Darren Tucker | 7336b90 | 2010-12-05 09:00:30 +1100 | [diff] [blame] | 1 | /* $OpenBSD: schnorr.c,v 1.5 2010/12/03 23:49:26 djm Exp $ */ |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 2 | /* |
| 3 | * Copyright (c) 2008 Damien Miller. All rights reserved. |
| 4 | * |
| 5 | * Permission to use, copy, modify, and distribute this software for any |
| 6 | * purpose with or without fee is hereby granted, provided that the above |
| 7 | * copyright notice and this permission notice appear in all copies. |
| 8 | * |
| 9 | * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| 10 | * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| 11 | * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR |
| 12 | * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
| 13 | * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN |
| 14 | * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF |
| 15 | * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. |
| 16 | */ |
| 17 | |
| 18 | /* |
| 19 | * Implementation of Schnorr signatures / zero-knowledge proofs, based on |
| 20 | * description in: |
| 21 | * |
| 22 | * F. Hao, P. Ryan, "Password Authenticated Key Exchange by Juggling", |
| 23 | * 16th Workshop on Security Protocols, Cambridge, April 2008 |
| 24 | * |
| 25 | * http://grouper.ieee.org/groups/1363/Research/contributions/hao-ryan-2008.pdf |
| 26 | */ |
| 27 | |
| 28 | #include "includes.h" |
| 29 | |
| 30 | #include <sys/types.h> |
| 31 | |
| 32 | #include <string.h> |
| 33 | #include <stdarg.h> |
| 34 | #include <stdio.h> |
| 35 | |
| 36 | #include <openssl/evp.h> |
| 37 | #include <openssl/bn.h> |
| 38 | |
| 39 | #include "xmalloc.h" |
| 40 | #include "buffer.h" |
| 41 | #include "log.h" |
| 42 | |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 43 | #include "schnorr.h" |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 44 | |
Darren Tucker | 8aae6ff | 2009-03-07 12:01:47 +1100 | [diff] [blame] | 45 | #include "openbsd-compat/openssl-compat.h" |
| 46 | |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 47 | /* #define SCHNORR_DEBUG */ /* Privacy-violating debugging */ |
| 48 | /* #define SCHNORR_MAIN */ /* Include main() selftest */ |
| 49 | |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 50 | #ifndef SCHNORR_DEBUG |
| 51 | # define SCHNORR_DEBUG_BN(a) |
| 52 | # define SCHNORR_DEBUG_BUF(a) |
| 53 | #else |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 54 | # define SCHNORR_DEBUG_BN(a) debug3_bn a |
| 55 | # define SCHNORR_DEBUG_BUF(a) debug3_buf a |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 56 | #endif /* SCHNORR_DEBUG */ |
| 57 | |
| 58 | /* |
| 59 | * Calculate hash component of Schnorr signature H(g || g^v || g^x || id) |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 60 | * using the hash function defined by "evp_md". Returns signature as |
| 61 | * bignum or NULL on error. |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 62 | */ |
| 63 | static BIGNUM * |
| 64 | schnorr_hash(const BIGNUM *p, const BIGNUM *q, const BIGNUM *g, |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 65 | const EVP_MD *evp_md, const BIGNUM *g_v, const BIGNUM *g_x, |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 66 | const u_char *id, u_int idlen) |
| 67 | { |
| 68 | u_char *digest; |
| 69 | u_int digest_len; |
| 70 | BIGNUM *h; |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 71 | Buffer b; |
