '0'; else if(isupper(xch)) val = xch - 'A' + 10; else if(islower(xch)) val = xch - 'a' + 36; else if(xch == '+') val = 62; else if(xch == '/') val = 63; else return -1; if(val < 0 || val >= r) return -1; return val; } /* end s_mp_tovalue() */ /* }}} */ /* {{{ s_mp_todigit(val, r, low) */ /* Convert val to a radix-r digit, if possible. If val is out of range for r, returns zero. Otherwise, returns an ASCII character denoting the value in the given radix. The results may be odd if you use a radix < 2 or > 64, you are expected to know what you're doing. */ char s_mp_todigit(int val, int r, int low) { char ch; if(val < 0 || val >= r) return 0; ch = s_dmap_1[val]; if(r <= 36 && low) ch = tolower(ch); return ch; } /* end s_mp_todigit() */ /* }}} */ /* {{{ s_mp_outlen(bits, radix) */ /* Return an estimate for how long a string is needed to hold a radix r representation of a number with 'bits' significant bits. Does not include space for a sign or a NUL terminator. */ int s_mp_outlen(int bits, int r) { return (int)((double)bits * LOG_V_2(r)); } /* end s_mp_outlen() */ /* }}} */ /* }}} */ /*------------------------------------------------------------------------*/ /* HERE THERE BE DRAGONS */ /* crc==4242132123, version==2, Sat Feb 02 06:43:52 2002 */ /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/mtest/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.1 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Added libtommath/mtest/mpi.h.      > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231  /* mpi.h by Michael J. Fromberger Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved Arbitrary precision integer arithmetic library$Id: mpi.h,v 1.1.1.1.2.1 2005/09/26 20:16:54 kennykb Exp $*/ #ifndef _H_MPI_ #define _H_MPI_ #include "mpi-config.h" #define MP_LT -1 #define MP_EQ 0 #define MP_GT 1 #if MP_DEBUG #undef MP_IOFUNC #define MP_IOFUNC 1 #endif #if MP_IOFUNC #include #include #endif #include #define MP_NEG 1 #define MP_ZPOS 0 /* Included for compatibility... */ #define NEG MP_NEG #define ZPOS MP_ZPOS #define MP_OKAY 0 /* no error, all is well */ #define MP_YES 0 /* yes (boolean result) */ #define MP_NO -1 /* no (boolean result) */ #define MP_MEM -2 /* out of memory */ #define MP_RANGE -3 /* argument out of range */ #define MP_BADARG -4 /* invalid parameter */ #define MP_UNDEF -5 /* answer is undefined */ #define MP_LAST_CODE MP_UNDEF #include "mpi-types.h" /* Included for compatibility... */ #define DIGIT_BIT MP_DIGIT_BIT #define DIGIT_MAX MP_DIGIT_MAX /* Macros for accessing the mp_int internals */ #define SIGN(MP) ((MP)->sign) #define USED(MP) ((MP)->used) #define ALLOC(MP) ((MP)->alloc) #define DIGITS(MP) ((MP)->dp) #define DIGIT(MP,N) (MP)->dp[(N)] #if MP_ARGCHK == 1 #define ARGCHK(X,Y) {if(!(X)){return (Y);}} #elif MP_ARGCHK == 2 #include #define ARGCHK(X,Y) assert(X) #else #define ARGCHK(X,Y) /* */ #endif /* This defines the maximum I/O base (minimum is 2) */ #define MAX_RADIX 64 typedef struct { mp_sign sign; /* sign of this quantity */ mp_size alloc; /* how many digits allocated */ mp_size used; /* how many digits used */ mp_digit *dp; /* the digits themselves */ } mp_int; /*------------------------------------------------------------------------*/ /* Default precision */ unsigned int mp_get_prec(void); void mp_set_prec(unsigned int prec); /*------------------------------------------------------------------------*/ /* Memory management */ mp_err mp_init(mp_int *mp); mp_err mp_init_array(mp_int mp[], int count); mp_err mp_init_size(mp_int *mp, mp_size prec); mp_err mp_init_copy(mp_int *mp, mp_int *from); mp_err mp_copy(mp_int *from, mp_int *to); void mp_exch(mp_int *mp1, mp_int *mp2); void mp_clear(mp_int *mp); void mp_clear_array(mp_int mp[], int count); void mp_zero(mp_int *mp); void mp_set(mp_int *mp, mp_digit d); mp_err mp_set_int(mp_int *mp, long z); mp_err mp_shrink(mp_int *a); /*------------------------------------------------------------------------*/ /* Single digit arithmetic */ mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b); mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b); mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b); mp_err mp_mul_2(mp_int *a, mp_int *c); mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r); mp_err mp_div_2(mp_int *a, mp_int *c); mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c); /*------------------------------------------------------------------------*/ /* Sign manipulations */ mp_err mp_abs(mp_int *a, mp_int *b); mp_err mp_neg(mp_int *a, mp_int *b); /*------------------------------------------------------------------------*/ /* Full arithmetic */ mp_err mp_add(mp_int *a, mp_int *b, mp_int *c); mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c); mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c); mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c); #if MP_SQUARE mp_err mp_sqr(mp_int *a, mp_int *b); #else #define mp_sqr(a, b) mp_mul(a, a, b) #endif mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r); mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r); mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c); mp_err mp_2expt(mp_int *a, mp_digit k); mp_err mp_sqrt(mp_int *a, mp_int *b); /*------------------------------------------------------------------------*/ /* Modular arithmetic */ #if MP_MODARITH mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c); mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c); mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c); mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c); mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c); #if MP_SQUARE mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c); #else #define mp_sqrmod(a, m, c) mp_mulmod(a, a, m, c) #endif mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c); mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c); #endif /* MP_MODARITH */ /*------------------------------------------------------------------------*/ /* Comparisons */ int mp_cmp_z(mp_int *a); int mp_cmp_d(mp_int *a, mp_digit d); int mp_cmp(mp_int *a, mp_int *b); int mp_cmp_mag(mp_int *a, mp_int *b); int mp_cmp_int(mp_int *a, long z); int mp_isodd(mp_int *a); int mp_iseven(mp_int *a); /*------------------------------------------------------------------------*/ /* Number theoretic */ #if MP_NUMTH mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c); mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c); mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y); mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c); #endif /* end MP_NUMTH */ /*------------------------------------------------------------------------*/ /* Input and output */ #if MP_IOFUNC void mp_print(mp_int *mp, FILE *ofp); #endif /* end MP_IOFUNC */ /*------------------------------------------------------------------------*/ /* Base conversion */ #define BITS 1 #define BYTES CHAR_BIT mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len); int mp_signed_bin_size(mp_int *mp); mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str); mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len); int mp_unsigned_bin_size(mp_int *mp); mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str); int mp_count_bits(mp_int *mp); #if MP_COMPAT_MACROS #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len)) #define mp_raw_size(mp) mp_signed_bin_size(mp) #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str)) #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len)) #define mp_mag_size(mp) mp_unsigned_bin_size(mp) #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str)) #endif mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix); int mp_radix_size(mp_int *mp, int radix); int mp_value_radix_size(int num, int qty, int radix); mp_err mp_toradix(mp_int *mp, unsigned char *str, int radix); int mp_char2value(char ch, int r); #define mp_tobinary(M, S) mp_toradix((M), (S), 2) #define mp_tooctal(M, S) mp_toradix((M), (S), 8) #define mp_todecimal(M, S) mp_toradix((M), (S), 10) #define mp_tohex(M, S) mp_toradix((M), (S), 16) /*------------------------------------------------------------------------*/ /* Error strings */ const char *mp_strerror(mp_err ec); #endif /* end _H_MPI_ */ /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/mtest/mpi.h,v $*/ /*$Revision: 1.1.1.1.2.1 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Added libtommath/mtest/mtest.c.      > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308  /* makes a bignum test harness with NUM tests per operation * * the output is made in the following format [one parameter per line] operation operand1 operand2 [... operandN] result1 result2 [... resultN] So for example "a * b mod n" would be mulmod a b n a*b mod n e.g. if a=3, b=4 n=11 then mulmod 3 4 11 1 */ #ifdef MP_8BIT #define THE_MASK 127 #else #define THE_MASK 32767 #endif #include #include #include #include "mpi.c" FILE *rng; void rand_num(mp_int *a) { int n, size; unsigned char buf[2048]; size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 101; buf[0] = (fgetc(rng)&1)?1:0; fread(buf+1, 1, size, rng); while (buf[1] == 0) buf[1] = fgetc(rng); mp_read_raw(a, buf, 1+size); } void rand_num2(mp_int *a) { int n, size; unsigned char buf[2048]; size = 10 + ((fgetc(rng)<<8) + fgetc(rng)) % 101; buf[0] = (fgetc(rng)&1)?1:0; fread(buf+1, 1, size, rng); while (buf[1] == 0) buf[1] = fgetc(rng); mp_read_raw(a, buf, 1+size); } #define mp_to64(a, b) mp_toradix(a, b, 64) int main(void) { int n, tmp; mp_int a, b, c, d, e; clock_t t1; char buf[4096]; mp_init(&a); mp_init(&b); mp_init(&c); mp_init(&d); mp_init(&e); /* initial (2^n - 1)^2 testing, makes sure the comba multiplier works [it has the new carry code] */ /* mp_set(&a, 1); for (n = 1; n < 8192; n++) { mp_mul(&a, &a, &c); printf("mul\n"); mp_to64(&a, buf); printf("%s\n%s\n", buf, buf); mp_to64(&c, buf); printf("%s\n", buf); mp_add_d(&a, 1, &a); mp_mul_2(&a, &a); mp_sub_d(&a, 1, &a); } */ rng = fopen("/dev/urandom", "rb"); if (rng == NULL) { rng = fopen("/dev/random", "rb"); if (rng == NULL) { fprintf(stderr, "\nWarning: stdin used as random source\n\n"); rng = stdin; } } t1 = clock(); for (;;) { #if 0 if (clock() - t1 > CLOCKS_PER_SEC) { sleep(2); t1 = clock(); } #endif n = fgetc(rng) % 15; if (n == 0) { /* add tests */ rand_num(&a); rand_num(&b); mp_add(&a, &b, &c); printf("add\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); mp_to64(&c, buf); printf("%s\n", buf); } else if (n == 1) { /* sub tests */ rand_num(&a); rand_num(&b); mp_sub(&a, &b, &c); printf("sub\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); mp_to64(&c, buf); printf("%s\n", buf); } else if (n == 2) { /* mul tests */ rand_num(&a); rand_num(&b); mp_mul(&a, &b, &c); printf("mul\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); mp_to64(&c, buf); printf("%s\n", buf); } else if (n == 3) { /* div tests */ rand_num(&a); rand_num(&b); mp_div(&a, &b, &c, &d); printf("div\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); mp_to64(&c, buf); printf("%s\n", buf); mp_to64(&d, buf); printf("%s\n", buf); } else if (n == 4) { /* sqr tests */ rand_num(&a); mp_sqr(&a, &b); printf("sqr\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); } else if (n == 5) { /* mul_2d test */ rand_num(&a); mp_copy(&a, &b); n = fgetc(rng) & 63; mp_mul_2d(&b, n, &b); mp_to64(&a, buf); printf("mul2d\n"); printf("%s\n", buf); printf("%d\n", n); mp_to64(&b, buf); printf("%s\n", buf); } else if (n == 6) { /* div_2d test */ rand_num(&a); mp_copy(&a, &b); n = fgetc(rng) & 63; mp_div_2d(&b, n, &b, NULL); mp_to64(&a, buf); printf("div2d\n"); printf("%s\n", buf); printf("%d\n", n); mp_to64(&b, buf); printf("%s\n", buf); } else if (n == 7) { /* gcd test */ rand_num(&a); rand_num(&b); a.sign = MP_ZPOS; b.sign = MP_ZPOS; mp_gcd(&a, &b, &c); printf("gcd\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); mp_to64(&c, buf); printf("%s\n", buf); } else if (n == 8) { /* lcm test */ rand_num(&a); rand_num(&b); a.sign = MP_ZPOS; b.sign = MP_ZPOS; mp_lcm(&a, &b, &c); printf("lcm\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); mp_to64(&c, buf); printf("%s\n", buf); } else if (n == 9) { /* exptmod test */ rand_num2(&a); rand_num2(&b); rand_num2(&c); // if (c.dp[0]&1) mp_add_d(&c, 1, &c); a.sign = b.sign = c.sign = 0; mp_exptmod(&a, &b, &c, &d); printf("expt\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); mp_to64(&c, buf); printf("%s\n", buf); mp_to64(&d, buf); printf("%s\n", buf); } else if (n == 10) { /* invmod test */ rand_num2(&a); rand_num2(&b); b.sign = MP_ZPOS; a.sign = MP_ZPOS; mp_gcd(&a, &b, &c); if (mp_cmp_d(&c, 1) != 0) continue; if (mp_cmp_d(&b, 1) == 0) continue; mp_invmod(&a, &b, &c); printf("invmod\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); mp_to64(&c, buf); printf("%s\n", buf); } else if (n == 11) { rand_num(&a); mp_mul_2(&a, &a); mp_div_2(&a, &b); printf("div2\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); } else if (n == 12) { rand_num2(&a); mp_mul_2(&a, &b); printf("mul2\n"); mp_to64(&a, buf); printf("%s\n", buf); mp_to64(&b, buf); printf("%s\n", buf); } else if (n == 13) { rand_num2(&a); tmp = abs(rand()) & THE_MASK; mp_add_d(&a, tmp, &b); printf("add_d\n"); mp_to64(&a, buf); printf("%s\n%d\n", buf, tmp); mp_to64(&b, buf); printf("%s\n", buf); } else if (n == 14) { rand_num2(&a); tmp = abs(rand()) & THE_MASK; mp_sub_d(&a, tmp, &b); printf("sub_d\n"); mp_to64(&a, buf); printf("%s\n%d\n", buf, tmp); mp_to64(&b, buf); printf("%s\n", buf); } } fclose(rng); return 0; } /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/mtest/mtest.c,v $*/ /*$Revision: 1.1.1.1.2.1 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Changes to libtommath/poster.pdf. cannot compute difference between binary files Changes to libtommath/pre_gen/mpi.c.  39 40 41 42 43 44 45 46 47 48 49 50 51 52 ... 186 187 188 189 190 191 192 193 194 195 196 197 198 199 ... 358 359 360 361 362 363 364 365 366 367 368 369 370 371 ... 434 435 436 437 438 439 440 441 442 443 444 445 446 447 ... 467 468 469 470 471 472 473 474 475 476 477 478 479 480 ... 568 569 570 571 572 573 574 575 576 577 578 579 580 581 ... 683 684 685 686 687 688 689 690 691 692 693 694 695 696 ... 