1 /* 2 * EAP server/peer: EAP-pwd shared routines 3 * Copyright (c) 2010, Dan Harkins <dharkins@lounge.org> 4 * 5 * This software may be distributed under the terms of the BSD license. 6 * See README for more details. 7 */ 8 9 #include "includes.h" 10 #include "common.h" 11 #include "utils/const_time.h" 12 #include "crypto/sha256.h" 13 #include "crypto/crypto.h" 14 #include "eap_defs.h" 15 #include "eap_pwd_common.h" 16 17 #define MAX_ECC_PRIME_LEN 66 18 19 20 /* The random function H(x) = HMAC-SHA256(0^32, x) */ 21 struct crypto_hash * eap_pwd_h_init(void) 22 { 23 u8 allzero[SHA256_MAC_LEN]; 24 os_memset(allzero, 0, SHA256_MAC_LEN); 25 return crypto_hash_init(CRYPTO_HASH_ALG_HMAC_SHA256, allzero, 26 SHA256_MAC_LEN); 27 } 28 29 30 void eap_pwd_h_update(struct crypto_hash *hash, const u8 *data, size_t len) 31 { 32 crypto_hash_update(hash, data, len); 33 } 34 35 36 void eap_pwd_h_final(struct crypto_hash *hash, u8 *digest) 37 { 38 size_t len = SHA256_MAC_LEN; 39 crypto_hash_finish(hash, digest, &len); 40 } 41 42 43 /* a counter-based KDF based on NIST SP800-108 */ 44 static int eap_pwd_kdf(const u8 *key, size_t keylen, const u8 *label, 45 size_t labellen, u8 *result, size_t resultbitlen) 46 { 47 struct crypto_hash *hash; 48 u8 digest[SHA256_MAC_LEN]; 49 u16 i, ctr, L; 50 size_t resultbytelen, len = 0, mdlen; 51 52 resultbytelen = (resultbitlen + 7) / 8; 53 ctr = 0; 54 L = htons(resultbitlen); 55 while (len < resultbytelen) { 56 ctr++; 57 i = htons(ctr); 58 hash = crypto_hash_init(CRYPTO_HASH_ALG_HMAC_SHA256, 59 key, keylen); 60 if (hash == NULL) 61 return -1; 62 if (ctr > 1) 63 crypto_hash_update(hash, digest, SHA256_MAC_LEN); 64 crypto_hash_update(hash, (u8 *) &i, sizeof(u16)); 65 crypto_hash_update(hash, label, labellen); 66 crypto_hash_update(hash, (u8 *) &L, sizeof(u16)); 67 mdlen = SHA256_MAC_LEN; 68 if (crypto_hash_finish(hash, digest, &mdlen) < 0) 69 return -1; 70 if ((len + mdlen) > resultbytelen) 71 os_memcpy(result + len, digest, resultbytelen - len); 72 else 73 os_memcpy(result + len, digest, mdlen); 74 len += mdlen; 75 } 76 77 /* since we're expanding to a bit length, mask off the excess */ 78 if (resultbitlen % 8) { 79 u8 mask = 0xff; 80 mask <<= (8 - (resultbitlen % 8)); 81 result[resultbytelen - 1] &= mask; 82 } 83 84 return 0; 85 } 86 87 88 EAP_PWD_group * get_eap_pwd_group(u16 num) 89 { 90 EAP_PWD_group *grp; 91 92 grp = os_zalloc(sizeof(EAP_PWD_group)); 93 if (!grp) 94 return NULL; 95 grp->group = crypto_ec_init(num); 96 if (!grp->group) { 97 wpa_printf(MSG_INFO, "EAP-pwd: unable to create EC group"); 98 os_free(grp); 99 return NULL; 100 } 101 102 grp->group_num = num; 103 wpa_printf(MSG_INFO, "EAP-pwd: provisioned group %d", num); 104 105 return grp; 106 } 107 108 109 static void buf_shift_right(u8 *buf, size_t len, size_t bits) 110 { 111 size_t i; 112 for (i = len - 1; i > 0; i--) 113 buf[i] = (buf[i - 1] << (8 - bits)) | (buf[i] >> bits); 114 buf[0] >>= bits; 115 } 116 117 118 /* 119 * compute a "random" secret point on an elliptic curve based 120 * on the password and identities. 