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annotate libtommath/bn_mp_kronecker.c @ 1663:c795520269f9

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Fallback for key gen without hard link support (#89) Add a non-atomic fallback for key generation on platforms where link() is not permitted (such as most stock Android installs) or on filesystems without hard link support (such as FAT).
author Matt Robinson <git@nerdoftheherd.com>
date Sat, 14 Mar 2020 14:37:35 +0000
parents f52919ffd3b1
children 1051e4eea25a
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1655
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1 #include "tommath_private.h"
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2 #ifdef BN_MP_KRONECKER_C
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3
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4 /* LibTomMath, multiple-precision integer library -- Tom St Denis
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5 *
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6 * LibTomMath is a library that provides multiple-precision
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7 * integer arithmetic as well as number theoretic functionality.
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8 *
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9 * The library was designed directly after the MPI library by
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10 * Michael Fromberger but has been written from scratch with
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11 * additional optimizations in place.
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12 *
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13 * SPDX-License-Identifier: Unlicense
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14 */
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15
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16 /*
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17 Kronecker symbol (a|p)
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18 Straightforward implementation of algorithm 1.4.10 in
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19 Henri Cohen: "A Course in Computational Algebraic Number Theory"
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20
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21 @book{cohen2013course,
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22 title={A course in computational algebraic number theory},
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23 author={Cohen, Henri},
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24 volume={138},
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25 year={2013},
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26 publisher={Springer Science \& Business Media}
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27 }
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28 */
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29 int mp_kronecker(const mp_int *a, const mp_int *p, int *c)
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30 {
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31 mp_int a1, p1, r;
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32
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33 int e = MP_OKAY;
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34 int v, k;
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35
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36 static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1};
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37
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38 if (mp_iszero(p) != MP_NO) {
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39 if ((a->used == 1) && (a->dp[0] == 1u)) {
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40 *c = 1;
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41 return e;
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42 } else {
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43 *c = 0;
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44 return e;
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45 }
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46 }
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47
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48 if ((mp_iseven(a) != MP_NO) && (mp_iseven(p) != MP_NO)) {
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49 *c = 0;
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50 return e;
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51 }
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52
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53 if ((e = mp_init_copy(&a1, a)) != MP_OKAY) {
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54 return e;
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55 }
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56 if ((e = mp_init_copy(&p1, p)) != MP_OKAY) {
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57 goto LBL_KRON_0;
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58 }
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59
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60 v = mp_cnt_lsb(&p1);
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61 if ((e = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) {
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62 goto LBL_KRON_1;
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63 }
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64
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65 if ((v & 0x1) == 0) {
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66 k = 1;
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67 } else {
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68 k = table[a->dp[0] & 7u];
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69 }
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70
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71 if (p1.sign == MP_NEG) {
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72 p1.sign = MP_ZPOS;
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73 if (a1.sign == MP_NEG) {
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74 k = -k;
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75 }
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76 }
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77
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78 if ((e = mp_init(&r)) != MP_OKAY) {
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79 goto LBL_KRON_1;
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80 }
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81
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82 for (;;) {
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83 if (mp_iszero(&a1) != MP_NO) {
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84 if (mp_cmp_d(&p1, 1uL) == MP_EQ) {
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85 *c = k;
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86 goto LBL_KRON;
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87 } else {
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88 *c = 0;
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89 goto LBL_KRON;
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90 }
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91 }
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92
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93 v = mp_cnt_lsb(&a1);
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94 if ((e = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) {
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95 goto LBL_KRON;
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96 }
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97
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98 if ((v & 0x1) == 1) {
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99 k = k * table[p1.dp[0] & 7u];
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100 }
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101
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102 if (a1.sign == MP_NEG) {
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103 /*
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104 * Compute k = (-1)^((a1)*(p1-1)/4) * k
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105 * a1.dp[0] + 1 cannot overflow because the MSB
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106 * of the type mp_digit is not set by definition
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107 */
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108 if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) {
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109 k = -k;
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110 }
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111 } else {
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112 /* compute k = (-1)^((a1-1)*(p1-1)/4) * k */
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113 if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) {
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114 k = -k;
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115 }
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116 }
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117
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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118 if ((e = mp_copy(&a1, &r)) != MP_OKAY) {
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119 goto LBL_KRON;
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120 }
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121 r.sign = MP_ZPOS;
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122 if ((e = mp_mod(&p1, &r, &a1)) != MP_OKAY) {
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123 goto LBL_KRON;
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124 }
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125 if ((e = mp_copy(&r, &p1)) != MP_OKAY) {
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126 goto LBL_KRON;
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127 }
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128 }
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129
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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130 LBL_KRON:
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131 mp_clear(&r);
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132 LBL_KRON_1:
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133 mp_clear(&p1);
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134 LBL_KRON_0:
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135 mp_clear(&a1);
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136
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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137 return e;
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138 }
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139
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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140 #endif
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141
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents:
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142 /* ref: HEAD -> master, tag: v1.1.0 */
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parents:
diff changeset
143 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
144 /* commit time: 2019-01-28 20:32:32 +0100 */