731 732 733 734 735 736 737 738 739 740 741 742 743 744 ... 773 774 775 776 777 778 779 780 781 782 783 784 785 786 ... 826 827 828 829 830 831 832 833 834 835 836 837 838 839 ... 936 937 938 939 940 941 942 943 944 945 946 947 948 949 ... 976 977 978 979 980 981 982 983 984 985 986 987 988 989 .... 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 .... 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 .... 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 .... 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 .... 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 .... 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 .... 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 .... 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 .... 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 .... 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 .... 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 .... 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 .... 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 .... 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 .... 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 .... 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 .... 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258 2259 2260 .... 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 .... 2312 2313 2314 2315 2316 2317 2318 2319 2320 2321 2322 2323 2324 2325 .... 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 .... 2441 2442 2443 2444 2445 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 .... 2481 2482 2483 2484 2485 2486 2487 2488 2489 2490 2491 2492 2493 2494 .... 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814 2815 2816 .... 2885 2886 2887 2888 2889 2890 2891 2892 2893 2894 2895 2896 2897 2898 .... 2952 2953 2954 2955 2956 2957 2958 2959 2960 2961 2962 2963 2964 2965 .... 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 .... 3117 3118 3119 3120 3121 3122 3123 3124 3125 3126 3127 3128 3129 3130 .... 3161 3162 3163 3164 3165 3166 3167 3168 3169 3170 3171 3172 3173 3174 .... 3219 3220 3221 3222 3223 3224 3225 3226 3227 3228 3229 3230 3231 3232 .... 3265 3266 3267 3268 3269 3270 3271 3272 3273 3274 3275 3276 3277 3278 .... 3296 3297 3298 3299 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 .... 3356 3357 3358 3359 3360 3361 3362 3363 3364 3365 3366 3367 3368 3369 .... 3388 3389 3390 3391 3392 3393 3394 3395 3396 3397 3398 3399 3400 3401 .... 3418 3419 3420 3421 3422 3423 3424 3425 3426 3427 3428 3429 3430 3431 .... 3467 3468 3469 3470 3471 3472 3473 3474 3475 3476 3477 3478 3479 3480 .... 3509 3510 3511 3512 3513 3514 3515 3516 3517 3518 3519 3520 3521 3522 .... 3685 3686 3687 3688 3689 3690 3691 3692 3693 3694 3695 3696 3697 3698 .... 3794 3795 3796 3797 3798 3799 3800 3801 3802 3803 3804 3805 3806 3807 .... 3899 3900 3901 3902 3903 3904 3905 3906 3907 3908 3909 3910 3911 3912 .... 3930 3931 3932 3933 3934 3935 3936 3937 3938 3939 3940 3941 3942 3943 3944 3945 3946 3947 3948 3949 .... 4026 4027 4028 4029 4030 4031 4032 4033 4034 4035 4036 4037 4038 4039 4040 4041 4042 4043 4044 4045 4046 4047 4048 4049 4050 4051 4052 .... 4065 4066 4067 4068 4069 4070 4071 4072 4073 4074 4075 4076 4077 4078 .... 4151 4152 4153 4154 4155 4156 4157 4158 4159 4160 4161 4162 4163 4164 4165 4166 4167 4168 4169 4170 4171 4172 4173 4174 4175 .... 4186 4187 4188 4189 4190 4191 4192 4193 4194 4195 4196 4197 4198 4199 .... 4246 4247 4248 4249 4250 4251 4252 4253 4254 4255 4256 4257 4258 4259 .... 4314 4315 4316 4317 4318 4319 4320 4321 4322 4323 4324 4325 4326 4327 .... 4361 4362 4363 4364 4365 4366 4367 4368 4369 4370 4371 4372 4373 4374 .... 4417 4418 4419 4420 4421 4422 4423 4424 4425 4426 4427 4428 4429 4430 .... 4443 4444 4445 4446 4447 4448 4449 4450 4451 4452 4453 4454 4455 4456 .... 4502 4503 4504 4505 4506 4507 4508 4509 4510 4511 4512 4513 4514 4515 .... 4620 4621 4622 4623 4624 4625 4626 4627 4628 4629 4630 4631 4632 4633 .... 4679 4680 4681 4682 4683 4684 4685 4686 4687 4688 4689 4690 4691 4692 .... 4745 4746 4747 4748 4749 4750 4751 4752 4753 4754 4755 4756 4757 4758 .... 4827 4828 4829 4830 4831 4832 4833 4834 4835 4836 4837 4838 4839 4840 .... 4913 4914 4915 4916 4917 4918 4919 4920 4921 4922 4923 4924 4925 4926 .... 4992 4993 4994 4995 4996 4997 4998 4999 5000 5001 5002 5003 5004 5005 .... 5013 5014 5015 5016 5017 5018 5019 5020 5021 5022 5023 5024 5025 5026 5027 5028 .... 5032 5033 5034 5035 5036 5037 5038 5039 5040 5041 5042 5043 5044 5045 .... 5165 5166 5167 5168 5169 5170 5171 5172 5173 5174 5175 5176 5177 5178 .... 5204 5205 5206 5207 5208 5209 5210 5211 5212 5213 5214 5215 5216 5217 .... 5254 5255 5256 5257 5258 5259 5260 5261 5262 5263 5264 5265 5266 5267 .... 5317 5318 5319 5320 5321 5322 5323 5324 5325 5326 5327 5328 5329 5330 .... 5366 5367 5368 5369 5370 5371 5372 5373 5374 5375 5376 5377 5378 5379 .... 5449 5450 5451 5452 5453 5454 5455 5456 5457 5458 5459 5460 5461 5462 .... 5552 5553 5554 5555 5556 5557 5558 5559 5560 5561 5562 5563 5564 5565 .... 5722 5723 5724 5725 5726 5727 5728 5729 5730 5731 5732 5733 5734 5735 .... 5774 5775 5776 5777 5778 5779 5780 5781 5782 5783 5784 5785 5786 5787 .... 5842 5843 5844 5845 5846 5847 5848 5849 5850 5851 5852 5853 5854 5855 5856 5857 5858 5859 .... 5901 5902 5903 5904 5905 5906 5907 5908 5909 5910 5911 5912 5913 5914 .... 5980 5981 5982 5983 5984 5985 5986 5987 5988 5989 5990 5991 5992 5993 .... 6003 6004 6005 6006 6007 6008 6009 6010 6011 6012 6013 6014 6015 6016 .... 6058 6059 6060 6061 6062 6063 6064 6065 6066 6067 6068 6069 6070 6071 .... 6141 6142 6143 6144 6145 6146 6147 6148 6149 6150 6151 6152 6153 6154 .... 6162 6163 6164 6165 6166 6167 6168 6169 6170 6171 6172 6173 6174 6175 6176 6177 .... 6182 6183 6184 6185 6186 6187 6188 6189 6190 6191 6192 6193 6194 6195 .... 6204 6205 6206 6207 6208 6209 6210 6211 6212 6213 6214 6215 6216 6217 6218 6219 .... 6238 6239 6240 6241 6242 6243 6244 6245 6246 6247 6248 6249 6250 6251 .... 6339 6340 6341 6342 6343 6344 6345 6346 6347 6348 6349 6350 6351 6352 .... 6399 6400 6401 6402 6403 6404 6405 6406 6407 6408 6409 6410 6411 6412 .... 6462 6463 6464 6465 6466 6467 6468 6469 6470 6471 6472 6473 6474 6475 .... 6509 6510 6511 6512 6513 6514 6515 6516 6517 6518 6519 6520 6521 6522 .... 6552 6553 6554 6555 6556 6557 6558 6559 6560 6561 6562 6563 6564 6565 .... 6605 6606 6607 6608 6609 6610 6611 6612 6613 6614 6615 6616 6617 6618 .... 6649 6650 6651 6652 6653 6654 6655 6656 6657 6658 6659 6660 6661 6662 .... 6682 6683 6684 6685 6686 6687 6688 6689 6690 6691 6692 6693 6694 6695 .... 6755 6756 6757 6758 6759 6760 6761 6762 6763 6764 6765 6766 6767 6768 .... 6783 6784 6785 6786 6787 6788 6789 6790 6791 6792 6793 6794 6795 6796 .... 6832 6833 6834 6835 6836 6837 6838 6839 6840 6841 6842 6843 6844 6845 .... 6867 6868 6869 6870 6871 6872 6873 6874 6875 6876 6877 6878 6879 6880 .... 6893 6894 6895 6896 6897 6898 6899 6900 6901 6902 6903 6904 6905 6906 .... 6952 6953 6954 6955 6956 6957 6958 6959 6960 6961 6962 6963 6964 6965 .... 6992 6993 6994 6995 6996 6997 6998 6999 7000 7001 7002 7003 7004 7005 .... 7074 7075 7076 7077 7078 7079 7080 7081 7082 7083 7084 7085 7086 7087 .... 7132 7133 7134 7135 7136 7137 7138 7139 7140 7141 7142 7143 7144 7145 .... 7222 7223 7224 7225 7226 7227 7228 7229 7230 7231 7232 7233 7234 7235 .... 7264 7265 7266 7267 7268 7269 7270 7271 7272 7273 7274 7275 7276 7277 .... 7297 7298 7299 7300 7301 7302 7303 7304 7305 7306 7307 7308 7309 7310 .... 7327 7328 7329 7330 7331 7332 7333 7334 7335 7336 7337 7338 7339 7340 .... 7376 7377 7378 7379 7380 7381 7382 7383 7384 7385 7386 7387 7388 7389 .... 7406 7407 7408 7409 7410 7411 7412 7413 7414 7415 7416 7417 7418 7419 .... 7691 7692 7693 7694 7695 7696 7697 7698 7699 7700 7701 7702 7703 7704 .... 7917 7918 7919 7920 7921 7922 7923 7924 7925 7926 7927 7928 7929 7930 .... 7991 7992 7993 7994 7995 7996 7997 7998 7999 8000 8001 8002 8003 8004 .... 8081 8082 8083 8084 8085 8086 8087 8088 8089 8090 8091 8092 8093 8094 .... 8108 8109 8110 8111 8112 8113 8114 8115 8116 8117 8118 8119 8120 8121 .... 8160 8161 8162 8163 8164 8165 8166 8167 8168 8169 8170 8171 8172 8173 .... 8195 8196 8197 8198 8199 8200 8201 8202 8203 8204 8205 8206 8207 8208 .... 8257 8258 8259 8260 8261 8262 8263 8264 8265 8266 8267 8268 8269 8270 .... 8295 8296 8297 8298 8299 8300 8301 8302 8303 8304 8305 8306 8307 8308 .... 8405 8406 8407 8408 8409 8410 8411 8412 8413 8414 8415 8416 8417 8418 .... 8424 8425 8426 8427 8428 8429 8430 8431 8432 8433 8434 8435 8436 8437 8438 .... 8658 8659 8660 8661 8662 8663 8664 8665 8666 8667 8668 8669 8670 8671 .... 8748 8749 8750 8751 8752 8753 8754 8755 8756 8757 8758 8759 8760 8761 .... 8828 8829 8830 8831 8832 8833 8834 8835 8836 8837 8838 8839 8840 8841 .... 8912 8913 8914 8915 8916 8917 8918 8919 8920 8921 8922 8923 8924 8925 .... 9002 9003 9004 9005 9006 9007 9008 9009 9010 9011 9012 9013 9014 9015 .... 9027 9028 9029 9030 9031 9032 9033 9034 9035 9036 9037 9038 9039 9040 9041 9042 9043 9044 9045 9046 9047 9048   /* generic reply for invalid code */ return "Invalid error code"; } #endif /* End: bn_error.c */ /* Start: bn_fast_mp_invmod.c */ #include #ifdef BN_FAST_MP_INVMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ c->sign = neg; res = MP_OKAY; LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); return res; } #endif /* End: bn_fast_mp_invmod.c */ /* Start: bn_fast_mp_montgomery_reduce.c */ #include #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* if A >= m then A = A - m */ if (mp_cmp_mag (x, n) != MP_LT) { return s_mp_sub (x, n, x); } return MP_OKAY; } #endif /* End: bn_fast_mp_montgomery_reduce.c */ /* Start: bn_fast_s_mp_mul_digs.c */ #include #ifdef BN_FAST_S_MP_MUL_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ while (tx++ < a->used && ty-- >= 0) { ... } */ iy = MIN(a->used-tx, ty+1); /* execute loop */ for (iz = 0; iz < iy; ++iz) { _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); } /* store term */ W[ix] = ((mp_digit)_W) & MP_MASK; /* make next carry */ _W = _W >> ((mp_word)DIGIT_BIT); ................................................................................ *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } #endif /* End: bn_fast_s_mp_mul_digs.c */ /* Start: bn_fast_s_mp_mul_high_digs.c */ #include #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } #endif /* End: bn_fast_s_mp_mul_high_digs.c */ /* Start: bn_fast_s_mp_sqr.c */ #include #ifdef BN_FAST_S_MP_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } } mp_clamp (b); return MP_OKAY; } #endif /* End: bn_fast_s_mp_sqr.c */ /* Start: bn_mp_2expt.c */ #include #ifdef BN_MP_2EXPT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ /* put the single bit in its place */ a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); return MP_OKAY; } #endif /* End: bn_mp_2expt.c */ /* Start: bn_mp_abs.c */ #include #ifdef BN_MP_ABS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ /* force the sign of b to positive */ b->sign = MP_ZPOS; return MP_OKAY; } #endif /* End: bn_mp_abs.c */ /* Start: bn_mp_add.c */ #include #ifdef BN_MP_ADD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ res = s_mp_sub (a, b, c); } } return res; } #endif /* End: bn_mp_add.c */ /* Start: bn_mp_add_d.c */ #include #ifdef BN_MP_ADD_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clamp(c); return MP_OKAY; } #endif /* End: bn_mp_add_d.c */ /* Start: bn_mp_addmod.c */ #include #ifdef BN_MP_ADDMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return res; } res = mp_mod (&t, c, d); mp_clear (&t); return res; } #endif /* End: bn_mp_addmod.c */ /* Start: bn_mp_and.c */ #include #ifdef BN_MP_AND_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } #endif /* End: bn_mp_and.c */ /* Start: bn_mp_clamp.c */ #include #ifdef BN_MP_CLAMP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ /* reset the sign flag if used == 0 */ if (a->used == 0) { a->sign = MP_ZPOS; } } #endif /* End: bn_mp_clamp.c */ /* Start: bn_mp_clear.c */ #include #ifdef BN_MP_CLEAR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ a->dp = NULL; a->alloc = a->used = 0; a->sign = MP_ZPOS; } } #endif /* End: bn_mp_clear.c */ /* Start: bn_mp_clear_multi.c */ #include #ifdef BN_MP_CLEAR_MULTI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ while (next_mp != NULL) { mp_clear(next_mp); next_mp = va_arg(args, mp_int*); } va_end(args); } #endif /* End: bn_mp_clear_multi.c */ /* Start: bn_mp_cmp.c */ #include #ifdef BN_MP_CMP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ return mp_cmp_mag(b, a); } else { return mp_cmp_mag(a, b); } } #endif /* End: bn_mp_cmp.c */ /* Start: bn_mp_cmp_d.c */ #include #ifdef BN_MP_CMP_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } else if (a->dp[0] < b) { return MP_LT; } else { return MP_EQ; } } #endif /* End: bn_mp_cmp_d.c */ /* Start: bn_mp_cmp_mag.c */ #include #ifdef BN_MP_CMP_MAG_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ return MP_LT; } } return MP_EQ; } #endif /* End: bn_mp_cmp_mag.c */ /* Start: bn_mp_cnt_lsb.c */ #include #ifdef BN_MP_CNT_LSB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ q >>= 4; } while (qq == 0); } return x; } #endif /* End: bn_mp_cnt_lsb.c */ /* Start: bn_mp_copy.c */ #include #ifdef BN_MP_COPY_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* copy used count and sign */ b->used = a->used; b->sign = a->sign; return MP_OKAY; } #endif /* End: bn_mp_copy.c */ /* Start: bn_mp_count_bits.c */ #include #ifdef BN_MP_COUNT_BITS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ while (q > ((mp_digit) 0)) { ++r; q >>= ((mp_digit) 1); } return r; } #endif /* End: bn_mp_count_bits.c */ /* Start: bn_mp_div.c */ #include #ifdef BN_MP_DIV_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ return res; } #endif #endif /* End: bn_mp_div.c */ /* Start: bn_mp_div_2.c */ #include #ifdef BN_MP_DIV_2_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } } b->sign = a->sign; mp_clamp (b); return MP_OKAY; } #endif /* End: bn_mp_div_2.c */ /* Start: bn_mp_div_2d.c */ #include #ifdef BN_MP_DIV_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_exch (&t, d); } mp_clear (&t); return MP_OKAY; } #endif /* End: bn_mp_div_2d.c */ /* Start: bn_mp_div_3.c */ #include #ifdef BN_MP_DIV_3_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } mp_clear(&q); return res; } #endif /* End: bn_mp_div_3.c */ /* Start: bn_mp_div_d.c */ #include #ifdef BN_MP_DIV_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clear(&q); return res; } #endif /* End: bn_mp_div_d.c */ /* Start: bn_mp_dr_is_modulus.c */ #include #ifdef BN_MP_DR_IS_MODULUS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return 0; } } return 1; } #endif /* End: bn_mp_dr_is_modulus.c */ /* Start: bn_mp_dr_reduce.c */ #include #ifdef BN_MP_DR_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ s_mp_sub(x, n, x); goto top; } return MP_OKAY; } #endif /* End: bn_mp_dr_reduce.c */ /* Start: bn_mp_dr_setup.c */ #include #ifdef BN_MP_DR_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * the number of bits in a mp_digit [e.g. DIGIT_BIT==31] */ *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - ((mp_word)a->dp[0])); } #endif /* End: bn_mp_dr_setup.c */ /* Start: bn_mp_exch.c */ #include #ifdef BN_MP_EXCH_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_int t; t = *a; *a = *b; *b = t; } #endif /* End: bn_mp_exch.c */ /* Start: bn_mp_expt_d.c */ #include #ifdef BN_MP_EXPT_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ b <<= 1; } mp_clear (&g); return MP_OKAY; } #endif /* End: bn_mp_expt_d.c */ /* Start: bn_mp_exptmod.c */ #include #ifdef BN_MP_EXPTMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ #else /* no invmod */ return MP_VAL; #endif } /* modified diminished radix reduction */ #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) if (mp_reduce_is_2k_l(P) == MP_YES) { return s_mp_exptmod(G, X, P, Y, 1); } #endif #ifdef BN_MP_DR_IS_MODULUS_C /* is it a DR modulus? */ ................................................................................ #endif #ifdef BN_MP_EXPTMOD_FAST_C } #endif } #endif /* End: bn_mp_exptmod.c */ /* Start: bn_mp_exptmod_fast.c */ #include #ifdef BN_MP_EXPTMOD_FAST_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clear (&M[x]); } return err; } #endif /* End: bn_mp_exptmod_fast.c */ /* Start: bn_mp_exteuclid.c */ #include #ifdef BN_MP_EXTEUCLID_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ err = MP_OKAY; _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); return err; } #endif /* End: bn_mp_exteuclid.c */ /* Start: bn_mp_fread.c */ #include #ifdef BN_MP_FREAD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } return MP_OKAY; } #endif /* End: bn_mp_fread.c */ /* Start: bn_mp_fwrite.c */ #include #ifdef BN_MP_FWRITE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } XFREE (buf); return MP_OKAY; } #endif /* End: bn_mp_fwrite.c */ /* Start: bn_mp_gcd.c */ #include #ifdef BN_MP_GCD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ res = MP_OKAY; LBL_V:mp_clear (&u); LBL_U:mp_clear (&v); return res; } #endif /* End: bn_mp_gcd.c */ /* Start: bn_mp_get_int.c */ #include #ifdef BN_MP_GET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ res = (res << DIGIT_BIT) | DIGIT(a,i); } /* force result to 32-bits always so it is consistent on non 32-bit platforms */ return res & 0xFFFFFFFFUL; } #endif /* End: bn_mp_get_int.c */ /* Start: bn_mp_grow.c */ #include #ifdef BN_MP_GROW_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ a->dp[i] = 0; } } return MP_OKAY; } #endif /* End: bn_mp_grow.c */ /* Start: bn_mp_init.c */ #include #ifdef BN_MP_INIT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ a->alloc = MP_PREC; a->sign = MP_ZPOS; return MP_OKAY; } #endif /* End: bn_mp_init.c */ /* Start: bn_mp_init_copy.c */ #include #ifdef BN_MP_INIT_COPY_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ if ((res = mp_init (a)) != MP_OKAY) { return res; } return mp_copy (b, a); } #endif /* End: bn_mp_init_copy.c */ /* Start: bn_mp_init_multi.c */ #include #ifdef BN_MP_INIT_MULTI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } va_end(args); return res; /* Assumed ok, if error flagged above. */ } #endif /* End: bn_mp_init_multi.c */ /* Start: bn_mp_init_set.c */ #include #ifdef BN_MP_INIT_SET_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return err; } mp_set(a, b); return err; } #endif /* End: bn_mp_init_set.c */ /* Start: bn_mp_init_set_int.c */ #include #ifdef BN_MP_INIT_SET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ int err; if ((err = mp_init(a)) != MP_OKAY) { return err; } return mp_set_int(a, b); } #endif /* End: bn_mp_init_set_int.c */ /* Start: bn_mp_init_size.c */ #include #ifdef BN_MP_INIT_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ a->dp[x] = 0; } return MP_OKAY; } #endif /* End: bn_mp_init_size.c */ /* Start: bn_mp_invmod.c */ #include #ifdef BN_MP_INVMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ #ifdef BN_MP_INVMOD_SLOW_C return mp_invmod_slow(a, b, c); #endif return MP_VAL; } #endif /* End: bn_mp_invmod.c */ /* Start: bn_mp_invmod_slow.c */ #include #ifdef BN_MP_INVMOD_SLOW_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_exch (&C, c); res = MP_OKAY; LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); return res; } #endif /* End: bn_mp_invmod_slow.c */ /* Start: bn_mp_is_square.c */ #include #ifdef BN_MP_IS_SQUARE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO; ERR:mp_clear(&t); return res; } #endif /* End: bn_mp_is_square.c */ /* Start: bn_mp_jacobi.c */ #include #ifdef BN_MP_JACOBI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ res = MP_OKAY; LBL_P1:mp_clear (&p1); LBL_A1:mp_clear (&a1); return res; } #endif /* End: bn_mp_jacobi.c */ /* Start: bn_mp_karatsuba_mul.c */ #include #ifdef BN_MP_KARATSUBA_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * let n represent half of the number of digits in * the min(a,b) * * a = a1 * B**n + a0 * b = b1 * B**n + b0 * * Then, a * b => a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0 * * Note that a1b1 and a0b0 are used twice and only need to be * computed once. So in total three half size (half # of * digit) multiplications are performed, a0b0, a1b1 and * (a1-b1)(a0-b0) * * Note that a multiplication of half the digits requires * 1/4th the number of single precision multiplications so in * total after one call 25% of the single precision multiplications * are saved. Note also that the call to mp_mul can end up back * in this function if the a0, a1, b0, or b1 are above the threshold. * This is known as divide-and-conquer and leads to the famous ................................................................................ /* now calc the products x0y0 and x1y1 */ /* after this x0 is no longer required, free temp [x0==t2]! */ if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY) goto X1Y1; /* x0y0 = x0*y0 */ if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) goto X1Y1; /* x1y1 = x1*y1 */ /* now calc x1-x0 and y1-y0 */ if (mp_sub (&x1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = x1 - x0 */ if (mp_sub (&y1, &y0, &x0) != MP_OKAY) goto X1Y1; /* t2 = y1 - y0 */ if (mp_mul (&t1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */ /* add x0y0 */ if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) goto X1Y1; /* t2 = x0y0 + x1y1 */ if (mp_sub (&x0, &t1, &t1) != MP_OKAY) goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))< #ifdef BN_MP_KARATSUBA_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* now calc the products x0*x0 and x1*x1 */ if (mp_sqr (&x0, &x0x0) != MP_OKAY) goto X1X1; /* x0x0 = x0*x0 */ if (mp_sqr (&x1, &x1x1) != MP_OKAY) goto X1X1; /* x1x1 = x1*x1 */ /* now calc (x1-x0)**2 */ if (mp_sub (&x1, &x0, &t1) != MP_OKAY) goto X1X1; /* t1 = x1 - x0 */ if (mp_sqr (&t1, &t1) != MP_OKAY) goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ /* add x0y0 */ if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY) goto X1X1; /* t2 = x0x0 + x1x1 */ if (mp_sub (&t2, &t1, &t1) != MP_OKAY) goto X1X1; /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))< #ifdef BN_MP_LCM_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ c->sign = MP_ZPOS; LBL_T: mp_clear_multi (&t1, &t2, NULL); return res; } #endif /* End: bn_mp_lcm.c */ /* Start: bn_mp_lshd.c */ #include #ifdef BN_MP_LSHD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ *top++ = 0; } } return MP_OKAY; } #endif /* End: bn_mp_lshd.c */ /* Start: bn_mp_mod.c */ #include #ifdef BN_MP_MOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ mp_exch (&t, c); } mp_clear (&t); return res; } #endif /* End: bn_mp_mod.c */ /* Start: bn_mp_mod_2d.c */ #include #ifdef BN_MP_MOD_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ c->dp[b / DIGIT_BIT] &= (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1)); mp_clamp (c); return MP_OKAY; } #endif /* End: bn_mp_mod_2d.c */ /* Start: bn_mp_mod_d.c */ #include #ifdef BN_MP_MOD_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ int mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) { return mp_div_d(a, b, NULL, c); } #endif /* End: bn_mp_mod_d.c */ /* Start: bn_mp_montgomery_calc_normalization.c */ #include #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } } } return MP_OKAY; } #endif /* End: bn_mp_montgomery_calc_normalization.c */ /* Start: bn_mp_montgomery_reduce.c */ #include #ifdef BN_MP_MONTGOMERY_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ if (mp_cmp_mag (x, n) != MP_LT) { return s_mp_sub (x, n, x); } return MP_OKAY; } #endif /* End: bn_mp_montgomery_reduce.c */ /* Start: bn_mp_montgomery_setup.c */ #include #ifdef BN_MP_MONTGOMERY_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* rho = -1/m mod b */ *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; return MP_OKAY; } #endif /* End: bn_mp_montgomery_setup.c */ /* Start: bn_mp_mul.c */ #include #ifdef BN_MP_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ #endif } c->sign = (c->used > 0) ? neg : MP_ZPOS; return res; } #endif /* End: bn_mp_mul.c */ /* Start: bn_mp_mul_2.c */ #include #ifdef BN_MP_MUL_2_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ *tmpb++ = 0; } } b->sign = a->sign; return MP_OKAY; } #endif /* End: bn_mp_mul_2.c */ /* Start: bn_mp_mul_2d.c */ #include #ifdef BN_MP_MUL_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } } mp_clamp (c); return MP_OKAY; } #endif /* End: bn_mp_mul_2d.c */ /* Start: bn_mp_mul_d.c */ #include #ifdef BN_MP_MUL_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ c->used = a->used + 1; mp_clamp(c); return MP_OKAY; } #endif /* End: bn_mp_mul_d.c */ /* Start: bn_mp_mulmod.c */ #include #ifdef BN_MP_MULMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* d = a * b (mod c) */ int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) { int res; mp_int t; if ((res = mp_init (&t)) != MP_OKAY) { return res; } ................................................................................ return res; } res = mp_mod (&t, c, d); mp_clear (&t); return res; } #endif /* End: bn_mp_mulmod.c */ /* Start: bn_mp_n_root.c */ #include #ifdef BN_MP_N_ROOT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ LBL_T3:mp_clear (&t3); LBL_T2:mp_clear (&t2); LBL_T1:mp_clear (&t1); return res; } #endif /* End: bn_mp_n_root.c */ /* Start: bn_mp_neg.c */ #include #ifdef BN_MP_NEG_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } else { b->sign = MP_ZPOS; } return MP_OKAY; } #endif /* End: bn_mp_neg.c */ /* Start: bn_mp_or.c */ #include #ifdef BN_MP_OR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } #endif /* End: bn_mp_or.c */ /* Start: bn_mp_prime_fermat.c */ #include #ifdef BN_MP_PRIME_FERMAT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ err = MP_OKAY; LBL_T:mp_clear (&t); return err; } #endif /* End: bn_mp_prime_fermat.c */ /* Start: bn_mp_prime_is_divisible.c */ #include #ifdef BN_MP_PRIME_IS_DIVISIBLE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return MP_OKAY; } } return MP_OKAY; } #endif /* End: bn_mp_prime_is_divisible.c */ /* Start: bn_mp_prime_is_prime.c */ #include #ifdef BN_MP_PRIME_IS_PRIME_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* passed the test */ *result = MP_YES; LBL_B:mp_clear (&b); return err; } #endif /* End: bn_mp_prime_is_prime.c */ /* Start: bn_mp_prime_miller_rabin.c */ #include #ifdef BN_MP_PRIME_MILLER_RABIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ *result = MP_YES; LBL_Y:mp_clear (&y); LBL_R:mp_clear (&r); LBL_N1:mp_clear (&n1); return err; } #endif /* End: bn_mp_prime_miller_rabin.c */ /* Start: bn_mp_prime_next_prime.c */ #include #ifdef BN_MP_PRIME_NEXT_PRIME_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ err = MP_OKAY; LBL_ERR: mp_clear(&b); return err; } #endif /* End: bn_mp_prime_next_prime.c */ /* Start: bn_mp_prime_rabin_miller_trials.c */ #include #ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } } return sizes[x-1].t + 1; } #endif /* End: bn_mp_prime_rabin_miller_trials.c */ /* Start: bn_mp_prime_random_ex.c */ #include #ifdef BN_MP_PRIME_RANDOM_EX_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* calc the maskAND value for the MSbyte*/ maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7))); /* calc the maskOR_msb */ maskOR_msb = 0; maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; if (flags & LTM_PRIME_2MSB_ON) { maskOR_msb |= 1 << ((size - 2) & 7); } else if (flags & LTM_PRIME_2MSB_OFF) { maskAND &= ~(1 << ((size - 2) & 7)); } /* get the maskOR_lsb */ maskOR_lsb = 1; if (flags & LTM_PRIME_BBS) { maskOR_lsb |= 3; } ................................................................................ error: XFREE(tmp); return err; } #endif /* End: bn_mp_prime_random_ex.c */ /* Start: bn_mp_radix_size.c */ #include #ifdef BN_MP_RADIX_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* return digs + 1, the 1 is for the NULL byte that would be required. */ *size = digs + 1; return MP_OKAY; } #endif /* End: bn_mp_radix_size.c */ /* Start: bn_mp_radix_smap.c */ #include #ifdef BN_MP_RADIX_SMAP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* chars used in radix conversions */ const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; #endif /* End: bn_mp_radix_smap.c */ /* Start: bn_mp_rand.c */ #include #ifdef BN_MP_RAND_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ return res; } } return MP_OKAY; } #endif /* End: bn_mp_rand.c */ /* Start: bn_mp_read_radix.c */ #include #ifdef BN_MP_READ_RADIX_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ if (mp_iszero(a) != 1) { a->sign = neg; } return MP_OKAY; } #endif /* End: bn_mp_read_radix.c */ /* Start: bn_mp_read_signed_bin.c */ #include #ifdef BN_MP_READ_SIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* read signed bin, big endian, first byte is 0==positive or 1==negative */ int mp_read_signed_bin (mp_int * a, unsigned char *b, int c) { int res; /* read magnitude */ if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) { return res; } ................................................................................ } else { a->sign = MP_NEG; } return MP_OKAY; } #endif /* End: bn_mp_read_signed_bin.c */ /* Start: bn_mp_read_unsigned_bin.c */ #include #ifdef BN_MP_READ_UNSIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* reads a unsigned char array, assumes the msb is stored first [big endian] */ int mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c) { int res; /* make sure there are at least two digits */ if (a->alloc < 2) { if ((res = mp_grow(a, 2)) != MP_OKAY) { return res; ................................................................................ a->used += 2; #endif } mp_clamp (a); return MP_OKAY; } #endif /* End: bn_mp_read_unsigned_bin.c */ /* Start: bn_mp_reduce.c */ #include #ifdef BN_MP_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ CLEANUP: mp_clear (&q); return res; } #endif /* End: bn_mp_reduce.c */ /* Start: bn_mp_reduce_2k.c */ #include #ifdef BN_MP_REDUCE_2K_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ ERR: mp_clear(&q); return res; } #endif /* End: bn_mp_reduce_2k.c */ /* Start: bn_mp_reduce_2k_l.c */ #include #ifdef BN_MP_REDUCE_2K_L_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ ERR: mp_clear(&q); return res; } #endif /* End: bn_mp_reduce_2k_l.c */ /* Start: bn_mp_reduce_2k_setup.c */ #include #ifdef BN_MP_REDUCE_2K_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ *d = tmp.dp[0]; mp_clear(&tmp); return MP_OKAY; } #endif /* End: bn_mp_reduce_2k_setup.c */ /* Start: bn_mp_reduce_2k_setup_l.c */ #include #ifdef BN_MP_REDUCE_2K_SETUP_L_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } ERR: mp_clear(&tmp); return res; } #endif /* End: bn_mp_reduce_2k_setup_l.c */ /* Start: bn_mp_reduce_is_2k.c */ #include #ifdef BN_MP_REDUCE_IS_2K_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } } return MP_YES; } #endif /* End: bn_mp_reduce_is_2k.c */ /* Start: bn_mp_reduce_is_2k_l.c */ #include #ifdef BN_MP_REDUCE_IS_2K_L_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } return MP_NO; } #endif /* End: bn_mp_reduce_is_2k_l.c */ /* Start: bn_mp_reduce_setup.c */ #include #ifdef BN_MP_REDUCE_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) { return res; } return mp_div (a, b, a, NULL); } #endif /* End: bn_mp_reduce_setup.c */ /* Start: bn_mp_rshd.c */ #include #ifdef BN_MP_RSHD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } /* remove excess digits */ a->used -= b; } #endif /* End: bn_mp_rshd.c */ /* Start: bn_mp_set.c */ #include #ifdef BN_MP_SET_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ void mp_set (mp_int * a, mp_digit b) { mp_zero (a); a->dp[0] = b & MP_MASK; a->used = (a->dp[0] != 0) ? 1 : 0; } #endif /* End: bn_mp_set.c */ /* Start: bn_mp_set_int.c */ #include #ifdef BN_MP_SET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ a->used += 1; } mp_clamp (a); return MP_OKAY; } #endif /* End: bn_mp_set_int.c */ /* Start: bn_mp_shrink.c */ #include #ifdef BN_MP_SHRINK_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ a->dp = tmp; a->alloc = a->used; } return MP_OKAY; } #endif /* End: bn_mp_shrink.c */ /* Start: bn_mp_signed_bin_size.c */ #include #ifdef BN_MP_SIGNED_BIN_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ /* get the size for an signed equivalent */ int mp_signed_bin_size (mp_int * a) { return 1 + mp_unsigned_bin_size (a); } #endif /* End: bn_mp_signed_bin_size.c */ /* Start: bn_mp_sqr.c */ #include #ifdef BN_MP_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ #endif } b->sign = MP_ZPOS; return res; } #endif /* End: bn_mp_sqr.c */ /* Start: bn_mp_sqrmod.c */ #include #ifdef BN_MP_SQRMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return res; } res = mp_mod (&t, b, c); mp_clear (&t); return res; } #endif /* End: bn_mp_sqrmod.c */ /* Start: bn_mp_sqrt.c */ #include #ifdef BN_MP_SQRT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ E1: mp_clear(&t2); E2: mp_clear(&t1); return res; } #endif /* End: bn_mp_sqrt.c */ /* Start: bn_mp_sub.c */ #include #ifdef BN_MP_SUB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ res = s_mp_sub (b, a, c); } } return res; } #endif /* End: bn_mp_sub.c */ /* Start: bn_mp_sub_d.c */ #include #ifdef BN_MP_SUB_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } mp_clamp(c); return MP_OKAY; } #endif /* End: bn_mp_sub_d.c */ /* Start: bn_mp_submod.c */ #include #ifdef BN_MP_SUBMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } res = mp_mod (&t, c, d); mp_clear (&t); return res; } #endif /* End: bn_mp_submod.c */ /* Start: bn_mp_to_signed_bin.c */ #include #ifdef BN_MP_TO_SIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return res; } b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1); return MP_OKAY; } #endif /* End: bn_mp_to_signed_bin.c */ /* Start: bn_mp_to_signed_bin_n.c */ #include #ifdef BN_MP_TO_SIGNED_BIN_N_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ if (*outlen < (unsigned long)mp_signed_bin_size(a)) { return MP_VAL; } *outlen = mp_signed_bin_size(a); return mp_to_signed_bin(a, b); } #endif /* End: bn_mp_to_signed_bin_n.c */ /* Start: bn_mp_to_unsigned_bin.c */ #include #ifdef BN_MP_TO_UNSIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } bn_reverse (b, x); mp_clear (&t); return MP_OKAY; } #endif /* End: bn_mp_to_unsigned_bin.c */ /* Start: bn_mp_to_unsigned_bin_n.c */ #include #ifdef BN_MP_TO_UNSIGNED_BIN_N_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) { return MP_VAL; } *outlen = mp_unsigned_bin_size(a); return mp_to_unsigned_bin(a, b); } #endif /* End: bn_mp_to_unsigned_bin_n.c */ /* Start: bn_mp_toom_mul.c */ #include #ifdef BN_MP_TOOM_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ &a0, &a1, &a2, &b0, &b1, &b2, &tmp1, &tmp2, NULL); return res; } #endif /* End: bn_mp_toom_mul.c */ /* Start: bn_mp_toom_sqr.c */ #include #ifdef BN_MP_TOOM_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ ERR: mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL); return res; } #endif /* End: bn_mp_toom_sqr.c */ /* Start: bn_mp_toradix.c */ #include #ifdef BN_MP_TORADIX_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ *str = '\0'; mp_clear (&t); return MP_OKAY; } #endif /* End: bn_mp_toradix.c */ /* Start: bn_mp_toradix_n.c */ #include #ifdef BN_MP_TORADIX_N_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clear (&t); return MP_OKAY; } #endif /* End: bn_mp_toradix_n.c */ /* Start: bn_mp_unsigned_bin_size.c */ #include #ifdef BN_MP_UNSIGNED_BIN_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ /* get the size for an unsigned equivalent */ int mp_unsigned_bin_size (mp_int * a) { int size = mp_count_bits (a); return (size / 8 + ((size & 7) != 0 ? 1 : 0)); } #endif /* End: bn_mp_unsigned_bin_size.c */ /* Start: bn_mp_xor.c */ #include #ifdef BN_MP_XOR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } #endif /* End: bn_mp_xor.c */ /* Start: bn_mp_zero.c */ #include #ifdef BN_MP_ZERO_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ tmp = a->dp; for (n = 0; n < a->alloc; n++) { *tmp++ = 0; } } #endif /* End: bn_mp_zero.c */ /* Start: bn_prime_tab.c */ #include #ifdef BN_PRIME_TAB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 #endif }; #endif /* End: bn_prime_tab.c */ /* Start: bn_reverse.c */ #include #ifdef BN_REVERSE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ s[ix] = s[iy]; s[iy] = t; ++ix; --iy; } } #endif /* End: bn_reverse.c */ /* Start: bn_s_mp_add.c */ #include #ifdef BN_S_MP_ADD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } mp_clamp (c); return MP_OKAY; } #endif /* End: bn_s_mp_add.c */ /* Start: bn_s_mp_exptmod.c */ #include #ifdef BN_S_MP_EXPTMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #ifdef MP_LOW_MEM #define TAB_SIZE 32 #else #define TAB_SIZE 256 #endif int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) ................................................................................ for (x = 1<<(winsize-1); x < (1 << winsize); x++) { mp_clear (&M[x]); } return err; } #endif /* End: bn_s_mp_exptmod.c */ /* Start: bn_s_mp_mul_digs.c */ #include #ifdef BN_S_MP_MUL_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ mp_exch (&t, c); mp_clear (&t); return MP_OKAY; } #endif /* End: bn_s_mp_mul_digs.c */ /* Start: bn_s_mp_mul_high_digs.c */ #include #ifdef BN_S_MP_MUL_HIGH_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } mp_clamp (&t); mp_exch (&t, c); mp_clear (&t); return MP_OKAY; } #endif /* End: bn_s_mp_mul_high_digs.c */ /* Start: bn_s_mp_sqr.c */ #include #ifdef BN_S_MP_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clamp (&t); mp_exch (&t, b); mp_clear (&t); return MP_OKAY; } #endif /* End: bn_s_mp_sqr.c */ /* Start: bn_s_mp_sub.c */ #include #ifdef BN_S_MP_SUB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clamp (c); return MP_OKAY; } #endif /* End: bn_s_mp_sub.c */ /* Start: bncore.c */ #include #ifdef BNCORE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ */ /* Known optimal configurations CPU /Compiler /MUL CUTOFF/SQR CUTOFF ------------------------------------------------------------- Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) AMD Athlon64 /GCC v3.4.4 / 74/ 124/LTM 0.34 */ int KARATSUBA_MUL_CUTOFF = 74, /* Min. number of digits before Karatsuba multiplication is used. */ KARATSUBA_SQR_CUTOFF = 124, /* Min. number of digits before Karatsuba squaring is used. */ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ TOOM_SQR_CUTOFF = 400; #endif /* End: bncore.c */ /* EOF */   > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > | > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > | | | | | | | | > > > > | | | | > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > < | > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > | < < | > > > > > > > > > > > > > > > > > > > > < | > > > > < | > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > | | | > > > >  39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 ... 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 ... 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 ... 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 ... 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 ... 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 ... 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 ... 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 ... 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 ... 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 ... 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 .... 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 .... 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 .... 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 .... 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 .... 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 .... 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 .... 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 .... 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 .... 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 .... 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 .... 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 .... 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 .... 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 .... 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 .... 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 .... 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 .... 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 .... 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 .... 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 .... 2429 2430 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 .... 2490 2491 2492 2493 2494 2495 2496 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 .... 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 .... 2606 2607 2608 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 .... 2932 2933 2934 2935 2936 2937 2938 2939 2940 2941 2942 2943 2944 2945 2946 2947 2948 2949 .... 3018 3019 3020 3021 3022 3023 3024 3025 3026 3027 3028 3029 3030 3031 3032 3033 3034 3035 .... 3089 3090 3091 3092 3093 3094 3095 3096 3097 3098 3099 3100 3101 3102 3103 3104 3105 3106 .... 3144 3145 3146 3147 3148 3149 3150 3151 3152 3153 3154 3155 3156 3157 3158 3159 3160 3161 .... 3262 3263 3264 3265 3266 3267 3268 3269 3270 3271 3272 3273 3274 3275 3276 3277 3278 3279 .... 3310 3311 3312 3313 3314 3315 3316 3317 3318 3319 3320 3321 3322 3323 3324 3325 3326 3327 .... 3372 3373 3374 3375 3376 3377 3378 3379 3380 3381 3382 3383 3384 3385 3386 3387 3388 3389 .... 3422 3423 3424 3425 3426 3427 3428 3429 3430 3431 3432 3433 3434 3435 3436 3437 3438 3439 .... 3457 3458 3459 3460 3461 3462 3463 3464 3465 3466 3467 3468 3469 3470 3471 3472 3473 3474 .... 3521 3522 3523 3524 3525 3526 3527 3528 3529 3530 3531 3532 3533 3534 3535 3536 3537 3538 .... 3557 3558 3559 3560 3561 3562 3563 3564 3565 3566 3567 3568 3569 3570 3571 3572 3573 3574 .... 3591 3592 3593 3594 3595 3596 3597 3598 3599 3600 3601 3602 3603 3604 3605 3606 3607 3608 .... 3644 3645 3646 3647 3648 3649 3650 3651 3652 3653 3654 3655 3656 3657 3658 3659 3660 3661 .... 3690 3691 3692 3693 3694 3695 3696 3697 3698 3699 3700 3701 3702 3703 3704 3705 3706 3707 .... 3870 3871 3872 3873 3874 3875 3876 3877 3878 3879 3880 3881 3882 3883 3884 3885 3886 3887 .... 3983 3984 3985 3986 3987 3988 3989 3990 3991 3992 3993 3994 3995 3996 3997 3998 3999 4000 .... 4092 4093 4094 4095 4096 4097 4098 4099 4100 4101 4102 4103 4104 4105 4106 4107 4108 4109 .... 4127 4128 4129 4130 4131 4132 4133 4134 4135 4136 4137 4138 4139 4140 4141 4142 4143 4144 4145 4146 .... 