Mercurial > dropbear
annotate libtommath/bn_mp_sqrtmod_prime.c @ 1665:7c17995bcdfb
Improve address logging on early exit messages (#83)
Change 'Early exit' and 'Exit before auth' messages to include the IP
address & port as part of the message.
This allows log scanning utilities such as 'fail2ban' to obtain the
offending IP address as part of the failure event instead of extracting
the PID from the message and then scanning the log again for match
'child connection from' messages
Signed-off-by: Kevin Darbyshire-Bryant <[email protected]>
author | Kevin Darbyshire-Bryant <6500011+ldir-EDB0@users.noreply.github.com> |
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date | Wed, 18 Mar 2020 15:28:56 +0000 |
parents | f52919ffd3b1 |
children | 1051e4eea25a |
rev | line source |
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1 #include "tommath_private.h" |
1436 | 2 #ifdef BN_MP_SQRTMOD_PRIME_C |
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis | |
4 * | |
5 * LibTomMath is a library that provides multiple-precision | |
6 * integer arithmetic as well as number theoretic functionality. | |
7 * | |
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8 * The library was designed directly after the MPI library by |
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9 * Michael Fromberger but has been written from scratch with |
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10 * additional optimizations in place. |
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11 * |
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12 * SPDX-License-Identifier: Unlicense |
1436 | 13 */ |
14 | |
15 /* Tonelli-Shanks algorithm | |
16 * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm | |
17 * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html | |
18 * | |
19 */ | |
20 | |
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21 int mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret) |
1436 | 22 { |
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23 int res, legendre; |
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24 mp_int t1, C, Q, S, Z, M, T, R, two; |
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25 mp_digit i; |
1436 | 26 |
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27 /* first handle the simple cases */ |
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28 if (mp_cmp_d(n, 0uL) == MP_EQ) { |
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29 mp_zero(ret); |
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30 return MP_OKAY; |
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31 } |
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32 if (mp_cmp_d(prime, 2uL) == MP_EQ) return MP_VAL; /* prime must be odd */ |
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33 if ((res = mp_jacobi(n, prime, &legendre)) != MP_OKAY) return res; |
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34 if (legendre == -1) return MP_VAL; /* quadratic non-residue mod prime */ |
1436 | 35 |
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36 if ((res = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) { |
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37 return res; |
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38 } |
1436 | 39 |
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40 /* SPECIAL CASE: if prime mod 4 == 3 |
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41 * compute directly: res = n^(prime+1)/4 mod prime |
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42 * Handbook of Applied Cryptography algorithm 3.36 |
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43 */ |
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44 if ((res = mp_mod_d(prime, 4uL, &i)) != MP_OKAY) goto cleanup; |
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45 if (i == 3u) { |
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46 if ((res = mp_add_d(prime, 1uL, &t1)) != MP_OKAY) goto cleanup; |
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47 if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; |
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48 if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; |
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49 if ((res = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup; |
1436 | 50 res = MP_OKAY; |
51 goto cleanup; | |
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52 } |
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53 |
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54 /* NOW: Tonelli-Shanks algorithm */ |
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55 |
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56 /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */ |
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57 if ((res = mp_copy(prime, &Q)) != MP_OKAY) goto cleanup; |
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58 if ((res = mp_sub_d(&Q, 1uL, &Q)) != MP_OKAY) goto cleanup; |
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59 /* Q = prime - 1 */ |
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60 mp_zero(&S); |
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61 /* S = 0 */ |
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62 while (mp_iseven(&Q) != MP_NO) { |
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63 if ((res = mp_div_2(&Q, &Q)) != MP_OKAY) goto cleanup; |
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64 /* Q = Q / 2 */ |
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65 if ((res = mp_add_d(&S, 1uL, &S)) != MP_OKAY) goto cleanup; |
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66 /* S = S + 1 */ |
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67 } |
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68 |
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69 /* find a Z such that the Legendre symbol (Z|prime) == -1 */ |
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70 if ((res = mp_set_int(&Z, 2uL)) != MP_OKAY) goto cleanup; |
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71 /* Z = 2 */ |
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72 while (1) { |
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73 if ((res = mp_jacobi(&Z, prime, &legendre)) != MP_OKAY) goto cleanup; |
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74 if (legendre == -1) break; |
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75 if ((res = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY) goto cleanup; |
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76 /* Z = Z + 1 */ |
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77 } |
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78 |
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79 if ((res = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup; |
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80 /* C = Z ^ Q mod prime */ |
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81 if ((res = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY) goto cleanup; |
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82 if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; |
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83 /* t1 = (Q + 1) / 2 */ |
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84 if ((res = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup; |
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85 /* R = n ^ ((Q + 1) / 2) mod prime */ |
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86 if ((res = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup; |
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87 /* T = n ^ Q mod prime */ |
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88 if ((res = mp_copy(&S, &M)) != MP_OKAY) goto cleanup; |
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89 /* M = S */ |
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90 if ((res = mp_set_int(&two, 2uL)) != MP_OKAY) goto cleanup; |
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91 |
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92 res = MP_VAL; |
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93 while (1) { |
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94 if ((res = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup; |
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95 i = 0; |
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96 while (1) { |
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97 if (mp_cmp_d(&t1, 1uL) == MP_EQ) break; |
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98 if ((res = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup; |
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99 i++; |
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100 } |
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101 if (i == 0u) { |
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102 if ((res = mp_copy(&R, ret)) != MP_OKAY) goto cleanup; |
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103 res = MP_OKAY; |
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104 goto cleanup; |
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105 } |
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106 if ((res = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup; |
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107 if ((res = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto cleanup; |
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108 if ((res = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup; |
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109 /* t1 = 2 ^ (M - i - 1) */ |
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110 if ((res = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY) goto cleanup; |
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111 /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */ |
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112 if ((res = mp_sqrmod(&t1, prime, &C)) != MP_OKAY) goto cleanup; |
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113 /* C = (t1 * t1) mod prime */ |
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114 if ((res = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY) goto cleanup; |
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115 /* R = (R * t1) mod prime */ |
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116 if ((res = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY) goto cleanup; |
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117 /* T = (T * C) mod prime */ |
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118 mp_set(&M, i); |
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119 /* M = i */ |
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120 } |
1436 | 121 |
122 cleanup: | |
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123 mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL); |
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124 return res; |
1436 | 125 } |
126 | |
127 #endif | |
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128 |
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129 /* ref: HEAD -> master, tag: v1.1.0 */ |
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130 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */ |
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131 /* commit time: 2019-01-28 20:32:32 +0100 */ |