121 */ 122 int compute_password_element(EAP_PWD_group *grp, u16 num, 123 const u8 *password, size_t password_len, 124 const u8 *id_server, size_t id_server_len, 125 const u8 *id_peer, size_t id_peer_len, 126 const u8 *token) 127 { 128 struct crypto_bignum *qr = NULL, *qnr = NULL, *one = NULL; 129 struct crypto_bignum *qr_or_qnr = NULL; 130 u8 qr_bin[MAX_ECC_PRIME_LEN]; 131 u8 qnr_bin[MAX_ECC_PRIME_LEN]; 132 u8 qr_or_qnr_bin[MAX_ECC_PRIME_LEN]; 133 u8 x_bin[MAX_ECC_PRIME_LEN]; 134 struct crypto_bignum *tmp1 = NULL, *tmp2 = NULL, *pm1 = NULL; 135 struct crypto_hash *hash; 136 unsigned char pwe_digest[SHA256_MAC_LEN], *prfbuf = NULL, ctr; 137 int ret = 0, check, res; 138 u8 found = 0; /* 0 (false) or 0xff (true) to be used as const_time_* 139 * mask */ 140 size_t primebytelen = 0, primebitlen; 141 struct crypto_bignum *x_candidate = NULL, *cofactor = NULL; 142 const struct crypto_bignum *prime; 143 u8 mask, found_ctr = 0, is_odd = 0; 144 145 if (grp->pwe) 146 return -1; 147 148 os_memset(x_bin, 0, sizeof(x_bin)); 149 150 prime = crypto_ec_get_prime(grp->group); 151 cofactor = crypto_bignum_init(); 152 grp->pwe = crypto_ec_point_init(grp->group); 153 tmp1 = crypto_bignum_init(); 154 pm1 = crypto_bignum_init(); 155 one = crypto_bignum_init_set((const u8 *) "\x01", 1); 156 if (!cofactor || !grp->pwe || !tmp1 || !pm1 || !one) { 157 wpa_printf(MSG_INFO, "EAP-pwd: unable to create bignums"); 158 goto fail; 159 } 160 161 if (crypto_ec_cofactor(grp->group, cofactor) < 0) { 162 wpa_printf(MSG_INFO, "EAP-pwd: unable to get cofactor for " 163 "curve"); 164 goto fail; 165 } 166 primebitlen = crypto_ec_prime_len_bits(grp->group); 167 primebytelen = crypto_ec_prime_len(grp->group); 168 if ((prfbuf = os_malloc(primebytelen)) == NULL) { 169 wpa_printf(MSG_INFO, "EAP-pwd: unable to malloc space for prf " 170 "buffer"); 171 goto fail; 172 } 173 if (crypto_bignum_sub(prime, one, pm1) < 0) 174 goto fail; 175 176 /* get a random quadratic residue and nonresidue */ 177 while (!qr || !qnr) { 178 if (crypto_bignum_rand(tmp1, prime) < 0) 179 goto fail; 180 res = crypto_bignum_legendre(tmp1, prime); 181 if (!qr && res == 1) { 182 qr = tmp1; 183 tmp1 = crypto_bignum_init(); 184 } else if (!qnr && res == -1) { 185 qnr = tmp1; 186 tmp1 = crypto_bignum_init(); 187 } 188 if (!tmp1) 189 goto fail; 190 } 191 if (crypto_bignum_to_bin(qr, qr_bin, sizeof(qr_bin), 192 primebytelen) < 0 || 193 crypto_bignum_to_bin(qnr, qnr_bin, sizeof(qnr_bin), 194 primebytelen) < 0) 195 goto fail; 196 197 os_memset(prfbuf, 0, primebytelen); 198 ctr = 0; 199 200 /* 201 * Run through the hunting-and-pecking loop 40 times to mask the time 202 * necessary to find PWE. The odds of PWE not being found in 40 loops is 203 * roughly 1 in 1 trillion. 204 */ 205 while (ctr < 40) { 206 ctr++; 207 208 /* 209 * compute counter-mode password value and stretch to prime 210 * pwd-seed = H(token | peer-id | server-id | password | 211 * counter) 212 */ 213 hash = eap_pwd_h_init(); 214 if (hash == NULL) 215 goto fail; 216 eap_pwd_h_update(hash, token, sizeof(u32)); 217 eap_pwd_h_update(hash, id_peer, id_peer_len); 218 eap_pwd_h_update(hash, id_server, id_server_len); 219 eap_pwd_h_update(hash, password, password_len); 220 eap_pwd_h_update(hash, &ctr, sizeof(ctr)); 221 eap_pwd_h_final(hash, pwe_digest); 222 223 is_odd = const_time_select_u8( 224 found, is_odd, pwe_digest[SHA256_MAC_LEN - 1] & 0x01); 225 if (eap_pwd_kdf(pwe_digest, SHA256_MAC_LEN, 226 (u8 *) "EAP-pwd Hunting And Pecking", 227 os_strlen("EAP-pwd Hunting And Pecking"), 228 prfbuf, primebitlen) < 0) 229 goto fail; 230 if (primebitlen % 8) 231 buf_shift_right(prfbuf, primebytelen, 232 8 - primebitlen % 8); 233 234 crypto_bignum_deinit(x_candidate, 1); 235 x_candidate = crypto_bignum_init_set(prfbuf, primebytelen); 236 if (!x_candidate) { 237 wpa_printf(MSG_INFO, 238 "EAP-pwd: unable to create x_candidate"); 239 goto fail; 240 } 241 242 if (crypto_bignum_cmp(x_candidate, prime) >= 0) 243 continue; 244 245 wpa_hexdump_key(MSG_DEBUG, "EAP-pwd: x_candidate", 246 prfbuf, primebytelen); 247 const_time_select_bin(found, x_bin, prfbuf, primebytelen, 248 x_bin); 249 250 /* 251 * compute y^2 using the equation of the curve 252 * 253 * y^2 = x^3 + ax + b 254 */ 255 tmp2 = crypto_ec_point_compute_y_sqr(grp->group, x_candidate); 256 if (!tmp2) 257 goto fail; 258 259 /* 260 * mask tmp2 so doing legendre won't leak timing info 261 * 262 * tmp1 is a random number between 1 and p-1 263 */ 264 if (crypto_bignum_rand(tmp1, pm1) < 0 || 265 crypto_bignum_mulmod(tmp2, tmp1, prime, tmp2) < 0 || 266 crypto_bignum_mulmod(tmp2, tmp1, prime, tmp2) < 0) 267 goto fail; 268 269 /* 270 * Now tmp2 (y^2) is masked, all values between 1 and p-1 271 * are equally probable. Multiplying by r^2 does not change 272 * whether or not tmp2 is a quadratic residue, just masks it. 273 * 274 * Flip a coin, multiply by the random quadratic residue or the 275 * random quadratic nonresidue and record heads or tails. 276 */ 277 mask = const_time_eq_u8(crypto_bignum_is_odd(tmp1), 1); 278 check = const_time_select_s8(mask, 1, -1); 279 const_time_select_bin(mask, qr_bin, qnr_bin, primebytelen, 280 qr_or_qnr_bin); 281 crypto_bignum_deinit(qr_or_qnr, 1); 282 qr_or_qnr = crypto_bignum_init_set(qr_or_qnr_bin, primebytelen); 283 if (!qr_or_qnr || 284 crypto_bignum_mulmod(tmp2, qr_or_qnr, prime, tmp2) < 0) 285 goto fail; 286 287 /* 288 * Now it's safe to do legendre, if check is 1 then it's 289 * a straightforward test (multiplying by qr does not 290 * change result), if check is -1 then it's the opposite test 291 * (multiplying a qr by qnr would make a qnr). 292 */ 293 res = crypto_bignum_legendre(tmp2, prime); 294 if (res == -2) 295 goto fail; 296 mask = const_time_eq(res, check); 297 found_ctr = const_time_select_u8(found, found_ctr, ctr); 298 found |= mask; 299 } 300 if (found == 0) { 301 wpa_printf(MSG_INFO, 302 "EAP-pwd: unable to find random point on curve for group %d, something's fishy", 303 num); 304 goto fail; 305 } 306 307 /* 308 * We know x_candidate is a quadratic residue so set it here. 309 */ 310 crypto_bignum_deinit(x_candidate, 1); 311 x_candidate = crypto_bignum_init_set(x_bin, primebytelen); 312 if (!x_candidate || 313 crypto_ec_point_solve_y_coord(grp->group, grp->pwe, x_candidate, 314 is_odd) != 0) { 315 wpa_printf(MSG_INFO, "EAP-pwd: Could not solve for y"); 316 goto fail; 317 } 318 319 /* 320 * If there's a solution to the equation then the point must be on the 321 * curve so why check again explicitly? OpenSSL code says this is 322 * required by X9.62. We're not X9.62 but it can't hurt