| 72 | int success = -1; |
| 73 | |
| 74 | if ((h = BN_new()) == NULL) { |
| 75 | error("%s: BN_new", __func__); |
| 76 | return NULL; |
| 77 | } |
| 78 | |
| 79 | buffer_init(&b); |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 80 | |
Damien Miller | 2591838 | 2009-02-21 12:45:18 +1100 | [diff] [blame] | 81 | /* h = H(g || p || q || g^v || g^x || id) */ |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 82 | buffer_put_bignum2(&b, g); |
Damien Miller | 2591838 | 2009-02-21 12:45:18 +1100 | [diff] [blame] | 83 | buffer_put_bignum2(&b, p); |
| 84 | buffer_put_bignum2(&b, q); |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 85 | buffer_put_bignum2(&b, g_v); |
| 86 | buffer_put_bignum2(&b, g_x); |
| 87 | buffer_put_string(&b, id, idlen); |
| 88 | |
| 89 | SCHNORR_DEBUG_BUF((buffer_ptr(&b), buffer_len(&b), |
| 90 | "%s: hashblob", __func__)); |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 91 | if (hash_buffer(buffer_ptr(&b), buffer_len(&b), evp_md, |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 92 | &digest, &digest_len) != 0) { |
| 93 | error("%s: hash_buffer", __func__); |
| 94 | goto out; |
| 95 | } |
| 96 | if (BN_bin2bn(digest, (int)digest_len, h) == NULL) { |
| 97 | error("%s: BN_bin2bn", __func__); |
| 98 | goto out; |
| 99 | } |
| 100 | success = 0; |
| 101 | SCHNORR_DEBUG_BN((h, "%s: h = ", __func__)); |
| 102 | out: |
| 103 | buffer_free(&b); |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 104 | bzero(digest, digest_len); |
| 105 | xfree(digest); |
| 106 | digest_len = 0; |
| 107 | if (success == 0) |
| 108 | return h; |
| 109 | BN_clear_free(h); |
| 110 | return NULL; |
| 111 | } |
| 112 | |
| 113 | /* |
| 114 | * Generate Schnorr signature to prove knowledge of private value 'x' used |
| 115 | * in public exponent g^x, under group defined by 'grp_p', 'grp_q' and 'grp_g' |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 116 | * using the hash function "evp_md". |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 117 | * 'idlen' bytes from 'id' will be included in the signature hash as an anti- |
| 118 | * replay salt. |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 119 | * |
| 120 | * On success, 0 is returned. The signature values are returned as *e_p |
| 121 | * (g^v mod p) and *r_p (v - xh mod q). The caller must free these values. |
| 122 | * On failure, -1 is returned. |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 123 | */ |
| 124 | int |
| 125 | schnorr_sign(const BIGNUM *grp_p, const BIGNUM *grp_q, const BIGNUM *grp_g, |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 126 | const EVP_MD *evp_md, const BIGNUM *x, const BIGNUM *g_x, |
| 127 | const u_char *id, u_int idlen, BIGNUM **r_p, BIGNUM **e_p) |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 128 | { |
| 129 | int success = -1; |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 130 | BIGNUM *h, *tmp, *v, *g_v, *r; |
| 131 | BN_CTX *bn_ctx; |
| 132 | |
| 133 | SCHNORR_DEBUG_BN((x, "%s: x = ", __func__)); |
| 134 | SCHNORR_DEBUG_BN((g_x, "%s: g_x = ", __func__)); |
| 135 | |
| 136 | /* Avoid degenerate cases: g^0 yields a spoofable signature */ |
| 137 | if (BN_cmp(g_x, BN_value_one()) <= 0) { |
| 138 | error("%s: g_x < 1", __func__); |
| 139 | return -1; |
| 140 | } |
Damien Miller | f7540cd | 2010-09-24 22:03:24 +1000 | [diff] [blame] | 141 | if (BN_cmp(g_x, grp_p) >= 0) { |
