Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 1 | #include "jpake.h" |
| 2 | |
| 3 | #include <openssl/crypto.h> |
| 4 | #include <openssl/sha.h> |
| 5 | #include <openssl/err.h> |
| 6 | #include <memory.h> |
| 7 | |
| 8 | /* |
| 9 | * In the definition, (xa, xb, xc, xd) are Alice's (x1, x2, x3, x4) or |
| 10 | * Bob's (x3, x4, x1, x2). If you see what I mean. |
| 11 | */ |
| 12 | |
| 13 | typedef struct |
| 14 | { |
| 15 | char *name; /* Must be unique */ |
| 16 | char *peer_name; |
| 17 | BIGNUM *p; |
| 18 | BIGNUM *g; |
| 19 | BIGNUM *q; |
| 20 | BIGNUM *gxc; /* Alice's g^{x3} or Bob's g^{x1} */ |
| 21 | BIGNUM *gxd; /* Alice's g^{x4} or Bob's g^{x2} */ |
| 22 | } JPAKE_CTX_PUBLIC; |
| 23 | |
| 24 | struct JPAKE_CTX |
| 25 | { |
| 26 | JPAKE_CTX_PUBLIC p; |
| 27 | BIGNUM *secret; /* The shared secret */ |
| 28 | BN_CTX *ctx; |
| 29 | BIGNUM *xa; /* Alice's x1 or Bob's x3 */ |
| 30 | BIGNUM *xb; /* Alice's x2 or Bob's x4 */ |
| 31 | BIGNUM *key; /* The calculated (shared) key */ |
| 32 | }; |
| 33 | |
| 34 | static void JPAKE_ZKP_init(JPAKE_ZKP *zkp) |
| 35 | { |
| 36 | zkp->gr = BN_new(); |
| 37 | zkp->b = BN_new(); |
| 38 | } |
| 39 | |
| 40 | static void JPAKE_ZKP_release(JPAKE_ZKP *zkp) |
| 41 | { |
| 42 | BN_free(zkp->b); |
| 43 | BN_free(zkp->gr); |
| 44 | } |
| 45 | |
| 46 | /* Two birds with one stone - make the global name as expected */ |
| 47 | #define JPAKE_STEP_PART_init JPAKE_STEP2_init |
| 48 | #define JPAKE_STEP_PART_release JPAKE_STEP2_release |
| 49 | |
| 50 | void JPAKE_STEP_PART_init(JPAKE_STEP_PART *p) |
| 51 | { |
| 52 | p->gx = BN_new(); |
| 53 | JPAKE_ZKP_init(&p->zkpx); |
| 54 | } |
| 55 | |
| 56 | void JPAKE_STEP_PART_release(JPAKE_STEP_PART *p) |
| 57 | { |
| 58 | JPAKE_ZKP_release(&p->zkpx); |
| 59 | BN_free(p->gx); |
| 60 | } |
| 61 | |
| 62 | void JPAKE_STEP1_init(JPAKE_STEP1 *s1) |
| 63 | { |
| 64 | JPAKE_STEP_PART_init(&s1->p1); |
| 65 | JPAKE_STEP_PART_init(&s1->p2); |
| 66 | } |
| 67 | |
| 68 | void JPAKE_STEP1_release(JPAKE_STEP1 *s1) |
| 69 | { |
| 70 | JPAKE_STEP_PART_release(&s1->p2); |
| 71 | JPAKE_STEP_PART_release(&s1->p1); |
| 72 | } |
| 73 | |
| 74 | static void JPAKE_CTX_init(JPAKE_CTX *ctx, const char *name, |
| 75 | const char *peer_name, const BIGNUM *p, |
| 76 | const BIGNUM *g, const BIGNUM *q, |
| 77 | const BIGNUM *secret) |
| 78 | { |
| 79 | ctx->p.name = OPENSSL_strdup(name); |
| 80 | ctx->p.peer_name = OPENSSL_strdup(peer_name); |
| 81 | ctx->p.p = BN_dup(p); |
| 82 | ctx->p.g = BN_dup(g); |
| 83 | ctx->p.q = BN_dup(q); |
| 84 | ctx->secret = BN_dup(secret); |
| 85 | |
| 86 | ctx->p.gxc = BN_new(); |
| 87 | ctx->p.gxd = BN_new(); |
| 88 | |
| 89 | ctx->xa = BN_new(); |
| 90 | ctx->xb = BN_new(); |
| 91 | ctx->key = BN_new(); |
| 92 | ctx->ctx = BN_CTX_new(); |
| 93 | } |
| 94 | |
| 95 | static void JPAKE_CTX_release(JPAKE_CTX *ctx) |
| 96 | { |
| 97 | BN_CTX_free(ctx->ctx); |
| 98 | BN_clear_free(ctx->key); |
| 99 | BN_clear_free(ctx->xb); |
| 100 | BN_clear_free(ctx->xa); |
| 101 | |
| 102 | BN_free(ctx->p.gxd); |
