Mercurial > dropbear
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 |
rev | line source |
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1655
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1 #include "tommath_private.h" |
1436 | 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 /* SPDX-License-Identifier: Unlicense */ |
1436 | 5 |
6 /* Tonelli-Shanks algorithm | |
7 * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm | |
8 * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html | |
9 * | |
10 */ | |
11 | |
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12 mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret) |
1436 | 13 { |
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14 mp_err err; |
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15 int legendre; |
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16 mp_int t1, C, Q, S, Z, M, T, R, two; |
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17 mp_digit i; |
1436 | 18 |
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19 /* first handle the simple cases */ |
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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 */ |
1436 | 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 } |
1436 | 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; |
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39 if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; |
1051e4eea25a
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40 if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; |
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41 if ((err = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup; |
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42 err = MP_OKAY; |
1436 | 43 goto cleanup; |
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44 } |
f52919ffd3b1
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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 */ |
f52919ffd3b1
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47 |
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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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55 if ((err = mp_div_2(&Q, &Q)) != MP_OKAY) goto cleanup; |
1655
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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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58 /* S = S + 1 */ |
f52919ffd3b1
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59 } |
f52919ffd3b1
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60 |
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61 /* find a Z such that the Legendre symbol (Z|prime) == -1 */ |
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62 mp_set_u32(&Z, 2u); |
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63 /* Z = 2 */ |
1692
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64 for (;;) { |
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65 if ((err = mp_kronecker(&Z, prime, &legendre)) != MP_OKAY) goto cleanup; |
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66 if (legendre == -1) break; |
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67 if ((err = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY) goto cleanup; |
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68 /* Z = Z + 1 */ |
f52919ffd3b1
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69 } |
f52919ffd3b1
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70 |
1692
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71 if ((err = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup; |
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72 /* C = Z ^ Q mod prime */ |
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73 if ((err = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY) goto cleanup; |
1051e4eea25a
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74 if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; |
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f52919ffd3b1
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75 /* t1 = (Q + 1) / 2 */ |
1692
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76 if ((err = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup; |
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update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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77 /* R = n ^ ((Q + 1) / 2) mod prime */ |
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78 if ((err = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup; |
1655
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79 /* T = n ^ Q mod prime */ |
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80 if ((err = mp_copy(&S, &M)) != MP_OKAY) goto cleanup; |
1655
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81 /* M = S */ |
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Update LibTomMath to 1.2.0 (#84)
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82 mp_set_u32(&two, 2u); |
1655
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83 |
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84 for (;;) { |
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85 if ((err = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup; |
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86 i = 0; |
1692
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87 for (;;) { |
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88 if (mp_cmp_d(&t1, 1uL) == MP_EQ) break; |
1692
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89 if ((err = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup; |
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90 i++; |
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91 } |
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92 if (i == 0u) { |
1692
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93 if ((err = mp_copy(&R, ret)) != MP_OKAY) goto cleanup; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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94 err = MP_OKAY; |
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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:
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|
96 } |
1692
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97 if ((err = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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98 if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto cleanup; |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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99 if ((err = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup; |
1655
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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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100 /* t1 = 2 ^ (M - i - 1) */ |
1692
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Update LibTomMath to 1.2.0 (#84)
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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:
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diff
changeset
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102 /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */ |
1692
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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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
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105 if ((err = mp_mulmod(&R, &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
|
106 /* R = (R * t1) mod prime */ |
1692
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
1655
diff
changeset
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107 if ((err = mp_mulmod(&T, &C, 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
|
108 /* T = (T * C) mod prime */ |
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
|
109 mp_set(&M, 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
|
110 /* M = 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
|
111 } |
1436 | 112 |
113 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
|
114 mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL); |
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Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents:
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115 return err; |
1436 | 116 } |
117 | |
118 #endif |