annotate libtommath/bn_mp_sqrtmod_prime.c @ 1715:3974f087d9c0

Disallow leading lines before the ident for server (#102) Per RFC4253 4.2 clients must be able to process other lines of data before the version string, server behavior is not defined neither with MUST/SHOULD nor with MAY. If server process up to 50 lines too - it may cause too long hanging session with invalid/evil client that consume host resources and potentially may lead to DDoS on poor embedded boxes. Let's require first line from client to be version string and fail early if it's not - matches both RFC and real OpenSSH behavior.
author Vladislav Grishenko <themiron@users.noreply.github.com>
date Mon, 15 Jun 2020 18:22:18 +0500
parents 1051e4eea25a
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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diff changeset
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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diff changeset
4 /* SPDX-License-Identifier: Unlicense */
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5
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6 /* Tonelli-Shanks algorithm
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7 * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
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8 * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
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9 *
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10 */
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11
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12 mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret)
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13 {
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14 mp_err err;
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diff changeset
15 int legendre;
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
16 mp_int t1, C, Q, S, Z, M, T, R, two;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
17 mp_digit i;
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18
1655
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diff changeset
19 /* first handle the simple cases */
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diff changeset
20 if (mp_cmp_d(n, 0uL) == MP_EQ) {
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21 mp_zero(ret);
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22 return MP_OKAY;
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23 }
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24 if (mp_cmp_d(prime, 2uL) == MP_EQ) return MP_VAL; /* prime must be odd */
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25 if ((err = mp_kronecker(n, prime, &legendre)) != MP_OKAY) return err;
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26 if (legendre == -1) return MP_VAL; /* quadratic non-residue mod prime */
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27
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28 if ((err = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) {
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29 return err;
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30 }
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31
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32 /* SPECIAL CASE: if prime mod 4 == 3
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33 * compute directly: err = n^(prime+1)/4 mod prime
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34 * Handbook of Applied Cryptography algorithm 3.36
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35 */
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36 if ((err = mp_mod_d(prime, 4uL, &i)) != MP_OKAY) goto cleanup;
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37 if (i == 3u) {
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38 if ((err = mp_add_d(prime, 1uL, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
39 if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
40 if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
41 if ((err = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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42 err = MP_OKAY;
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60fc6476e044 Update to libtommath v1.0
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43 goto cleanup;
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44 }
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45
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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46 /* NOW: Tonelli-Shanks algorithm */
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47
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diff changeset
48 /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */
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49 if ((err = mp_copy(prime, &Q)) != MP_OKAY) goto cleanup;
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50 if ((err = mp_sub_d(&Q, 1uL, &Q)) != MP_OKAY) goto cleanup;
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51 /* Q = prime - 1 */
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52 mp_zero(&S);
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53 /* S = 0 */
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54 while (MP_IS_EVEN(&Q)) {
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diff changeset
55 if ((err = mp_div_2(&Q, &Q)) != MP_OKAY) goto cleanup;
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
56 /* Q = Q / 2 */
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57 if ((err = mp_add_d(&S, 1uL, &S)) != MP_OKAY) goto cleanup;
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diff changeset
58 /* S = S + 1 */
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59 }
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diff changeset
60
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
61 /* find a Z such that the Legendre symbol (Z|prime) == -1 */
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62 mp_set_u32(&Z, 2u);
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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63 /* Z = 2 */
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64 for (;;) {
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diff changeset
65 if ((err = mp_kronecker(&Z, prime, &legendre)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
66 if (legendre == -1) break;
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diff changeset
67 if ((err = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY) goto cleanup;
1655
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
68 /* Z = Z + 1 */
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diff changeset
69 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
70
1692
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diff changeset
71 if ((err = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup;
1655
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
72 /* C = Z ^ Q mod prime */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
73 if ((err = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
74 if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
1655
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
75 /* t1 = (Q + 1) / 2 */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
76 if ((err = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup;
1655
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
77 /* R = n ^ ((Q + 1) / 2) mod prime */
1692
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Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
78 if ((err = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup;
1655
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 /* T = n ^ Q mod prime */
1692
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Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
80 if ((err = mp_copy(&S, &M)) != MP_OKAY) goto cleanup;
1655
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
81 /* M = S */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
82 mp_set_u32(&two, 2u);
1655
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
83
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
84 for (;;) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
85 if ((err = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup;
1655
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
86 i = 0;
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
87 for (;;) {
1655
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
88 if (mp_cmp_d(&t1, 1uL) == MP_EQ) break;
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
89 if ((err = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup;
1655
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
90 i++;
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
91 }
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
92 if (i == 0u) {
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
93 if ((err = mp_copy(&R, ret)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
94 err = MP_OKAY;
1655
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
95 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
96 }
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
97 if ((err = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
98 if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
99 if ((err = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
1655
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
100 /* t1 = 2 ^ (M - i - 1) */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
101 if ((err = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
1655
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
102 /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
103 if ((err = mp_sqrmod(&t1, prime, &C)) != MP_OKAY) goto cleanup;
1655
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
104 /* C = (t1 * t1) mod prime */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
105 if ((err = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY) goto cleanup;
1655
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106 /* R = (R * t1) mod prime */
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107 if ((err = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY) goto cleanup;
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108 /* T = (T * C) mod prime */
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109 mp_set(&M, i);
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110 /* M = i */
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111 }
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112
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113 cleanup:
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114 mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
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115 return err;
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116 }
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117
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118 #endif