Mercurial > dropbear

annotate libtommath/bn_mp_prime_frobenius_underwood.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
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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