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annotate libtommath/bn_mp_kronecker.c @ 1861:2b3a8026a6ce

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Add re-exec for server This allows ASLR to re-randomize the address space for every connection, preventing some vulnerabilities from being exploitable by repeated probing. Overhead (memory and time) is yet to be confirmed. At present this is only enabled on Linux. Other BSD platforms with fexecve() would probably also work though have not been tested.
author Matt Johnston <matt@ucc.asn.au>
date Sun, 30 Jan 2022 10:14:56 +0800
parents 1051e4eea25a
children
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 /* 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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parents:
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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