just to be sure. 323 */ 324 if (!crypto_ec_point_is_on_curve(grp->group, grp->pwe)) { 325 wpa_printf(MSG_INFO, "EAP-pwd: point is not on curve"); 326 goto fail; 327 } 328 329 if (!crypto_bignum_is_one(cofactor)) { 330 /* make sure the point is not in a small sub-group */ 331 if (crypto_ec_point_mul(grp->group, grp->pwe, cofactor, 332 grp->pwe) != 0) { 333 wpa_printf(MSG_INFO, 334 "EAP-pwd: cannot multiply generator by order"); 335 goto fail; 336 } 337 if (crypto_ec_point_is_at_infinity(grp->group, grp->pwe)) { 338 wpa_printf(MSG_INFO, "EAP-pwd: point is at infinity"); 339 goto fail; 340 } 341 } 342 wpa_printf(MSG_DEBUG, "EAP-pwd: found a PWE in %02d tries", found_ctr); 343 344 if (0) { 345 fail: 346 crypto_ec_point_deinit(grp->pwe, 1); 347 grp->pwe = NULL; 348 ret = 1; 349 } 350 /* cleanliness and order.... */ 351 crypto_bignum_deinit(cofactor, 1); 352 crypto_bignum_deinit(x_candidate, 1); 353 crypto_bignum_deinit(pm1, 0); 354 crypto_bignum_deinit(tmp1, 1); 355 crypto_bignum_deinit(tmp2, 1); 356 crypto_bignum_deinit(qr, 1); 357 crypto_bignum_deinit(qnr, 1); 358 crypto_bignum_deinit(qr_or_qnr, 1); 359 crypto_bignum_deinit(one, 0); 360 bin_clear_free(prfbuf, primebytelen); 361 os_memset(qr_bin, 0, sizeof(qr_bin)); 362 os_memset(qnr_bin, 0, sizeof(qnr_bin)); 363 os_memset(qr_or_qnr_bin, 0, sizeof(qr_or_qnr_bin)); 364 os_memset(pwe_digest, 0, sizeof(pwe_digest)); 365 366 return ret; 367 } 368 369 370 int compute_keys(EAP_PWD_group *grp, const struct crypto_bignum *k, 371 const struct crypto_bignum *peer_scalar, 372 const struct crypto_bignum *server_scalar, 373 const u8 *confirm_peer, const u8 *confirm_server, 374 const u32 *ciphersuite, u8 *msk, u8 *emsk, u8 *session_id) 375 { 376 struct crypto_hash *hash; 377 u8 mk[SHA256_MAC_LEN], *cruft; 378 u8 msk_emsk[EAP_MSK_LEN + EAP_EMSK_LEN]; 379 size_t prime_len, order_len; 380 381 prime_len = crypto_ec_prime_len(grp->group); 382 order_len = crypto_ec_order_len(grp->group); 383 384 cruft = os_malloc(prime_len); 385 if (!cruft) 386 return -1; 387 388 /* 389 * first compute the session-id = TypeCode | H(ciphersuite | scal_p | 390 * scal_s) 391 */ 392 session_id[0] = EAP_TYPE_PWD; 393 hash = eap_pwd_h_init(); 394 if (hash == NULL) { 395 os_free(cruft); 396 return -1; 397 } 398 eap_pwd_h_update(hash, (const u8 *) ciphersuite, sizeof(u32)); 399 crypto_bignum_to_bin(peer_scalar, cruft, order_len, order_len); 400 eap_pwd_h_update(hash, cruft, order_len); 401 crypto_bignum_to_bin(server_scalar, cruft, order_len, order_len); 402 eap_pwd_h_update(hash, cruft, order_len); 403 eap_pwd_h_final(hash, &session_id[1]); 404 405 /* then compute MK = H(k | confirm-peer | confirm-server) */ 406 hash = eap_pwd_h_init(); 407 if (hash == NULL) { 408 os_free(cruft); 409 return -1; 410 } 411 crypto_bignum_to_bin(k, cruft, prime_len, prime_len); 412 eap_pwd_h_update(hash, cruft, prime_len); 413 os_free(cruft); 414 eap_pwd_h_update(hash, confirm_peer, SHA256_MAC_LEN); 415 eap_pwd_h_update(hash, confirm_server, SHA256_MAC_LEN); 416 eap_pwd_h_final(hash, mk); 417 418 /* stretch the mk with the session-id to get MSK | EMSK */ 419 if (eap_pwd_kdf(mk, SHA256_MAC_LEN, 420 session_id, SHA256_MAC_LEN + 1, 421 msk_emsk, (EAP_MSK_LEN + EAP_EMSK_LEN) * 