Mercurial > dropbear
annotate libtommath/bn_mp_kronecker.c @ 1689:d2d3b5ba6c64
update travis to Ubuntu focal to provide chacha20
author | Matt Johnston <matt@ucc.asn.au> |
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date | Tue, 26 May 2020 23:13:48 +0800 |
parents | f52919ffd3b1 |
children | 1051e4eea25a |
rev | line source |
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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 * |
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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 */ |