| 142 | error("%s: g_x > g", __func__); |
| 143 | return -1; |
| 144 | } |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 145 | |
| 146 | h = g_v = r = tmp = v = NULL; |
| 147 | if ((bn_ctx = BN_CTX_new()) == NULL) { |
| 148 | error("%s: BN_CTX_new", __func__); |
| 149 | goto out; |
| 150 | } |
| 151 | if ((g_v = BN_new()) == NULL || |
| 152 | (r = BN_new()) == NULL || |
| 153 | (tmp = BN_new()) == NULL) { |
| 154 | error("%s: BN_new", __func__); |
| 155 | goto out; |
| 156 | } |
| 157 | |
| 158 | /* |
| 159 | * v must be a random element of Zq, so 1 <= v < q |
| 160 | * we also exclude v = 1, since g^1 looks dangerous |
| 161 | */ |
| 162 | if ((v = bn_rand_range_gt_one(grp_p)) == NULL) { |
| 163 | error("%s: bn_rand_range2", __func__); |
| 164 | goto out; |
| 165 | } |
| 166 | SCHNORR_DEBUG_BN((v, "%s: v = ", __func__)); |
| 167 | |
| 168 | /* g_v = g^v mod p */ |
| 169 | if (BN_mod_exp(g_v, grp_g, v, grp_p, bn_ctx) == -1) { |
| 170 | error("%s: BN_mod_exp (g^v mod p)", __func__); |
| 171 | goto out; |
| 172 | } |
| 173 | SCHNORR_DEBUG_BN((g_v, "%s: g_v = ", __func__)); |
| 174 | |
| 175 | /* h = H(g || g^v || g^x || id) */ |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 176 | if ((h = schnorr_hash(grp_p, grp_q, grp_g, evp_md, g_v, g_x, |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 177 | id, idlen)) == NULL) { |
| 178 | error("%s: schnorr_hash failed", __func__); |
| 179 | goto out; |
| 180 | } |
| 181 | |
| 182 | /* r = v - xh mod q */ |
| 183 | if (BN_mod_mul(tmp, x, h, grp_q, bn_ctx) == -1) { |
| 184 | error("%s: BN_mod_mul (tmp = xv mod q)", __func__); |
| 185 | goto out; |
| 186 | } |
| 187 | if (BN_mod_sub(r, v, tmp, grp_q, bn_ctx) == -1) { |
| 188 | error("%s: BN_mod_mul (r = v - tmp)", __func__); |
| 189 | goto out; |
| 190 | } |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 191 | SCHNORR_DEBUG_BN((g_v, "%s: e = ", __func__)); |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 192 | SCHNORR_DEBUG_BN((r, "%s: r = ", __func__)); |
| 193 | |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 194 | *e_p = g_v; |
| 195 | *r_p = r; |
| 196 | |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 197 | success = 0; |
| 198 | out: |
| 199 | BN_CTX_free(bn_ctx); |
| 200 | if (h != NULL) |
| 201 | BN_clear_free(h); |
| 202 | if (v != NULL) |
| 203 | BN_clear_free(v); |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 204 | BN_clear_free(tmp); |
| 205 | |
| 206 | return success; |
| 207 | } |
| 208 | |
| 209 | /* |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 210 | * Generate Schnorr signature to prove knowledge of private value 'x' used |
| 211 | * in public exponent g^x, under group defined by 'grp_p', 'grp_q' and 'grp_g' |
| 212 | * using a SHA256 hash. |
| 213 | * 'idlen' bytes from 'id' will be included in the signature hash as an anti- |
| 214 | * replay salt. |
| 215 | * On success, 0 is returned and *siglen bytes of signature are returned in |
| 216 | * *sig (caller to free). Returns -1 on failure. |
| 217 | */ |
| 218 | int |
| 219 | schnorr_sign_buf(const BIGNUM *grp_p, const BIGNUM *grp_q, const BIGNUM *grp_g, |
| 220 | const BIGNUM *x, const BIGNUM *g_x, const u_char *id, u_int idlen, |
| 221 | u_char **sig, u_int *siglen) |
| 222 | { |
| 223 | Buffer b; |
| 224 | BIGNUM *r, *e; |
| 225 | |
