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annotate libtommath/bn_mp_kronecker.c @ 1722:912c8ca0728f

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Added signature for changeset 4877afd51e04
author Matt Johnston <matt@ucc.asn.au>
date Mon, 15 Jun 2020 23:51:45 +0800
parents 1051e4eea25a
children
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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 /* SPDX-License-Identifier: Unlicense */
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6
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7 /*
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8 Kronecker symbol (a|p)
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9 Straightforward implementation of algorithm 1.4.10 in
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10 Henri Cohen: "A Course in Computational Algebraic Number Theory"
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11
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12 @book{cohen2013course,
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13 title={A course in computational algebraic number theory},
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14 author={Cohen, Henri},
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15 volume={138},
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16 year={2013},
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17 publisher={Springer Science \& Business Media}
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18 }
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19 */
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20 mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c)
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21 {
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22 mp_int a1, p1, r;
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23 mp_err err;
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24 int v, k;
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25
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26 static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1};
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27
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28 if (MP_IS_ZERO(p)) {
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29 if ((a->used == 1) && (a->dp[0] == 1u)) {
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30 *c = 1;
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31 } else {
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32 *c = 0;
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33 }
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34 return MP_OKAY;
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35 }
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36
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37 if (MP_IS_EVEN(a) && MP_IS_EVEN(p)) {
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38 *c = 0;
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39 return MP_OKAY;
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40 }
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41
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42 if ((err = mp_init_copy(&a1, a)) != MP_OKAY) {
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43 return err;
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44 }
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45 if ((err = mp_init_copy(&p1, p)) != MP_OKAY) {
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46 goto LBL_KRON_0;
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47 }
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48
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49 v = mp_cnt_lsb(&p1);
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50 if ((err = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) {
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51 goto LBL_KRON_1;
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52 }
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53
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54 if ((v & 1) == 0) {
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55 k = 1;
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56 } else {
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57 k = table[a->dp[0] & 7u];
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58 }
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59
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60 if (p1.sign == MP_NEG) {
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61 p1.sign = MP_ZPOS;
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62 if (a1.sign == MP_NEG) {
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63 k = -k;
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64 }
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65 }
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66
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67 if ((err = mp_init(&r)) != MP_OKAY) {
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68 goto LBL_KRON_1;
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69 }
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70
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71 for (;;) {
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72 if (MP_IS_ZERO(&a1)) {
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73 if (mp_cmp_d(&p1, 1uL) == MP_EQ) {
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74 *c = k;
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75 goto LBL_KRON;
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76 } else {
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77 *c = 0;
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78 goto LBL_KRON;
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79 }
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80 }
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81
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82 v = mp_cnt_lsb(&a1);
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83 if ((err = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) {
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84 goto LBL_KRON;
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85 }
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86
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87 if ((v & 1) == 1) {
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88 k = k * table[p1.dp[0] & 7u];
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89 }
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90
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91 if (a1.sign == MP_NEG) {
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92 /*
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93 * Compute k = (-1)^((a1)*(p1-1)/4) * k
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94 * a1.dp[0] + 1 cannot overflow because the MSB
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95 * of the type mp_digit is not set by definition
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96 */
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97 if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) {
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98 k = -k;
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99 }
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100 } else {
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101 /* compute k = (-1)^((a1-1)*(p1-1)/4) * k */
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102 if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) {
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103 k = -k;
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104 }
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105 }
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106
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107 if ((err = mp_copy(&a1, &r)) != MP_OKAY) {
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108 goto LBL_KRON;
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109 }
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110 r.sign = MP_ZPOS;
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111 if ((err = mp_mod(&p1, &r, &a1)) != MP_OKAY) {
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112 goto LBL_KRON;
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113 }
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114 if ((err = mp_copy(&r, &p1)) != MP_OKAY) {
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115 goto LBL_KRON;
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116 }
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117 }
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118
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119 LBL_KRON:
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120 mp_clear(&r);
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121 LBL_KRON_1:
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122 mp_clear(&p1);
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123 LBL_KRON_0:
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124 mp_clear(&a1);
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125
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126 return err;
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127 }
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128
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129 #endif