4223 4224 4225 4226 4227 4228 4229 4230 4231 4232 4233 4234 4235 4236 4237 4238 4239 4240 4241 4242 4243 4244 4245 4246 4247 4248 4249 .... 4262 4263 4264 4265 4266 4267 4268 4269 4270 4271 4272 4273 4274 4275 4276 4277 4278 4279 .... 4352 4353 4354 4355 4356 4357 4358 4359 4360 4361 4362 4363 4364 4365 4366 4367 4368 4369 4370 4371 4372 4373 4374 4375 4376 .... 4387 4388 4389 4390 4391 4392 4393 4394 4395 4396 4397 4398 4399 4400 4401 4402 4403 4404 .... 4451 4452 4453 4454 4455 4456 4457 4458 4459 4460 4461 4462 4463 4464 4465 4466 4467 4468 .... 4523 4524 4525 4526 4527 4528 4529 4530 4531 4532 4533 4534 4535 4536 4537 4538 4539 4540 .... 4574 4575 4576 4577 4578 4579 4580 4581 4582 4583 4584 4585 4586 4587 4588 4589 4590 4591 .... 4634 4635 4636 4637 4638 4639 4640 4641 4642 4643 4644 4645 4646 4647 4648 4649 4650 4651 .... 4664 4665 4666 4667 4668 4669 4670 4671 4672 4673 4674 4675 4676 4677 4678 4679 4680 4681 .... 4727 4728 4729 4730 4731 4732 4733 4734 4735 4736 4737 4738 4739 4740 4741 4742 4743 4744 .... 4849 4850 4851 4852 4853 4854 4855 4856 4857 4858 4859 4860 4861 4862 4863 4864 4865 4866 .... 4912 4913 4914 4915 4916 4917 4918 4919 4920 4921 4922 4923 4924 4925 4926 4927 4928 4929 .... 4982 4983 4984 4985 4986 4987 4988 4989 4990 4991 4992 4993 4994 4995 4996 4997 4998 4999 .... 5068 5069 5070 5071 5072 5073 5074 5075 5076 5077 5078 5079 5080 5081 5082 5083 5084 5085 .... 5158 5159 5160 5161 5162 5163 5164 5165 5166 5167 5168 5169 5170 5171 5172 5173 5174 5175 .... 5241 5242 5243 5244 5245 5246 5247 5248 5249 5250 5251 5252 5253 5254 5255 5256 5257 5258 .... 5266 5267 5268 5269 5270 5271 5272 5273 5274 5275 5276 5277 5278 5279 5280 .... 5284 5285 5286 5287 5288 5289 5290 5291 5292 5293 5294 5295 5296 5297 5298 5299 5300 5301 .... 5421 5422 5423 5424 5425 5426 5427 5428 5429 5430 5431 5432 5433 5434 5435 5436 5437 5438 .... 5464 5465 5466 5467 5468 5469 5470 5471 5472 5473 5474 5475 5476 5477 5478 5479 5480 5481 .... 5518 5519 5520 5521 5522 5523 5524 5525 5526 5527 5528 5529 5530 5531 5532 5533 5534 5535 .... 5585 5586 5587 5588 5589 5590 5591 5592 5593 5594 5595 5596 5597 5598 5599 5600 5601 5602 .... 5638 5639 5640 5641 5642 5643 5644 5645 5646 5647 5648 5649 5650 5651 5652 5653 5654 5655 .... 5725 5726 5727 5728 5729 5730 5731 5732 5733 5734 5735 5736 5737 5738 5739 5740 5741 5742 .... 5832 5833 5834 5835 5836 5837 5838 5839 5840 5841 5842 5843 5844 5845 5846 5847 5848 5849 .... 6006 6007 6008 6009 6010 6011 6012 6013 6014 6015 6016 6017 6018 6019 6020 6021 6022 6023 .... 6062 6063 6064 6065 6066 6067 6068 6069 6070 6071 6072 6073 6074 6075 6076 6077 6078 6079 .... 6134 6135 6136 6137 6138 6139 6140 6141 6142 6143 6144 6145 6146 6147 6148 6149 .... 6191 6192 6193 6194 6195 6196 6197 6198 6199 6200 6201 6202 6203 6204 6205 6206 6207 6208 .... 6274 6275 6276 6277 6278 6279 6280 6281 6282 6283 6284 6285 6286 6287 6288 6289 6290 6291 .... 6301 6302 6303 6304 6305 6306 6307 6308 6309 6310 6311 6312 6313 6314 6315 6316 6317 6318 .... 6360 6361 6362 6363 6364 6365 6366 6367 6368 6369 6370 6371 6372 6373 6374 6375 6376 6377 .... 6447 6448 6449 6450 6451 6452 6453 6454 6455 6456 6457 6458 6459 6460 6461 6462 6463 6464 .... 6472 6473 6474 6475 6476 6477 6478 6479 6480 6481 6482 6483 6484 6485 6486 .... 6491 6492 6493 6494 6495 6496 6497 6498 6499 6500 6501 6502 6503 6504 6505 6506 6507 6508 .... 6517 6518 6519 6520 6521 6522 6523 6524 6525 6526 6527 6528 6529 6530 6531 .... 6550 6551 6552 6553 6554 6555 6556 6557 6558 6559 6560 6561 6562 6563 6564 6565 6566 6567 .... 6655 6656 6657 6658 6659 6660 6661 6662 6663 6664 6665 6666 6667 6668 6669 6670 6671 6672 .... 6719 6720 6721 6722 6723 6724 6725 6726 6727 6728 6729 6730 6731 6732 6733 6734 6735 6736 .... 6786 6787 6788 6789 6790 6791 6792 6793 6794 6795 6796 6797 6798 6799 6800 6801 6802 6803 .... 6837 6838 6839 6840 6841 6842 6843 6844 6845 6846 6847 6848 6849 6850 6851 6852 6853 6854 .... 6884 6885 6886 6887 6888 6889 6890 6891 6892 6893 6894 6895 6896 6897 6898 6899 6900 6901 .... 6941 6942 6943 6944 6945 6946 6947 6948 6949 6950 6951 6952 6953 6954 6955 6956 6957 6958 .... 6989 6990 6991 6992 6993 6994 6995 6996 6997 6998 6999 7000 7001 7002 7003 7004 7005 7006 .... 7026 7027 7028 7029 7030 7031 7032 7033 7034 7035 7036 7037 7038 7039 7040 7041 7042 7043 .... 7103 7104 7105 7106 7107 7108 7109 7110 7111 7112 7113 7114 7115 7116 7117 7118 7119 7120 .... 7135 7136 7137 7138 7139 7140 7141 7142 7143 7144 7145 7146 7147 7148 7149 7150 7151 7152 .... 7188 7189 7190 7191 7192 7193 7194 7195 7196 7197 7198 7199 7200 7201 7202 7203 7204 7205 .... 7227 7228 7229 7230 7231 7232 7233 7234 7235 7236 7237 7238 7239 7240 7241 7242 7243 7244 .... 7257 7258 7259 7260 7261 7262 7263 7264 7265 7266 7267 7268 7269 7270 7271 7272 7273 7274 .... 7320 7321 7322 7323 7324 7325 7326 7327 7328 7329 7330 7331 7332 7333 7334 7335 7336 7337 .... 7364 7365 7366 7367 7368 7369 7370 7371 7372 7373 7374 7375 7376 7377 7378 7379 7380 7381 .... 7450 7451 7452 7453 7454 7455 7456 7457 7458 7459 7460 7461 7462 7463 7464 7465 7466 7467 .... 7512 7513 7514 7515 7516 7517 7518 7519 7520 7521 7522 7523 7524 7525 7526 7527 7528 7529 .... 7606 7607 7608 7609 7610 7611 7612 7613 7614 7615 7616 7617 7618 7619 7620 7621 7622 7623 .... 7652 7653 7654 7655 7656 7657 7658 7659 7660 7661 7662 7663 7664 7665 7666 7667 7668 7669 .... 7689 7690 7691 7692 7693 7694 7695 7696 7697 7698 7699 7700 7701 7702 7703 7704 7705 7706 .... 7723 7724 7725 7726 7727 7728 7729 7730 7731 7732 7733 7734 7735 7736 7737 7738 7739 7740 .... 7776 7777 7778 7779 7780 7781 7782 7783 7784 7785 7786 7787 7788 7789 7790 7791 7792 7793 .... 7810 7811 7812 7813 7814 7815 7816 7817 7818 7819 7820 7821 7822 7823 7824 7825 7826 7827 .... 8099 8100 8101 8102 8103 8104 8105 8106 8107 8108 8109 8110 8111 8112 8113 8114 8115 8116 .... 8329 8330 8331 8332 8333 8334 8335 8336 8337 8338 8339 8340 8341 8342 8343 8344 8345 8346 .... 8407 8408 8409 8410 8411 8412 8413 8414 8415 8416 8417 8418 8419 8420 8421 8422 8423 8424 .... 8501 8502 8503 8504 8505 8506 8507 8508 8509 8510 8511 8512 8513 8514 8515 8516 8517 8518 .... 8532 8533 8534 8535 8536 8537 8538 8539 8540 8541 8542 8543 8544 8545 8546 8547 8548 8549 .... 8588 8589 8590 8591 8592 8593 8594 8595 8596 8597 8598 8599 8600 8601 8602 8603 8604 8605 .... 8627 8628 8629 8630 8631 8632 8633 8634 8635 8636 8637 8638 8639 8640 8641 8642 8643 8644 .... 8693 8694 8695 8696 8697 8698 8699 8700 8701 8702 8703 8704 8705 8706 8707 8708 8709 8710 .... 8735 8736 8737 8738 8739 8740 8741 8742 8743 8744 8745 8746 8747 8748 8749 8750 8751 8752 .... 8849 8850 8851 8852 8853 8854 8855 8856 8857 8858 8859 8860 8861 8862 8863 8864 8865 8866 .... 8872 8873 8874 8875 8876 8877 8878 8879 8880 8881 8882 8883 8884 8885 .... 9105 9106 9107 9108 9109 9110 9111 9112 9113 9114 9115 9116 9117 9118 9119 9120 9121 9122 .... 9199 9200 9201 9202 9203 9204 9205 9206 9207 9208 9209 9210 9211 9212 9213 9214 9215 9216 .... 9283 9284 9285 9286 9287 9288 9289 9290 9291 9292 9293 9294 9295 9296 9297 9298 9299 9300 .... 9371 9372 9373 9374 9375 9376 9377 9378 9379 9380 9381 9382 9383 9384 9385 9386 9387 9388 .... 9465 9466 9467 9468 9469 9470 9471 9472 9473 9474 9475 9476 9477 9478 9479 9480 9481 9482 .... 9494 9495 9496 9497 9498 9499 9500 9501 9502 9503 9504 9505 9506 9507 9508 9509 9510 9511 9512 9513 9514 9515 9516 9517 9518 9519   /* generic reply for invalid code */ return "Invalid error code"; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_error.c */ /* Start: bn_fast_mp_invmod.c */ #include #ifdef BN_FAST_MP_INVMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ c->sign = neg; res = MP_OKAY; LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_fast_mp_invmod.c */ /* Start: bn_fast_mp_montgomery_reduce.c */ #include #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* if A >= m then A = A - m */ if (mp_cmp_mag (x, n) != MP_LT) { return s_mp_sub (x, n, x); } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_fast_mp_montgomery_reduce.c */ /* Start: bn_fast_s_mp_mul_digs.c */ #include #ifdef BN_FAST_S_MP_MUL_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ while (tx++ < a->used && ty-- >= 0) { ... } */ iy = MIN(a->used-tx, ty+1); /* execute loop */ for (iz = 0; iz < iy; ++iz) { _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); } /* store term */ W[ix] = ((mp_digit)_W) & MP_MASK; /* make next carry */ _W = _W >> ((mp_word)DIGIT_BIT); ................................................................................ *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_fast_s_mp_mul_digs.c */ /* Start: bn_fast_s_mp_mul_high_digs.c */ #include #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_fast_s_mp_mul_high_digs.c */ /* Start: bn_fast_s_mp_sqr.c */ #include #ifdef BN_FAST_S_MP_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } } mp_clamp (b); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_fast_s_mp_sqr.c */ /* Start: bn_mp_2expt.c */ #include #ifdef BN_MP_2EXPT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ /* put the single bit in its place */ a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_2expt.c */ /* Start: bn_mp_abs.c */ #include #ifdef BN_MP_ABS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ /* force the sign of b to positive */ b->sign = MP_ZPOS; return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_abs.c */ /* Start: bn_mp_add.c */ #include #ifdef BN_MP_ADD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ res = s_mp_sub (a, b, c); } } return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_add.c */ /* Start: bn_mp_add_d.c */ #include #ifdef BN_MP_ADD_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clamp(c); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_add_d.c */ /* Start: bn_mp_addmod.c */ #include #ifdef BN_MP_ADDMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return res; } res = mp_mod (&t, c, d); mp_clear (&t); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_addmod.c */ /* Start: bn_mp_and.c */ #include #ifdef BN_MP_AND_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_and.c */ /* Start: bn_mp_clamp.c */ #include #ifdef BN_MP_CLAMP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ /* reset the sign flag if used == 0 */ if (a->used == 0) { a->sign = MP_ZPOS; } } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_clamp.c */ /* Start: bn_mp_clear.c */ #include #ifdef BN_MP_CLEAR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ a->dp = NULL; a->alloc = a->used = 0; a->sign = MP_ZPOS; } } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_clear.c */ /* Start: bn_mp_clear_multi.c */ #include #ifdef BN_MP_CLEAR_MULTI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ while (next_mp != NULL) { mp_clear(next_mp); next_mp = va_arg(args, mp_int*); } va_end(args); } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_clear_multi.c */ /* Start: bn_mp_cmp.c */ #include #ifdef BN_MP_CMP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ return mp_cmp_mag(b, a); } else { return mp_cmp_mag(a, b); } } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_cmp.c */ /* Start: bn_mp_cmp_d.c */ #include #ifdef BN_MP_CMP_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } else if (a->dp[0] < b) { return MP_LT; } else { return MP_EQ; } } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_cmp_d.c */ /* Start: bn_mp_cmp_mag.c */ #include #ifdef BN_MP_CMP_MAG_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ return MP_LT; } } return MP_EQ; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_cmp_mag.c */ /* Start: bn_mp_cnt_lsb.c */ #include #ifdef BN_MP_CNT_LSB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ q >>= 4; } while (qq == 0); } return x; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_cnt_lsb.c */ /* Start: bn_mp_copy.c */ #include #ifdef BN_MP_COPY_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* copy used count and sign */ b->used = a->used; b->sign = a->sign; return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_copy.c */ /* Start: bn_mp_count_bits.c */ #include #ifdef BN_MP_COUNT_BITS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ while (q > ((mp_digit) 0)) { ++r; q >>= ((mp_digit) 1); } return r; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_count_bits.c */ /* Start: bn_mp_div.c */ #include #ifdef BN_MP_DIV_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ return res; } #endif #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_div.c */ /* Start: bn_mp_div_2.c */ #include #ifdef BN_MP_DIV_2_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } } b->sign = a->sign; mp_clamp (b); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_div_2.c */ /* Start: bn_mp_div_2d.c */ #include #ifdef BN_MP_DIV_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_exch (&t, d); } mp_clear (&t); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_div_2d.c */ /* Start: bn_mp_div_3.c */ #include #ifdef BN_MP_DIV_3_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } mp_clear(&q); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_div_3.c */ /* Start: bn_mp_div_d.c */ #include #ifdef BN_MP_DIV_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clear(&q); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_div_d.c */ /* Start: bn_mp_dr_is_modulus.c */ #include #ifdef BN_MP_DR_IS_MODULUS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return 0; } } return 1; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_dr_is_modulus.c */ /* Start: bn_mp_dr_reduce.c */ #include #ifdef BN_MP_DR_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ s_mp_sub(x, n, x); goto top; } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_dr_reduce.c */ /* Start: bn_mp_dr_setup.c */ #include #ifdef BN_MP_DR_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * the number of bits in a mp_digit [e.g. DIGIT_BIT==31] */ *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - ((mp_word)a->dp[0])); } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_dr_setup.c */ /* Start: bn_mp_exch.c */ #include #ifdef BN_MP_EXCH_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_int t; t = *a; *a = *b; *b = t; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_exch.c */ /* Start: bn_mp_expt_d.c */ #include #ifdef BN_MP_EXPT_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ b <<= 1; } mp_clear (&g); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_expt_d.c */ /* Start: bn_mp_exptmod.c */ #include #ifdef BN_MP_EXPTMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ #else /* no invmod */ return MP_VAL; #endif } /* modified diminished radix reduction */ #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C) if (mp_reduce_is_2k_l(P) == MP_YES) { return s_mp_exptmod(G, X, P, Y, 1); } #endif #ifdef BN_MP_DR_IS_MODULUS_C /* is it a DR modulus? */ ................................................................................ #endif #ifdef BN_MP_EXPTMOD_FAST_C } #endif } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_exptmod.c */ /* Start: bn_mp_exptmod_fast.c */ #include #ifdef BN_MP_EXPTMOD_FAST_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clear (&M[x]); } return err; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_exptmod_fast.c */ /* Start: bn_mp_exteuclid.c */ #include #ifdef BN_MP_EXTEUCLID_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ err = MP_OKAY; _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); return err; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_exteuclid.c */ /* Start: bn_mp_fread.c */ #include #ifdef BN_MP_FREAD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_fread.c */ /* Start: bn_mp_fwrite.c */ #include #ifdef BN_MP_FWRITE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } XFREE (buf); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_fwrite.c */ /* Start: bn_mp_gcd.c */ #include #ifdef BN_MP_GCD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ res = MP_OKAY; LBL_V:mp_clear (&u); LBL_U:mp_clear (&v); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_gcd.c */ /* Start: bn_mp_get_int.c */ #include #ifdef BN_MP_GET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ res = (res << DIGIT_BIT) | DIGIT(a,i); } /* force result to 32-bits always so it is consistent on non 32-bit platforms */ return res & 0xFFFFFFFFUL; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_get_int.c */ /* Start: bn_mp_grow.c */ #include #ifdef BN_MP_GROW_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ a->dp[i] = 0; } } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_grow.c */ /* Start: bn_mp_init.c */ #include #ifdef BN_MP_INIT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ a->alloc = MP_PREC; a->sign = MP_ZPOS; return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_init.c */ /* Start: bn_mp_init_copy.c */ #include #ifdef BN_MP_INIT_COPY_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ if ((res = mp_init (a)) != MP_OKAY) { return res; } return mp_copy (b, a); } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_init_copy.c */ /* Start: bn_mp_init_multi.c */ #include #ifdef BN_MP_INIT_MULTI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } va_end(args); return res; /* Assumed ok, if error flagged above. */ } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_init_multi.c */ /* Start: bn_mp_init_set.c */ #include #ifdef BN_MP_INIT_SET_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return err; } mp_set(a, b); return err; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_init_set.c */ /* Start: bn_mp_init_set_int.c */ #include #ifdef BN_MP_INIT_SET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ int err; if ((err = mp_init(a)) != MP_OKAY) { return err; } return mp_set_int(a, b); } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_init_set_int.c */ /* Start: bn_mp_init_size.c */ #include #ifdef BN_MP_INIT_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ a->dp[x] = 0; } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_init_size.c */ /* Start: bn_mp_invmod.c */ #include #ifdef BN_MP_INVMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ #ifdef BN_MP_INVMOD_SLOW_C return mp_invmod_slow(a, b, c); #endif return MP_VAL; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_invmod.c */ /* Start: bn_mp_invmod_slow.c */ #include #ifdef BN_MP_INVMOD_SLOW_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_exch (&C, c); res = MP_OKAY; LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_invmod_slow.c */ /* Start: bn_mp_is_square.c */ #include #ifdef BN_MP_IS_SQUARE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO; ERR:mp_clear(&t); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_is_square.c */ /* Start: bn_mp_jacobi.c */ #include #ifdef BN_MP_JACOBI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ res = MP_OKAY; LBL_P1:mp_clear (&p1); LBL_A1:mp_clear (&a1); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_jacobi.c */ /* Start: bn_mp_karatsuba_mul.c */ #include #ifdef BN_MP_KARATSUBA_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * let n represent half of the number of digits in * the min(a,b) * * a = a1 * B**n + a0 * b = b1 * B**n + b0 * * Then, a * b => a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 * * Note that a1b1 and a0b0 are used twice and only need to be * computed once. So in total three half size (half # of * digit) multiplications are performed, a0b0, a1b1 and * (a1+b1)(a0+b0) * * Note that a multiplication of half the digits requires * 1/4th the number of single precision multiplications so in * total after one call 25% of the single precision multiplications * are saved. Note also that the call to mp_mul can end up back * in this function if the a0, a1, b0, or b1 are above the threshold. * This is known as divide-and-conquer and leads to the famous ................................................................................ /* now calc the products x0y0 and x1y1 */ /* after this x0 is no longer required, free temp [x0==t2]! */ if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY) goto X1Y1; /* x0y0 = x0*y0 */ if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) goto X1Y1; /* x1y1 = x1*y1 */ /* now calc x1+x0 and y1+y0 */ if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = x1 - x0 */ if (s_mp_add (&y1, &y0, &x0) != MP_OKAY) goto X1Y1; /* t2 = y1 - y0 */ if (mp_mul (&t1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ /* add x0y0 */ if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) goto X1Y1; /* t2 = x0y0 + x1y1 */ if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))< #ifdef BN_MP_KARATSUBA_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* now calc the products x0*x0 and x1*x1 */ if (mp_sqr (&x0, &x0x0) != MP_OKAY) goto X1X1; /* x0x0 = x0*x0 */ if (mp_sqr (&x1, &x1x1) != MP_OKAY) goto X1X1; /* x1x1 = x1*x1 */ /* now calc (x1+x0)**2 */ if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) goto X1X1; /* t1 = x1 - x0 */ if (mp_sqr (&t1, &t1) != MP_OKAY) goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ /* add x0y0 */ if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY) goto X1X1; /* t2 = x0x0 + x1x1 */ if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY) goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))< #ifdef BN_MP_LCM_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ c->sign = MP_ZPOS; LBL_T: mp_clear_multi (&t1, &t2, NULL); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_lcm.c */ /* Start: bn_mp_lshd.c */ #include #ifdef BN_MP_LSHD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ *top++ = 0; } } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_lshd.c */ /* Start: bn_mp_mod.c */ #include #ifdef BN_MP_MOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ mp_exch (&t, c); } mp_clear (&t); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_mod.c */ /* Start: bn_mp_mod_2d.c */ #include #ifdef BN_MP_MOD_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ c->dp[b / DIGIT_BIT] &= (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1)); mp_clamp (c); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_mod_2d.c */ /* Start: bn_mp_mod_d.c */ #include #ifdef BN_MP_MOD_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ int mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) { return mp_div_d(a, b, NULL, c); } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_mod_d.c */ /* Start: bn_mp_montgomery_calc_normalization.c */ #include #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } } } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_montgomery_calc_normalization.c */ /* Start: bn_mp_montgomery_reduce.c */ #include #ifdef BN_MP_MONTGOMERY_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ if (mp_cmp_mag (x, n) != MP_LT) { return s_mp_sub (x, n, x); } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_montgomery_reduce.c */ /* Start: bn_mp_montgomery_setup.c */ #include #ifdef BN_MP_MONTGOMERY_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* rho = -1/m mod b */ *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_montgomery_setup.c */ /* Start: bn_mp_mul.c */ #include #ifdef BN_MP_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ #endif } c->sign = (c->used > 0) ? neg : MP_ZPOS; return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_mul.c */ /* Start: bn_mp_mul_2.c */ #include #ifdef BN_MP_MUL_2_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ *tmpb++ = 0; } } b->sign = a->sign; return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_mul_2.c */ /* Start: bn_mp_mul_2d.c */ #include #ifdef BN_MP_MUL_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } } mp_clamp (c); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_mul_2d.c */ /* Start: bn_mp_mul_d.c */ #include #ifdef BN_MP_MUL_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ c->used = a->used + 1; mp_clamp(c); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_mul_d.c */ /* Start: bn_mp_mulmod.c */ #include #ifdef BN_MP_MULMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* d = a * b (mod c) */ int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) { int res; mp_int t; if ((res = mp_init (&t)) != MP_OKAY) { return res; } ................................................................................ return res; } res = mp_mod (&t, c, d); mp_clear (&t); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_mulmod.c */ /* Start: bn_mp_n_root.c */ #include #ifdef BN_MP_N_ROOT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ LBL_T3:mp_clear (&t3); LBL_T2:mp_clear (&t2); LBL_T1:mp_clear (&t1); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_n_root.c */ /* Start: bn_mp_neg.c */ #include #ifdef BN_MP_NEG_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } else { b->sign = MP_ZPOS; } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_neg.c */ /* Start: bn_mp_or.c */ #include #ifdef BN_MP_OR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_or.c */ /* Start: bn_mp_prime_fermat.c */ #include #ifdef BN_MP_PRIME_FERMAT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ err = MP_OKAY; LBL_T:mp_clear (&t); return err; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_prime_fermat.c */ /* Start: bn_mp_prime_is_divisible.c */ #include #ifdef BN_MP_PRIME_IS_DIVISIBLE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return MP_OKAY; } } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_prime_is_divisible.c */ /* Start: bn_mp_prime_is_prime.c */ #include #ifdef BN_MP_PRIME_IS_PRIME_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* passed the test */ *result = MP_YES; LBL_B:mp_clear (&b); return err; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_prime_is_prime.c */ /* Start: bn_mp_prime_miller_rabin.c */ #include #ifdef BN_MP_PRIME_MILLER_RABIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ *result = MP_YES; LBL_Y:mp_clear (&y); LBL_R:mp_clear (&r); LBL_N1:mp_clear (&n1); return err; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_prime_miller_rabin.c */ /* Start: bn_mp_prime_next_prime.c */ #include #ifdef BN_MP_PRIME_NEXT_PRIME_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ err = MP_OKAY; LBL_ERR: mp_clear(&b); return err; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_prime_next_prime.c */ /* Start: bn_mp_prime_rabin_miller_trials.c */ #include #ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } } return sizes[x-1].t + 1; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_prime_rabin_miller_trials.c */ /* Start: bn_mp_prime_random_ex.c */ #include #ifdef BN_MP_PRIME_RANDOM_EX_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* calc the maskAND value for the MSbyte*/ maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7))); /* calc the maskOR_msb */ maskOR_msb = 0; maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; if (flags & LTM_PRIME_2MSB_ON) { maskOR_msb |= 0x80 >> ((9 - size) & 7); } /* get the maskOR_lsb */ maskOR_lsb = 1; if (flags & LTM_PRIME_BBS) { maskOR_lsb |= 3; } ................................................................................ error: XFREE(tmp); return err; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_prime_random_ex.c */ /* Start: bn_mp_radix_size.c */ #include #ifdef BN_MP_RADIX_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ /* return digs + 1, the 1 is for the NULL byte that would be required. */ *size = digs + 1; return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_radix_size.c */ /* Start: bn_mp_radix_smap.c */ #include #ifdef BN_MP_RADIX_SMAP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* chars used in radix conversions */ const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_radix_smap.c */ /* Start: bn_mp_rand.c */ #include #ifdef BN_MP_RAND_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ return res; } } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_rand.c */ /* Start: bn_mp_read_radix.c */ #include #ifdef BN_MP_READ_RADIX_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ if (mp_iszero(a) != 1) { a->sign = neg; } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_read_radix.c */ /* Start: bn_mp_read_signed_bin.c */ #include #ifdef BN_MP_READ_SIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* read signed bin, big endian, first byte is 0==positive or 1==negative */ int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c) { int res; /* read magnitude */ if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) { return res; } ................................................................................ } else { a->sign = MP_NEG; } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_read_signed_bin.c */ /* Start: bn_mp_read_unsigned_bin.c */ #include #ifdef BN_MP_READ_UNSIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ /* reads a unsigned char array, assumes the msb is stored first [big endian] */ int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c) { int res; /* make sure there are at least two digits */ if (a->alloc < 2) { if ((res = mp_grow(a, 2)) != MP_OKAY) { return res; ................................................................................ a->used += 2; #endif } mp_clamp (a); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_read_unsigned_bin.c */ /* Start: bn_mp_reduce.c */ #include #ifdef BN_MP_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ CLEANUP: mp_clear (&q); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_reduce.c */ /* Start: bn_mp_reduce_2k.c */ #include #ifdef BN_MP_REDUCE_2K_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ ERR: mp_clear(&q); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_reduce_2k.c */ /* Start: bn_mp_reduce_2k_l.c */ #include #ifdef BN_MP_REDUCE_2K_L_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ ERR: mp_clear(&q); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_reduce_2k_l.c */ /* Start: bn_mp_reduce_2k_setup.c */ #include #ifdef BN_MP_REDUCE_2K_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ *d = tmp.dp[0]; mp_clear(&tmp); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_reduce_2k_setup.c */ /* Start: bn_mp_reduce_2k_setup_l.c */ #include #ifdef BN_MP_REDUCE_2K_SETUP_L_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } ERR: mp_clear(&tmp); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_reduce_2k_setup_l.c */ /* Start: bn_mp_reduce_is_2k.c */ #include #ifdef BN_MP_REDUCE_IS_2K_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } } return MP_YES; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_reduce_is_2k.c */ /* Start: bn_mp_reduce_is_2k_l.c */ #include #ifdef BN_MP_REDUCE_IS_2K_L_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } return MP_NO; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_reduce_is_2k_l.c */ /* Start: bn_mp_reduce_setup.c */ #include #ifdef BN_MP_REDUCE_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) { return res; } return mp_div (a, b, a, NULL); } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_reduce_setup.c */ /* Start: bn_mp_rshd.c */ #include #ifdef BN_MP_RSHD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } /* remove excess digits */ a->used -= b; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_rshd.c */ /* Start: bn_mp_set.c */ #include #ifdef BN_MP_SET_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ void mp_set (mp_int * a, mp_digit b) { mp_zero (a); a->dp[0] = b & MP_MASK; a->used = (a->dp[0] != 0) ? 1 : 0; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_set.c */ /* Start: bn_mp_set_int.c */ #include #ifdef BN_MP_SET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ a->used += 1; } mp_clamp (a); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_set_int.c */ /* Start: bn_mp_shrink.c */ #include #ifdef BN_MP_SHRINK_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ a->dp = tmp; a->alloc = a->used; } return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_shrink.c */ /* Start: bn_mp_signed_bin_size.c */ #include #ifdef BN_MP_SIGNED_BIN_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ /* get the size for an signed equivalent */ int mp_signed_bin_size (mp_int * a) { return 1 + mp_unsigned_bin_size (a); } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_signed_bin_size.c */ /* Start: bn_mp_sqr.c */ #include #ifdef BN_MP_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ #endif } b->sign = MP_ZPOS; return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_sqr.c */ /* Start: bn_mp_sqrmod.c */ #include #ifdef BN_MP_SQRMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return res; } res = mp_mod (&t, b, c); mp_clear (&t); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_sqrmod.c */ /* Start: bn_mp_sqrt.c */ #include #ifdef BN_MP_SQRT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ E1: mp_clear(&t2); E2: mp_clear(&t1); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_sqrt.c */ /* Start: bn_mp_sub.c */ #include #ifdef BN_MP_SUB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ res = s_mp_sub (b, a, c); } } return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_sub.c */ /* Start: bn_mp_sub_d.c */ #include #ifdef BN_MP_SUB_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } mp_clamp(c); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_sub_d.c */ /* Start: bn_mp_submod.c */ #include #ifdef BN_MP_SUBMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } res = mp_mod (&t, c, d); mp_clear (&t); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_submod.c */ /* Start: bn_mp_to_signed_bin.c */ #include #ifdef BN_MP_TO_SIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ return res; } b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_to_signed_bin.c */ /* Start: bn_mp_to_signed_bin_n.c */ #include #ifdef BN_MP_TO_SIGNED_BIN_N_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ if (*outlen < (unsigned long)mp_signed_bin_size(a)) { return MP_VAL; } *outlen = mp_signed_bin_size(a); return mp_to_signed_bin(a, b); } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_to_signed_bin_n.c */ /* Start: bn_mp_to_unsigned_bin.c */ #include #ifdef BN_MP_TO_UNSIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } bn_reverse (b, x); mp_clear (&t); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_to_unsigned_bin.c */ /* Start: bn_mp_to_unsigned_bin_n.c */ #include #ifdef BN_MP_TO_UNSIGNED_BIN_N_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) { return MP_VAL; } *outlen = mp_unsigned_bin_size(a); return mp_to_unsigned_bin(a, b); } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_to_unsigned_bin_n.c */ /* Start: bn_mp_toom_mul.c */ #include #ifdef BN_MP_TOOM_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ &a0, &a1, &a2, &b0, &b1, &b2, &tmp1, &tmp2, NULL); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_toom_mul.c */ /* Start: bn_mp_toom_sqr.c */ #include #ifdef BN_MP_TOOM_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ ERR: mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL); return res; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_toom_sqr.c */ /* Start: bn_mp_toradix.c */ #include #ifdef BN_MP_TORADIX_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ *str = '\0'; mp_clear (&t); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_toradix.c */ /* Start: bn_mp_toradix_n.c */ #include #ifdef BN_MP_TORADIX_N_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clear (&t); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_toradix_n.c */ /* Start: bn_mp_unsigned_bin_size.c */ #include #ifdef BN_MP_UNSIGNED_BIN_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ /* get the size for an unsigned equivalent */ int mp_unsigned_bin_size (mp_int * a) { int size = mp_count_bits (a); return (size / 8 + ((size & 7) != 0 ? 1 : 0)); } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_unsigned_bin_size.c */ /* Start: bn_mp_xor.c */ #include #ifdef BN_MP_XOR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_xor.c */ /* Start: bn_mp_zero.c */ #include #ifdef BN_MP_ZERO_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ tmp = a->dp; for (n = 0; n < a->alloc; n++) { *tmp++ = 0; } } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_mp_zero.c */ /* Start: bn_prime_tab.c */ #include #ifdef BN_PRIME_TAB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 #endif }; #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_prime_tab.c */ /* Start: bn_reverse.c */ #include #ifdef BN_REVERSE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ s[ix] = s[iy]; s[iy] = t; ++ix; --iy; } } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_reverse.c */ /* Start: bn_s_mp_add.c */ #include #ifdef BN_S_MP_ADD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ } mp_clamp (c); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_s_mp_add.c */ /* Start: bn_s_mp_exptmod.c */ #include #ifdef BN_S_MP_EXPTMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #ifdef MP_LOW_MEM #define TAB_SIZE 32 #else #define TAB_SIZE 256 #endif int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) ................................................................................ for (x = 1<<(winsize-1); x < (1 << winsize); x++) { mp_clear (&M[x]); } return err; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_s_mp_exptmod.c */ /* Start: bn_s_mp_mul_digs.c */ #include #ifdef BN_S_MP_MUL_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ mp_exch (&t, c); mp_clear (&t); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_s_mp_mul_digs.c */ /* Start: bn_s_mp_mul_high_digs.c */ #include #ifdef BN_S_MP_MUL_HIGH_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ } mp_clamp (&t); mp_exch (&t, c); mp_clear (&t); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_s_mp_mul_high_digs.c */ /* Start: bn_s_mp_sqr.c */ #include #ifdef BN_S_MP_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clamp (&t); mp_exch (&t, b); mp_clear (&t); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_s_mp_sqr.c */ /* Start: bn_s_mp_sub.c */ #include #ifdef BN_S_MP_SUB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis ................................................................................ mp_clamp (c); return MP_OKAY; } #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bn_s_mp_sub.c */ /* Start: bncore.c */ #include #ifdef BNCORE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * ................................................................................ */ /* Known optimal configurations CPU /Compiler /MUL CUTOFF/SQR CUTOFF ------------------------------------------------------------- Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) AMD Athlon64 /GCC v3.4.4 / 80/ 120/LTM 0.35 */ int KARATSUBA_MUL_CUTOFF = 80, /* Min. number of digits before Karatsuba multiplication is used. */ KARATSUBA_SQR_CUTOFF = 120, /* Min. number of digits before Karatsuba squaring is used. */ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ TOOM_SQR_CUTOFF = 400; #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/pre_gen/mpi.c,v $*/ /*$Revision: 1.1.1.1.2.2 $*/ /*$Date: 2005/09/26 20:16:54 $*/ /* End: bncore.c */ /* EOF */  Changes to libtommath/tommath.h.  19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ... 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 ... 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 ... 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 ... 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 ... 572 573 574 575 576 577 578  #include #include #include #include #include #undef MIN #define MIN(x,y) ((x)<(y)?(x):(y)) #undef MAX #define MAX(x,y) ((x)>(y)?(x):(y)) #ifdef __cplusplus extern "C" { /* C++ compilers don't like assigning void * to mp_digit * */ #define OPT_CAST(x) (x *) ................................................................................ #define XMALLOC malloc #define XFREE free #define XREALLOC realloc #define XCALLOC calloc #else /* prototypes for our heap functions */ extern void *XMALLOC(size_t n); extern void *REALLOC(void *p, size_t n); extern void *XCALLOC(size_t n, size_t s); extern void XFREE(void *p); #endif #endif /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ ................................................................................ #define MP_YES 1 /* yes response */ #define MP_NO 0 /* no response */ /* Primality generation flags */ #define LTM_PRIME_BBS 0x0001 /* BBS style prime */ #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ #define LTM_PRIME_2MSB_OFF 0x0004 /* force 2nd MSB to 0 */ #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ typedef int mp_err; /* you'll have to tune these... */ extern int KARATSUBA_MUL_CUTOFF, KARATSUBA_SQR_CUTOFF, ................................................................................ /* define this to use lower memory usage routines (exptmods mostly) */ /* #define MP_LOW_MEM */ /* default precision */ #ifndef MP_PREC #ifndef MP_LOW_MEM #define MP_PREC 64 /* default digits of precision */ #else #define MP_PREC 8 /* default digits of precision */ #endif #endif /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1)) ................................................................................ */ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); /* ---> radix conversion <--- */ int mp_count_bits(mp_int *a); int mp_unsigned_bin_size(mp_int *a); int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c); int mp_to_unsigned_bin(mp_int *a, unsigned char *b); int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); int mp_signed_bin_size(mp_int *a); int mp_read_signed_bin(mp_int *a, unsigned char *b, int c); int mp_to_signed_bin(mp_int *a, unsigned char *b); int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); int mp_read_radix(mp_int *a, const char *str, int radix); int mp_toradix(mp_int *a, char *str, int radix); int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); int mp_radix_size(mp_int *a, int radix, int *size); ................................................................................ #ifdef __cplusplus } #endif #endif   | | > > | | > | < | | | | > > > >  19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 ... 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 ... 146 147 148 149 150 151 152 153 154 155 156 157 158 159 ... 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 ... 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 ... 574 575 576 577 578 579 580 581 582 583 584  #include #include #include #include #include #ifndef MIN #define MIN(x,y) ((x)<(y)?(x):(y)) #endif #ifndef MAX #define MAX(x,y) ((x)>(y)?