| 226 | if (schnorr_sign(grp_p, grp_q, grp_g, EVP_sha256(), |
| 227 | x, g_x, id, idlen, &r, &e) != 0) |
| 228 | return -1; |
| 229 | |
| 230 | /* Signature is (e, r) */ |
| 231 | buffer_init(&b); |
| 232 | /* XXX sigtype-hash as string? */ |
| 233 | buffer_put_bignum2(&b, e); |
| 234 | buffer_put_bignum2(&b, r); |
| 235 | *siglen = buffer_len(&b); |
| 236 | *sig = xmalloc(*siglen); |
| 237 | memcpy(*sig, buffer_ptr(&b), *siglen); |
| 238 | SCHNORR_DEBUG_BUF((buffer_ptr(&b), buffer_len(&b), |
| 239 | "%s: sigblob", __func__)); |
| 240 | buffer_free(&b); |
| 241 | |
| 242 | BN_clear_free(r); |
| 243 | BN_clear_free(e); |
| 244 | |
| 245 | return 0; |
| 246 | } |
| 247 | |
| 248 | /* |
| 249 | * Verify Schnorr signature { r (v - xh mod q), e (g^v mod p) } against |
| 250 | * public exponent g_x (g^x) under group defined by 'grp_p', 'grp_q' and |
| 251 | * 'grp_g' using hash "evp_md". |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 252 | * Signature hash will be salted with 'idlen' bytes from 'id'. |
| 253 | * Returns -1 on failure, 0 on incorrect signature or 1 on matching signature. |
| 254 | */ |
| 255 | int |
| 256 | schnorr_verify(const BIGNUM *grp_p, const BIGNUM *grp_q, const BIGNUM *grp_g, |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 257 | const EVP_MD *evp_md, const BIGNUM *g_x, const u_char *id, u_int idlen, |
| 258 | const BIGNUM *r, const BIGNUM *e) |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 259 | { |
| 260 | int success = -1; |
Darren Tucker | 7336b90 | 2010-12-05 09:00:30 +1100 | [diff] [blame] | 261 | BIGNUM *h = NULL, *g_xh = NULL, *g_r = NULL, *gx_q = NULL; |
| 262 | BIGNUM *expected = NULL; |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 263 | BN_CTX *bn_ctx; |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 264 | |
| 265 | SCHNORR_DEBUG_BN((g_x, "%s: g_x = ", __func__)); |
| 266 | |
| 267 | /* Avoid degenerate cases: g^0 yields a spoofable signature */ |
| 268 | if (BN_cmp(g_x, BN_value_one()) <= 0) { |
Darren Tucker | 7336b90 | 2010-12-05 09:00:30 +1100 | [diff] [blame] | 269 | error("%s: g_x <= 1", __func__); |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 270 | return -1; |
| 271 | } |
Damien Miller | f7540cd | 2010-09-24 22:03:24 +1000 | [diff] [blame] | 272 | if (BN_cmp(g_x, grp_p) >= 0) { |
| 273 | error("%s: g_x >= p", __func__); |
| 274 | return -1; |
| 275 | } |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 276 | |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 277 | h = g_xh = g_r = expected = NULL; |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 278 | if ((bn_ctx = BN_CTX_new()) == NULL) { |
| 279 | error("%s: BN_CTX_new", __func__); |
| 280 | goto out; |
| 281 | } |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 282 | if ((g_xh = BN_new()) == NULL || |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 283 | (g_r = BN_new()) == NULL || |
Darren Tucker | 7336b90 | 2010-12-05 09:00:30 +1100 | [diff] [blame] | 284 | (gx_q = BN_new()) == NULL || |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 285 | (expected = BN_new()) == NULL) { |
| 286 | error("%s: BN_new", __func__); |
| 287 | goto out; |
| 288 | } |
| 289 | |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 290 | SCHNORR_DEBUG_BN((e, "%s: e = ", __func__)); |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 291 | SCHNORR_DEBUG_BN((r, "%s: r = ", __func__)); |