8) < 0) { 422 return -1; 423 } 424 425 os_memcpy(msk, msk_emsk, EAP_MSK_LEN); 426 os_memcpy(emsk, msk_emsk + EAP_MSK_LEN, EAP_EMSK_LEN); 427 428 return 1; 429 } 430 431 432 static int eap_pwd_element_coord_ok(const struct crypto_bignum *prime, 433 const u8 *buf, size_t len) 434 { 435 struct crypto_bignum *val; 436 int ok = 1; 437 438 val = crypto_bignum_init_set(buf, len); 439 if (!val || crypto_bignum_is_zero(val) || 440 crypto_bignum_cmp(val, prime) >= 0) 441 ok = 0; 442 crypto_bignum_deinit(val, 0); 443 return ok; 444 } 445 446 447 struct crypto_ec_point * eap_pwd_get_element(EAP_PWD_group *group, 448 const u8 *buf) 449 { 450 struct crypto_ec_point *element; 451 const struct crypto_bignum *prime; 452 size_t prime_len; 453 struct crypto_bignum *cofactor = NULL; 454 455 prime = crypto_ec_get_prime(group->group); 456 prime_len = crypto_ec_prime_len(group->group); 457 458 /* RFC 5931, 2.8.5.2.2: 0 < x,y < p */ 459 if (!eap_pwd_element_coord_ok(prime, buf, prime_len) || 460 !eap_pwd_element_coord_ok(prime, buf + prime_len, prime_len)) { 461 wpa_printf(MSG_INFO, "EAP-pwd: Invalid coordinate in element"); 462 return NULL; 463 } 464 465 element = crypto_ec_point_from_bin(group->group, buf); 466 if (!element) { 467 wpa_printf(MSG_INFO, "EAP-pwd: EC point from element failed"); 468 return NULL; 469 } 470 471 /* RFC 5931, 2.8.5.2.2: on curve and not the point at infinity */ 472 if (!crypto_ec_point_is_on_curve(group->group, element) || 473 crypto_ec_point_is_at_infinity(group->group, element)) { 474 wpa_printf(MSG_INFO, "EAP-pwd: Invalid element"); 475 goto fail; 476 } 477 478 cofactor = crypto_bignum_init(); 479 if (!cofactor || crypto_ec_cofactor(group->group, cofactor) < 0) { 480 wpa_printf(MSG_INFO, 481 "EAP-pwd: Unable to get cofactor for curve"); 482 goto fail; 483 } 484 485 if (!crypto_bignum_is_one(cofactor)) { 486 struct crypto_ec_point *point; 487 int ok = 1; 488 489 /* check to ensure peer's element is not in a small sub-group */ 490 point = crypto_ec_point_init(group->group); 491 if (!point || 492 crypto_ec_point_mul(group->group, element, 493 cofactor, point) != 0 || 494 crypto_ec_point_is_at_infinity(group->group, point)) 495 ok = 0; 496 crypto_ec_point_deinit(point, 0); 497 498 if (!ok) { 499 wpa_printf(MSG_INFO, 500 "EAP-pwd: Small sub-group check on peer element failed"); 501 goto fail; 502 } 503 } 504 505 out: 506 crypto_bignum_deinit(cofactor, 0); 507 return element; 508 fail: 509 crypto_ec_point_deinit(element, 0); 510 element = NULL; 511 goto out; 512 } 513 514 515 struct crypto_bignum * eap_pwd_get_scalar(EAP_PWD_group *group, const u8 *buf) 516 { 517 struct crypto_bignum *scalar; 518 const struct crypto_bignum *order; 519 size_t order_len; 520 521 order = crypto_ec_get_order(group->group); 522 order_len = crypto_ec_order_len(group->group); 523 524 /* RFC 5931, 2.8.5.2: 1 < scalar < r */ 525 scalar = crypto_bignum_init_set(buf, order_len); 526 if (!scalar || crypto_bignum_is_zero(scalar) || 527 crypto_bignum_is_one(scalar) || 528 crypto_bignum_cmp(scalar, order) >= 0) { 529 wpa_printf(MSG_INFO, "EAP-pwd: received scalar is invalid"); 530 crypto_bignum_deinit(scalar, 0); 531 scalar = NULL; 532 } 533 534 return scalar; 535 } 536