(x):(y)) #endif #ifdef __cplusplus extern "C" { /* C++ compilers don't like assigning void * to mp_digit * */ #define OPT_CAST(x) (x *) ................................................................................ #define XMALLOC malloc #define XFREE free #define XREALLOC realloc #define XCALLOC calloc #else /* prototypes for our heap functions */ extern void *XMALLOC(size_t n); extern void *XREALLOC(void *p, size_t n); extern void *XCALLOC(size_t n, size_t s); extern void XFREE(void *p); #endif #endif /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ ................................................................................ #define MP_YES 1 /* yes response */ #define MP_NO 0 /* no response */ /* Primality generation flags */ #define LTM_PRIME_BBS 0x0001 /* BBS style prime */ #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ typedef int mp_err; /* you'll have to tune these... */ extern int KARATSUBA_MUL_CUTOFF, KARATSUBA_SQR_CUTOFF, ................................................................................ /* define this to use lower memory usage routines (exptmods mostly) */ /* #define MP_LOW_MEM */ /* default precision */ #ifndef MP_PREC #ifndef MP_LOW_MEM #define MP_PREC 32 /* default digits of precision */ #else #define MP_PREC 8 /* default digits of precision */ #endif #endif /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1)) ................................................................................ */ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); /* ---> radix conversion <--- */ int mp_count_bits(mp_int *a); int mp_unsigned_bin_size(mp_int *a); int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); int mp_to_unsigned_bin(mp_int *a, unsigned char *b); int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); int mp_signed_bin_size(mp_int *a); int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); int mp_to_signed_bin(mp_int *a, unsigned char *b); int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); int mp_read_radix(mp_int *a, const char *str, int radix); int mp_toradix(mp_int *a, char *str, int radix); int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); int mp_radix_size(mp_int *a, int radix, int *size); ................................................................................ #ifdef __cplusplus } #endif #endif /*$Source: /root/tcl/repos-to-convert/tcl/libtommath/tommath.h,v $*/ /*$Revision: 1.1.1.1.2.4 $*/ /*$Date: 2005/09/26 20:16:54 $*/  Changes to libtommath/tommath.pdf. cannot compute difference between binary files Changes to libtommath/tommath.src.  62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 .... 2771 2772 2773 2774 2775 2776 2777 2778 2779 2780 2781 2782 2783 2784 2785 2786 2787 2788 2789 2790 2791 2792 2793 2794 2795 2796 2797 2798 2799 2800 2801 2802 2803 2804 .... 2813 2814 2815 2816 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 2833 .... 2846 2847 2848 2849 2850 2851 2852 2853 2854 2855 2856 2857 2858 2859 2860 .... 3242 3243 3244 3245 3246 3247 3248 3249 3250 3251 3252 3253 3254 3255 3256 3257 3258 3259 .... 3277 3278 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290 3291 3292 3293 3294 3295 3296 .... 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317 3318 3319 .... 4031 4032 4033 4034 4035 4036 4037 4038 4039 4040 4041 4042 4043 4044 4045  Greg Rose \\ QUALCOMM Australia \\ \end{tabular} %\end{small} } } \maketitle This text has been placed in the public domain. This text corresponds to the v0.35 release of the LibTomMath project. \begin{alltt} Tom St Denis 111 Banning Rd Ottawa, Ontario K2L 1C3 ................................................................................ \subsection{Karatsuba Multiplication} Karatsuba \cite{KARA} multiplication when originally proposed in 1962 was among the first set of algorithms to break the$O(n^2)$barrier for general purpose multiplication. Given two polynomial basis representations$f(x) = ax + b$and$g(x) = cx + d$, Karatsuba proved with light algebra \cite{KARAP} that the following polynomial is equivalent to multiplication of the two integers the polynomials represent. f(x) \cdot g(x) = acx^2 + ((a - b)(c - d) - (ac + bd))x + bd Using the observation that$ac$and$bd$could be re-used only three half sized multiplications would be required to produce the product. Applying this algorithm recursively, the work factor becomes$O(n^{lg(3)})$which is substantially better than the work factor$O(n^2)$of the Comba technique. It turns out what Karatsuba did not know or at least did not publish was that this is simply polynomial basis multiplication with the points$\zeta_0$,$\zeta_{\infty}$and$-\zeta_{-1}$. Consider the resultant system of equations. \begin{center} \begin{tabular}{rcrcrcrc}$\zeta_{0}$&$=$& & & & &$w_0$\\$-\zeta_{-1}$&$=$&$-w_2$&$+$&$w_1$&$-$&$w_0$\\$\zeta_{\infty}$&$=$&$w_2$& & & & \\ \end{tabular} \end{center} By adding the first and last equation to the equation in the middle the term$w_1$can be isolated and all three coefficients solved for. The simplicity of this system of equations has made Karatsuba fairly popular. In fact the cutoff point is often fairly low\footnote{With LibTomMath 0.18 it is 70 and 109 digits for the Intel P4 and AMD Athlon respectively.} making it an ideal algorithm to speed up certain public key cryptosystems such as RSA and Diffie-Hellman. It is worth noting that the point$\zeta_1$could be substituted for$-\zeta_{-1}$. In this case the first and third row are subtracted instead of added to the second row. \newpage\begin{figure}[!here] \begin{small} \begin{center} \begin{tabular}{l} \hline Algorithm \textbf{mp\_karatsuba\_mul}. \\ \textbf{Input}. mp\_int$a$and mp\_int$b$\\ ................................................................................ 5.$y0 \leftarrow b \mbox{ (mod }\beta^B\mbox{)}$\\ 6.$x1 \leftarrow \lfloor a / \beta^B \rfloor$(\textit{mp\_rshd}) \\ 7.$y1 \leftarrow \lfloor b / \beta^B \rfloor$\\ \\ Calculate the three products. \\ 8.$x0y0 \leftarrow x0 \cdot y0$(\textit{mp\_mul}) \\ 9.$x1y1 \leftarrow x1 \cdot y1$\\ 10.$t1 \leftarrow x1 - x0$(\textit{mp\_sub}) \\ 11.$x0 \leftarrow y1 - y0$\\ 12.$t1 \leftarrow t1 \cdot x0$\\ \\ Calculate the middle term. \\ 13.$x0 \leftarrow x0y0 + x1y1$\\ 14.$t1 \leftarrow x0 - t1$\\ \\ Calculate the final product. \\ 15.$t1 \leftarrow t1 \cdot \beta^B$(\textit{mp\_lshd}) \\ 16.$x1y1 \leftarrow x1y1 \cdot \beta^{2B}$\\ 17.$t1 \leftarrow x0y0 + t1$\\ 18.$c \leftarrow t1 + x1y1$\\ 19. Clear all of the temporary variables. \\ ................................................................................ \index{radix point} In order to split the two inputs into their respective halves, a suitable \textit{radix point} must be chosen. The radix point chosen must be used for both of the inputs meaning that it must be smaller than the smallest input. Step 3 chooses the radix point$B$as half of the smallest input \textbf{used} count. After the radix point is chosen the inputs are split into lower and upper halves. Step 4 and 5 compute the lower halves. Step 6 and 7 computer the upper halves. After the halves have been computed the three intermediate half-size products must be computed. Step 8 and 9 compute the trivial products$x0 \cdot y0$and$x1 \cdot y1$. The mp\_int$x0$is used as a temporary variable after$x1 - x0$has been computed. By using$x0$instead of an additional temporary variable, the algorithm can avoid an addition memory allocation operation. The remaining steps 13 through 18 compute the Karatsuba polynomial through a variety of digit shifting and addition operations. EXAM,bn_mp_karatsuba_mul.c The new coding element in this routine, not seen in previous routines, is the usage of goto statements. The conventional ................................................................................ \subsection{Karatsuba Squaring} Let$f(x) = ax + b$represent the polynomial basis representation of a number to square. Let$h(x) = \left ( f(x) \right )^2$represent the square of the polynomial. The Karatsuba equation can be modified to square a number with the following equation. h(x) = a^2x^2 + \left (a^2 + b^2 - (a - b)^2 \right )x + b^2 Upon closer inspection this equation only requires the calculation of three half-sized squares:$a^2$,$b^2$and$(a - b)^2$. As in Karatsuba multiplication, this algorithm can be applied recursively on the input and will achieve an asymptotic running time of$O \left ( n^{lg(3)} \right )$. If the asymptotic times of Karatsuba squaring and multiplication are the same, why not simply use the multiplication algorithm instead? The answer to this arises from the cutoff point for squaring. As in multiplication there exists a cutoff point, at which the time required for a Comba based squaring and a Karatsuba based squaring meet. Due to the overhead inherent in the Karatsuba method, the cutoff point is fairly high. For example, on an AMD Athlon XP processor with$\beta = 2^{28}$, the cutoff point is around 127 digits. ................................................................................ 3.$B \leftarrow \lfloor a.used / 2 \rfloor$\\ 4.$x0 \leftarrow a \mbox{ (mod }\beta^B\mbox{)}$(\textit{mp\_mod\_2d}) \\ 5.$x1 \leftarrow \lfloor a / \beta^B \rfloor$(\textit{mp\_lshd}) \\ \\ Calculate the three squares. \\ 6.$x0x0 \leftarrow x0^2$(\textit{mp\_sqr}) \\ 7.$x1x1 \leftarrow x1^2$\\ 8.$t1 \leftarrow x1 - x0$(\textit{mp\_sub}) \\ 9.$t1 \leftarrow t1^2$\\ \\ Compute the middle term. \\ 10.$t2 \leftarrow x0x0 + x1x1$(\textit{s\_mp\_add}) \\ 11.$t1 \leftarrow t2 - t1$\\ \\ Compute final product. \\ 12.$t1 \leftarrow t1\beta^B$(\textit{mp\_lshd}) \\ 13.$x1x1 \leftarrow x1x1\beta^{2B}$\\ 14.$t1 \leftarrow t1 + x0x0$\\ 15.$b \leftarrow t1 + x1x1$\\ 16. Return(\textit{MP\_OKAY}). \\ ................................................................................ This algorithm computes the square of an input$a$using the Karatsuba technique. This algorithm is very similar to the Karatsuba based multiplication algorithm with the exception that the three half-size multiplications have been replaced with three half-size squarings. The radix point for squaring is simply placed exactly in the middle of the digits when the input has an odd number of digits, otherwise it is placed just below the middle. Step 3, 4 and 5 compute the two halves required using$B$as the radix point. The first two squares in steps 6 and 7 are rather straightforward while the last square is of a more compact form. By expanding$\left (x1 - x0 \right )^2$, the$x1^2$and$x0^2$terms in the middle disappear, that is$x1^2 + x0^2 - (x1 - x0)^2 = 2 \cdot x0 \cdot x1$. Now if$5n$single precision additions and a squaring of$n$-digits is faster than multiplying two$n$-digit numbers and doubling then this method is faster. Assuming no further recursions occur, the difference can be estimated with the following inequality. Let$p$represent the cost of a single precision addition and$q$the cost of a single precision multiplication both in terms of time\footnote{Or machine clock cycles.}. ................................................................................ \begin{tabular}{l} \hline Algorithm \textbf{mp\_montgomery\_setup}. \\ \textbf{Input}. mp\_int$n$($n > 1$and$(n, 2) = 1$) \\ \textbf{Output}.$\rho \equiv -1/n_0 \mbox{ (mod }\beta\mbox{)}$\\ \hline \\ 1.$b \leftarrow n_0$\\ 2. If$b$is even return(\textit{MP\_VAL}) \\ 3.$x \leftarrow ((b + 2) \mbox{ AND } 4) << 1) + b$\\ 4. for$k$from 0 to$\lceil lg(lg(\beta)) \rceil - 2$do \\ \hspace{3mm}4.1$x \leftarrow x \cdot (2 - bx)$\\ 5.$\rho \leftarrow \beta - x \mbox{ (mod }\beta\mbox{)}$\\ 6. Return(\textit{MP\_OKAY}). \\ \hline \end{tabular} \end{center}   | | | | | < | | | | | | | | | |  62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 .... 2771 2772 2773 2774 2775 2776 2777 2778 2779 2780 2781 2782 2783 2784 2785 2786 2787 2788 2789 2790 2791 2792 2793 2794 2795 2796 2797 2798 2799 2800 2801 2802 2803 .... 2812 2813 2814 2815 2816 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 .... 2845 2846 2847 2848 2849 2850 2851 2852 2853 2854 2855 2856 2857 2858 2859 .... 3241 3242 3243 3244 3245 3246 3247 3248 3249 3250 3251 3252 3253 3254 3255 3256 3257 3258 .... 3276 3277 3278 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290 3291 3292 3293 3294 3295 .... 3304 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317 3318 .... 4030 4031 4032 4033 4034 4035 4036 4037 4038 4039 4040 4041 4042 4043 4044  Greg Rose \\ QUALCOMM Australia \\ \end{tabular} %\end{small} } } \maketitle This text has been placed in the public domain. This text corresponds to the v0.36 release of the LibTomMath project. \begin{alltt} Tom St Denis 111 Banning Rd Ottawa, Ontario K2L 1C3 ................................................................................ \subsection{Karatsuba Multiplication} Karatsuba \cite{KARA} multiplication when originally proposed in 1962 was among the first set of algorithms to break the$O(n^2)$barrier for general purpose multiplication. Given two polynomial basis representations$f(x) = ax + b$and$g(x) = cx + d$, Karatsuba proved with light algebra \cite{KARAP} that the following polynomial is equivalent to multiplication of the two integers the polynomials represent. f(x) \cdot g(x) = acx^2 + ((a + b)(c + d) - (ac + bd))x + bd Using the observation that$ac$and$bd$could be re-used only three half sized multiplications would be required to produce the product. Applying this algorithm recursively, the work factor becomes$O(n^{lg(3)})$which is substantially better than the work factor$O(n^2)$of the Comba technique. It turns out what Karatsuba did not know or at least did not publish was that this is simply polynomial basis multiplication with the points$\zeta_0$,$\zeta_{\infty}$and$\zeta_{1}$. Consider the resultant system of equations. \begin{center} \begin{tabular}{rcrcrcrc}$\zeta_{0}$&$=$& & & & &$w_0$\\$\zeta_{1}$&$=$&$w_2$&$+$&$w_1$&$+$&$w_0$\\$\zeta_{\infty}$&$=$&$w_2$& & & & \\ \end{tabular} \end{center} By adding the first and last equation to the equation in the middle the term$w_1\$ can be isolated and all three coefficients solved for. The simplicity of this system of equations has made Karatsuba fairly popular. In fact the cutoff point is often fairly l`