| 292 | |
Darren Tucker | 7336b90 | 2010-12-05 09:00:30 +1100 | [diff] [blame] | 293 | /* gx_q = (g^x)^q must === 1 mod p */ |
| 294 | if (BN_mod_exp(gx_q, g_x, grp_q, grp_p, bn_ctx) == -1) { |
| 295 | error("%s: BN_mod_exp (g_x^q mod p)", __func__); |
| 296 | goto out; |
| 297 | } |
| 298 | if (BN_cmp(gx_q, BN_value_one()) != 0) { |
| 299 | error("%s: Invalid signature (g^x)^q != 1 mod p", __func__); |
| 300 | goto out; |
| 301 | } |
| 302 | |
| 303 | SCHNORR_DEBUG_BN((g_xh, "%s: g_xh = ", __func__)); |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 304 | /* h = H(g || g^v || g^x || id) */ |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 305 | if ((h = schnorr_hash(grp_p, grp_q, grp_g, evp_md, e, g_x, |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 306 | id, idlen)) == NULL) { |
| 307 | error("%s: schnorr_hash failed", __func__); |
| 308 | goto out; |
| 309 | } |
| 310 | |
| 311 | /* g_xh = (g^x)^h */ |
| 312 | if (BN_mod_exp(g_xh, g_x, h, grp_p, bn_ctx) == -1) { |
| 313 | error("%s: BN_mod_exp (g_x^h mod p)", __func__); |
| 314 | goto out; |
| 315 | } |
| 316 | SCHNORR_DEBUG_BN((g_xh, "%s: g_xh = ", __func__)); |
| 317 | |
| 318 | /* g_r = g^r */ |
| 319 | if (BN_mod_exp(g_r, grp_g, r, grp_p, bn_ctx) == -1) { |
| 320 | error("%s: BN_mod_exp (g_x^h mod p)", __func__); |
| 321 | goto out; |
| 322 | } |
| 323 | SCHNORR_DEBUG_BN((g_r, "%s: g_r = ", __func__)); |
| 324 | |
| 325 | /* expected = g^r * g_xh */ |
| 326 | if (BN_mod_mul(expected, g_r, g_xh, grp_p, bn_ctx) == -1) { |
| 327 | error("%s: BN_mod_mul (expected = g_r mod p)", __func__); |
| 328 | goto out; |
| 329 | } |
| 330 | SCHNORR_DEBUG_BN((expected, "%s: expected = ", __func__)); |
| 331 | |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 332 | /* Check e == expected */ |
| 333 | success = BN_cmp(expected, e) == 0; |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 334 | out: |
| 335 | BN_CTX_free(bn_ctx); |
| 336 | if (h != NULL) |
| 337 | BN_clear_free(h); |
Darren Tucker | 7336b90 | 2010-12-05 09:00:30 +1100 | [diff] [blame] | 338 | if (gx_q != NULL) |
| 339 | BN_clear_free(gx_q); |
| 340 | if (g_xh != NULL) |
| 341 | BN_clear_free(g_xh); |
| 342 | if (g_r != NULL) |
| 343 | BN_clear_free(g_r); |
| 344 | if (expected != NULL) |
| 345 | BN_clear_free(expected); |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 346 | return success; |
| 347 | } |
| 348 | |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 349 | /* |
| 350 | * Verify Schnorr signature 'sig' of length 'siglen' against public exponent |
| 351 | * g_x (g^x) under group defined by 'grp_p', 'grp_q' and 'grp_g' using a |
| 352 | * SHA256 hash. |
| 353 | * Signature hash will be salted with 'idlen' bytes from 'id'. |
| 354 | * Returns -1 on failure, 0 on incorrect signature or 1 on matching signature. |
| 355 | */ |
| 356 | int |
| 357 | schnorr_verify_buf(const BIGNUM *grp_p, const BIGNUM *grp_q, |
| 358 | const BIGNUM *grp_g, |
| 359 | const BIGNUM *g_x, const u_char *id, u_int idlen, |
| 360 | const u_char *sig, u_int siglen) |
| 361 | { |
| 362 | Buffer b; |
| 363 | int ret = -1; |
| 364 | u_int rlen; |
| 365 | BIGNUM *r, *e; |
| 366 | |
| 367 | e = r = NULL; |
| 368 | if ((e = BN_new()) == NULL || |
| 369 | (r = BN_new()) == NULL) { |
| 370 | error("%s: BN_new", __func__); |
| 371 | goto out; |
| 372 | } |
| 373 | |
| 374 | /* Extract g^v and r from signature blob */ |
