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>
date Wed, 18 Mar 2020 15:28:56 +0000
parents f52919ffd3b1
children 1051e4eea25a
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_SQRTMOD_PRIME_C
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
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4 *
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5 * LibTomMath is a library that provides multiple-precision
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6 * integer arithmetic as well as number theoretic functionality.
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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
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13 */
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14
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15 /* Tonelli-Shanks algorithm
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16 * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
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17 * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
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18 *
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19 */
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20
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21 int mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret)
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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;
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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 */
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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 }
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39
1655
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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;
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50 res = MP_OKAY;
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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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parents: 1436
diff changeset
73 if ((res = mp_jacobi(&Z, prime, &legendre)) != MP_OKAY) goto cleanup;
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
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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diff changeset
78
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
79 if ((res = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup;
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diff changeset
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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diff changeset
82 if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
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diff changeset
83 /* t1 = (Q + 1) / 2 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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84 if ((res = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
85 /* R = n ^ ((Q + 1) / 2) mod prime */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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86 if ((res = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup;
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
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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Steffen Jaeckel <s_jaeckel@gmx.de>
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90 if ((res = mp_set_int(&two, 2uL)) != MP_OKAY) goto cleanup;
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parents: 1436
diff changeset
91
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92 res = MP_VAL;
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93 while (1) {
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parents: 1436
diff changeset
94 if ((res = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup;
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diff changeset
95 i = 0;
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96 while (1) {
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diff changeset
97 if (mp_cmp_d(&t1, 1uL) == MP_EQ) break;
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diff changeset
98 if ((res = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup;
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diff changeset
99 i++;
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100 }
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diff changeset
101 if (i == 0u) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
102 if ((res = mp_copy(&R, ret)) != MP_OKAY) goto cleanup;
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diff changeset
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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parents: 1436
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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
60fc6476e044 Update to libtommath v1.0
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parents:
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121
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122 cleanup:
1655
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diff changeset
123 mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
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124 return res;
1436
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
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125 }
60fc6476e044 Update to libtommath v1.0
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parents:
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126
60fc6476e044 Update to libtommath v1.0
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parents:
diff changeset
127 #endif
1655
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diff changeset
128
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129 /* ref: HEAD -> master, tag: v1.1.0 */
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diff changeset
130 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
131 /* commit time: 2019-01-28 20:32:32 +0100 */