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annotate libtommath/bn_mp_prime_frobenius_underwood.c @ 1868:66a3fabe4870

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merge
author Matt Johnston <matt@ucc.asn.au>
date Tue, 01 Feb 2022 15:51:01 +0800
parents 1051e4eea25a
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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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_PRIME_FROBENIUS_UNDERWOOD_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 * See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
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9 */
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10 #ifndef LTM_USE_ONLY_MR
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11
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12 #ifdef MP_8BIT
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13 /*
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14 * floor of positive solution of
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15 * (2^16)-1 = (a+4)*(2*a+5)
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16 * TODO: Both values are smaller than N^(1/4), would have to use a bigint
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17 * for a instead but any a biger than about 120 are already so rare that
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18 * it is possible to ignore them and still get enough pseudoprimes.
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19 * But it is still a restriction of the set of available pseudoprimes
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20 * which makes this implementation less secure if used stand-alone.
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21 */
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22 #define LTM_FROBENIUS_UNDERWOOD_A 177
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23 #else
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24 #define LTM_FROBENIUS_UNDERWOOD_A 32764
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25 #endif
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26 mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result)
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27 {
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28 mp_int T1z, T2z, Np1z, sz, tz;
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29
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30 int a, ap2, length, i, j;
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31 mp_err err;
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32
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33 *result = MP_NO;
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34
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35 if ((err = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) {
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36 return err;
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37 }
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38
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39 for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) {
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40 /* TODO: That's ugly! No, really, it is! */
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41 if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) ||
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42 (a==14) || (a==18) || (a==23) || (a==26) || (a==28)) {
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43 continue;
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44 }
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45 /* (32764^2 - 4) < 2^31, no bigint for >MP_8BIT needed) */
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46 mp_set_u32(&T1z, (uint32_t)a);
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47
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48 if ((err = mp_sqr(&T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
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49
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50 if ((err = mp_sub_d(&T1z, 4uL, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
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51
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52 if ((err = mp_kronecker(&T1z, N, &j)) != MP_OKAY) goto LBL_FU_ERR;
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53
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54 if (j == -1) {
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55 break;
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56 }
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57
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58 if (j == 0) {
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59 /* composite */
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60 goto LBL_FU_ERR;
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61 }
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62 }
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63 /* Tell it a composite and set return value accordingly */
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64 if (a >= LTM_FROBENIUS_UNDERWOOD_A) {
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65 err = MP_ITER;
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66 goto LBL_FU_ERR;
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67 }
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68 /* Composite if N and (a+4)*(2*a+5) are not coprime */
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69 mp_set_u32(&T1z, (uint32_t)((a+4)*((2*a)+5)));
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70
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71 if ((err = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
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72
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73 if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) goto LBL_FU_ERR;
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74
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75 ap2 = a + 2;
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76 if ((err = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) goto LBL_FU_ERR;
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77
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78 mp_set(&sz, 1uL);
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79 mp_set(&tz, 2uL);
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80 length = mp_count_bits(&Np1z);
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81
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82 for (i = length - 2; i >= 0; i--) {
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83 /*
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84 * temp = (sz*(a*sz+2*tz))%N;
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85 * tz = ((tz-sz)*(tz+sz))%N;
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86 * sz = temp;
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87 */
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88 if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
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89
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90 /* a = 0 at about 50% of the cases (non-square and odd input) */
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91 if (a != 0) {
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92 if ((err = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
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93 if ((err = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
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94 }
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95
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96 if ((err = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
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97 if ((err = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
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98 if ((err = mp_add(&sz, &tz, &sz)) != MP_OKAY) goto LBL_FU_ERR;
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99 if ((err = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) goto LBL_FU_ERR;
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100 if ((err = mp_mod(&tz, N, &tz)) != MP_OKAY) goto LBL_FU_ERR;
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101 if ((err = mp_mod(&T1z, N, &sz)) != MP_OKAY) goto LBL_FU_ERR;
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102 if (s_mp_get_bit(&Np1z, (unsigned int)i) == MP_YES) {
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103 /*
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104 * temp = (a+2) * sz + tz
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105 * tz = 2 * tz - sz
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106 * sz = temp
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107 */
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108 if (a == 0) {
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109 if ((err = mp_mul_2(&sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
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110 } else {
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111 if ((err = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
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112 }
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113 if ((err = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
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114 if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
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115 if ((err = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) goto LBL_FU_ERR;
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116 mp_exch(&sz, &T1z);
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117 }
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118 }
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119
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120 mp_set_u32(&T1z, (uint32_t)((2 * a) + 5));
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121 if ((err = mp_mod(&T1z, N, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
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122 if (MP_IS_ZERO(&sz) && (mp_cmp(&tz, &T1z) == MP_EQ)) {
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123 *result = MP_YES;
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124 }
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125
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126 LBL_FU_ERR:
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127 mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL);
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128 return err;
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129 }
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130
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131 #endif
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132 #endif