| 375 | buffer_init(&b); |
| 376 | buffer_append(&b, sig, siglen); |
| 377 | SCHNORR_DEBUG_BUF((buffer_ptr(&b), buffer_len(&b), |
| 378 | "%s: sigblob", __func__)); |
| 379 | buffer_get_bignum2(&b, e); |
| 380 | buffer_get_bignum2(&b, r); |
| 381 | rlen = buffer_len(&b); |
| 382 | buffer_free(&b); |
| 383 | if (rlen != 0) { |
| 384 | error("%s: remaining bytes in signature %d", __func__, rlen); |
| 385 | goto out; |
| 386 | } |
| 387 | |
| 388 | ret = schnorr_verify(grp_p, grp_q, grp_g, EVP_sha256(), |
| 389 | g_x, id, idlen, r, e); |
| 390 | out: |
| 391 | BN_clear_free(e); |
| 392 | BN_clear_free(r); |
| 393 | |
| 394 | return ret; |
| 395 | } |
| 396 | |
| 397 | /* Helper functions */ |
| 398 | |
| 399 | /* |
| 400 | * Generate uniformly distributed random number in range (1, high). |
| 401 | * Return number on success, NULL on failure. |
| 402 | */ |
| 403 | BIGNUM * |
| 404 | bn_rand_range_gt_one(const BIGNUM *high) |
| 405 | { |
| 406 | BIGNUM *r, *tmp; |
| 407 | int success = -1; |
| 408 | |
| 409 | if ((tmp = BN_new()) == NULL) { |
| 410 | error("%s: BN_new", __func__); |
| 411 | return NULL; |
| 412 | } |
| 413 | if ((r = BN_new()) == NULL) { |
| 414 | error("%s: BN_new failed", __func__); |
| 415 | goto out; |
| 416 | } |
| 417 | if (BN_set_word(tmp, 2) != 1) { |
| 418 | error("%s: BN_set_word(tmp, 2)", __func__); |
| 419 | goto out; |
| 420 | } |
| 421 | if (BN_sub(tmp, high, tmp) == -1) { |
| 422 | error("%s: BN_sub failed (tmp = high - 2)", __func__); |
| 423 | goto out; |
| 424 | } |
| 425 | if (BN_rand_range(r, tmp) == -1) { |
| 426 | error("%s: BN_rand_range failed", __func__); |
| 427 | goto out; |
| 428 | } |
| 429 | if (BN_set_word(tmp, 2) != 1) { |
| 430 | error("%s: BN_set_word(tmp, 2)", __func__); |
| 431 | goto out; |
| 432 | } |
| 433 | if (BN_add(r, r, tmp) == -1) { |
| 434 | error("%s: BN_add failed (r = r + 2)", __func__); |
| 435 | goto out; |
| 436 | } |
| 437 | success = 0; |
| 438 | out: |
| 439 | BN_clear_free(tmp); |
| 440 | if (success == 0) |
| 441 | return r; |
| 442 | BN_clear_free(r); |
| 443 | return NULL; |
| 444 | } |
| 445 | |
| 446 | /* |
| 447 | * Hash contents of buffer 'b' with hash 'md'. Returns 0 on success, |
| 448 | * with digest via 'digestp' (caller to free) and length via 'lenp'. |
| 449 | * Returns -1 on failure. |
| 450 | */ |
| 451 | int |
| 452 | hash_buffer(const u_char *buf, u_int len, const EVP_MD *md, |
| 453 | u_char **digestp, u_int *lenp) |
| 454 | { |
| 455 | u_char digest[EVP_MAX_MD_SIZE]; |
| 456 | u_int digest_len; |
| 457 | EVP_MD_CTX evp_md_ctx; |
| 458 | int success = -1; |
| 459 | |
| 460 | EVP_MD_CTX_init(&evp_md_ctx); |
| 461 | |
| 462 | if (EVP_DigestInit_ex(&evp_md_ctx, md, NULL) != 1) { |
| 463 | error("%s: EVP_DigestInit_ex", __func__); |
| 464 | goto out; |
| 465 | } |
| 466 | if (EVP_DigestUpdate(&evp_md_ctx, buf, len) != 1) { |
| 467 | error("%s: EVP_DigestUpdate", __func__); |
| 468 | goto out; |
| 469 | } |
| 470 | if (EVP_DigestFinal_ex(&evp_md_ctx, digest, &digest_len) != 1) { |
| 471 | error("%s: EVP_DigestFinal_ex", __func__); |
| 472 | goto out; |
| 473 | } |
| 474 | *digestp = xmalloc(digest_len); |
| 475 | *lenp = digest_len; |
| 476 | memcpy(*digestp, digest, *lenp); |
| 477 | success = 0; |
| 478 | out: |
| 479 | EVP_MD_CTX_cleanup(&evp_md_ctx); |
| 480 | bzero(digest, sizeof(digest)); |
