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annotate libtommath/bn_mp_kronecker.c @ 1680:5e763ad6e2e0

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author Matt Johnston <matt@ucc.asn.au>
date Sun, 24 May 2020 13:34:19 +0800
parents f52919ffd3b1
children 1051e4eea25a
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1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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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
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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
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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
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137 return e;
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138 }
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139
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140 #endif
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141
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142 /* ref: HEAD -> master, tag: v1.1.0 */
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143 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
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144 /* commit time: 2019-01-28 20:32:32 +0100 */