| 481 | digest_len = 0; |
| 482 | return success; |
| 483 | } |
| 484 | |
| 485 | /* print formatted string followed by bignum */ |
| 486 | void |
| 487 | debug3_bn(const BIGNUM *n, const char *fmt, ...) |
| 488 | { |
| 489 | char *out, *h; |
| 490 | va_list args; |
| 491 | |
| 492 | out = NULL; |
| 493 | va_start(args, fmt); |
| 494 | vasprintf(&out, fmt, args); |
| 495 | va_end(args); |
| 496 | if (out == NULL) |
| 497 | fatal("%s: vasprintf failed", __func__); |
| 498 | |
| 499 | if (n == NULL) |
| 500 | debug3("%s(null)", out); |
| 501 | else { |
| 502 | h = BN_bn2hex(n); |
| 503 | debug3("%s0x%s", out, h); |
| 504 | free(h); |
| 505 | } |
| 506 | free(out); |
| 507 | } |
| 508 | |
| 509 | /* print formatted string followed by buffer contents in hex */ |
| 510 | void |
| 511 | debug3_buf(const u_char *buf, u_int len, const char *fmt, ...) |
| 512 | { |
| 513 | char *out, h[65]; |
| 514 | u_int i, j; |
| 515 | va_list args; |
| 516 | |
| 517 | out = NULL; |
| 518 | va_start(args, fmt); |
| 519 | vasprintf(&out, fmt, args); |
| 520 | va_end(args); |
| 521 | if (out == NULL) |
| 522 | fatal("%s: vasprintf failed", __func__); |
| 523 | |
| 524 | debug3("%s length %u%s", out, len, buf == NULL ? " (null)" : ""); |
| 525 | free(out); |
| 526 | if (buf == NULL) |
| 527 | return; |
| 528 | |
| 529 | *h = '\0'; |
| 530 | for (i = j = 0; i < len; i++) { |
| 531 | snprintf(h + j, sizeof(h) - j, "%02x", buf[i]); |
| 532 | j += 2; |
| 533 | if (j >= sizeof(h) - 1 || i == len - 1) { |
| 534 | debug3(" %s", h); |
| 535 | *h = '\0'; |
| 536 | j = 0; |
| 537 | } |
| 538 | } |
| 539 | } |
| 540 | |
| 541 | /* |
| 542 | * Construct a MODP group from hex strings p (which must be a safe |
| 543 | * prime) and g, automatically calculating subgroup q as (p / 2) |
| 544 | */ |
| 545 | struct modp_group * |
| 546 | modp_group_from_g_and_safe_p(const char *grp_g, const char *grp_p) |
| 547 | { |
| 548 | struct modp_group *ret; |
| 549 | |
| 550 | ret = xmalloc(sizeof(*ret)); |
| 551 | ret->p = ret->q = ret->g = NULL; |
| 552 | if (BN_hex2bn(&ret->p, grp_p) == 0 || |
| 553 | BN_hex2bn(&ret->g, grp_g) == 0) |
| 554 | fatal("%s: BN_hex2bn", __func__); |
| 555 | /* Subgroup order is p/2 (p is a safe prime) */ |
| 556 | if ((ret->q = BN_new()) == NULL) |
| 557 | fatal("%s: BN_new", __func__); |
| 558 | if (BN_rshift1(ret->q, ret->p) != 1) |
| 559 | fatal("%s: BN_rshift1", __func__); |
| 560 | |
| 561 | return ret; |
| 562 | } |
| 563 | |
| 564 | void |
| 565 | modp_group_free(struct modp_group *grp) |
| 566 | { |
| 567 | if (grp->g != NULL) |
| 568 | BN_clear_free(grp->g); |
| 569 | if (grp->p != NULL) |
| 570 | BN_clear_free(grp->p); |
| 571 | if (grp->q != NULL) |
| 572 | BN_clear_free(grp->q); |
| 573 | bzero(grp, sizeof(*grp)); |
| 574 | xfree(grp); |
| 575 | } |
| 576 | |
| 577 | /* main() function for self-test */ |
| 578 | |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 579 | #ifdef SCHNORR_MAIN |
| 580 | static void |
| 581 | schnorr_selftest_one(const BIGNUM *grp_p, const BIGNUM *grp_q, |
| 582 | const BIGNUM *grp_g, const BIGNUM *x) |
| 583 | { |
| 584 | BIGNUM *g_x; |
| 585 | u_char *sig; |
| 586 | u_int siglen; |
| 587 | BN_CTX *bn_ctx; |
| 588 | |
| 589 | if ((bn_ctx = BN_CTX_new()) == NULL) |
| 590 | fatal("%s: BN_CTX_new", __func__); |
| 591 | if ((g_x = BN_new()) == NULL) |
| 592 | fatal("%s: BN_new", __func__); |
| 593 | |
| 594 | if (BN_mod_exp(g_x, grp_g, x, grp_p, bn_ctx) == -1) |
| 595 | fatal("%s: g_x", __func__); |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 596 | if (schnorr_sign_buf(grp_p, grp_q, grp_g, x, g_x, "junk", 4, |
| 597 | &sig, &siglen)) |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 598 | fatal("%s: schnorr_sign", __func__); |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 599 | if (schnorr_verify_buf(grp_p, grp_q, grp_g, g_x, "junk", 4, |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 600 | sig, siglen) != 1) |
| 601 | fatal("%s: verify fail", __func__); |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 602 | if (schnorr_verify_buf(grp_p, grp_q, grp_g, g_x, "JUNK", 4, |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 603 | sig, siglen) != 0) |
| 604 | fatal("%s: verify should have failed (bad ID)", __func__); |
| 605 | sig[4] ^= 1; |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 606 | if (schnorr_verify_buf(grp_p, grp_q, grp_g, g_x, "junk", 4, |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 607 | sig, siglen) != 0) |
| 608 | fatal("%s: verify should have failed (bit error)", __func__); |
| 609 | xfree(sig); |
| 610 | BN_free(g_x); |
| 611 | BN_CTX_free(bn_ctx); |
| 612 | } |
| 613 | |
| 614 | static void |
| 615 | schnorr_selftest(void) |
| 616 | { |
| 617 | BIGNUM *x; |
Damien Miller | cee8523 | 2009-03-06 00:58:22 +1100 | [diff] [blame] | 618 | struct modp_group *grp; |
Damien Miller | 01ed227 | 2008-11-05 16:20:46 +1100 | [diff] [blame] | 619 | u_int i; |
| 620 | char *hh; |
| 621 | |
| 622 | grp = jpake_default_group(); |
| 623 | if ((x = BN_new()) == NULL) |
| 624 | fatal("%s: BN_new", __func__); |
| 625 | SCHNORR_DEBUG_BN((grp->p, "%s: grp->p = ", __func__)); |
| 626 | SCHNORR_DEBUG_BN((grp->q, "%s: grp->q = ", __func__)); |
| 627 | SCHNORR_DEBUG_BN((grp->g, "%s: grp->g = ", __func__)); |
| 628 | |
| 629 | /* [1, 20) */ |
| 630 | for (i = 1; i < 20; i++) { |
| 631 | printf("x = %u\n", i); |
| 632 | fflush(stdout); |
| 633 | if (BN_set_word(x, i) != 1) |
| 634 | fatal("%s: set x word", __func__); |
| 635 | schnorr_selftest_one(grp->p, grp->q, grp->g, x); |
| 636 | } |
| 637 | |
| 638 | /* 100 x random [0, p) */ |
| 639 | for (i = 0; i < 100; i++) { |
| 640 | if (BN_rand_range(x, grp->p) != 1) |
| 641 | fatal("%s: BN_rand_range", __func__); |
| 642 | hh = BN_bn2hex(x); |
| 643 | printf("x = (random) 0x%s\n", hh); |
| 644 | free(hh); |
| 645 | fflush(stdout); |
| 646 | schnorr_selftest_one(grp->p, grp->q, grp->g, x); |
| 647 | } |
| 648 | |
| 649 | /* [q-20, q) */ |
| 650 | if (BN_set_word(x, 20) != 1) |
| 651 | fatal("%s: BN_set_word (x = 20)", __func__); |
| 652 | if (BN_sub(x, grp->q, x) != 1) |
| 653 | fatal("%s: BN_sub (q - x)", __func__); |
| 654 | for (i = 0; i < 19; i++) { |
| 655 | hh = BN_bn2hex(x); |
| 656 | printf("x = (q - %d) 0x%s\n", 20 - i, hh); |
| 657 | free(hh); |
| 658 | fflush(stdout); |
| 659 | schnorr_selftest_one(grp->p, grp->q, grp->g, x); |
| 660 | if (BN_add(x, x, BN_value_one()) != 1) |
| 661 | fatal("%s: BN_add (x + 1)", __func__); |
| 662 | } |
| 663 | BN_free(x); |
| 664 | } |
| 665 | |
| 666 | int |
| 667 | main(int argc, char **argv) |
| 668 | { |
| 669 | log_init(argv[0], SYSLOG_LEVEL_DEBUG3, SYSLOG_FACILITY_USER, 1); |
| 670 | |
| 671 | schnorr_selftest(); |
| 672 | return 0; |
| 673 | } |
| 674 | #endif |
| 675 | |