| 103 | BN_free(ctx->p.gxc); |
| 104 | |
| 105 | BN_clear_free(ctx->secret); |
| 106 | BN_free(ctx->p.q); |
| 107 | BN_free(ctx->p.g); |
| 108 | BN_free(ctx->p.p); |
| 109 | OPENSSL_free(ctx->p.peer_name); |
| 110 | OPENSSL_free(ctx->p.name); |
| 111 | |
| 112 | memset(ctx, '\0', sizeof *ctx); |
| 113 | } |
| 114 | |
| 115 | JPAKE_CTX *JPAKE_CTX_new(const char *name, const char *peer_name, |
| 116 | const BIGNUM *p, const BIGNUM *g, const BIGNUM *q, |
| 117 | const BIGNUM *secret) |
| 118 | { |
| 119 | JPAKE_CTX *ctx = OPENSSL_malloc(sizeof *ctx); |
| 120 | |
| 121 | JPAKE_CTX_init(ctx, name, peer_name, p, g, q, secret); |
| 122 | |
| 123 | return ctx; |
| 124 | } |
| 125 | |
| 126 | void JPAKE_CTX_free(JPAKE_CTX *ctx) |
| 127 | { |
| 128 | JPAKE_CTX_release(ctx); |
| 129 | OPENSSL_free(ctx); |
| 130 | } |
| 131 | |
| 132 | static void hashlength(SHA_CTX *sha, size_t l) |
| 133 | { |
| 134 | unsigned char b[2]; |
| 135 | |
| 136 | OPENSSL_assert(l <= 0xffff); |
| 137 | b[0] = l >> 8; |
| 138 | b[1] = l&0xff; |
| 139 | SHA1_Update(sha, b, 2); |
| 140 | } |
| 141 | |
| 142 | static void hashstring(SHA_CTX *sha, const char *string) |
| 143 | { |
| 144 | size_t l = strlen(string); |
| 145 | |
| 146 | hashlength(sha, l); |
| 147 | SHA1_Update(sha, string, l); |
| 148 | } |
| 149 | |
| 150 | static void hashbn(SHA_CTX *sha, const BIGNUM *bn) |
| 151 | { |
| 152 | size_t l = BN_num_bytes(bn); |
| 153 | unsigned char *bin = OPENSSL_malloc(l); |
| 154 | |
| 155 | hashlength(sha, l); |
| 156 | BN_bn2bin(bn, bin); |
| 157 | SHA1_Update(sha, bin, l); |
| 158 | OPENSSL_free(bin); |
| 159 | } |
| 160 | |
| 161 | /* h=hash(g, g^r, g^x, name) */ |
| 162 | static void zkp_hash(BIGNUM *h, const BIGNUM *zkpg, const JPAKE_STEP_PART *p, |
| 163 | const char *proof_name) |
| 164 | { |
| 165 | unsigned char md[SHA_DIGEST_LENGTH]; |
| 166 | SHA_CTX sha; |
| 167 | |
| 168 | /* |
| 169 | * XXX: hash should not allow moving of the boundaries - Java code |
| 170 | * is flawed in this respect. Length encoding seems simplest. |
| 171 | */ |
| 172 | SHA1_Init(&sha); |
| 173 | hashbn(&sha, zkpg); |
| 174 | OPENSSL_assert(!BN_is_zero(p->zkpx.gr)); |
| 175 | hashbn(&sha, p->zkpx.gr); |
| 176 | hashbn(&sha, p->gx); |
| 177 | hashstring(&sha, proof_name); |
| 178 | SHA1_Final(md, &sha); |
| 179 | BN_bin2bn(md, SHA_DIGEST_LENGTH, h); |
| 180 | } |
| 181 | |
| 182 | /* |
| 183 | * Prove knowledge of x |
| 184 | * Note that p->gx has already been calculated |
| 185 | */ |
| 186 | static void generate_zkp(JPAKE_STEP_PART *p, const BIGNUM *x, |
| 187 | const BIGNUM *zkpg, JPAKE_CTX *ctx) |
| 188 | { |
| 189 | BIGNUM *r = BN_new(); |
| 190 | BIGNUM *h = BN_new(); |
| 191 | BIGNUM *t = BN_new(); |
| 192 | |
| 193 | /* |
| 194 | * r in [0,q) |
| 195 | * XXX: Java chooses r in [0, 2^160) - i.e. distribution not uniform |
| 196 | */ |
| 197 | BN_rand_range(r, ctx->p.q); |
| 198 | /* g^r */ |
| 199 | BN_mod_exp(p->zkpx.gr, zkpg, r, ctx->p.p, ctx->ctx); |
| 200 | |
| 201 | /* h=hash... */ |
| 202 | zkp_hash(h, zkpg, p, ctx->p.name); |
| 203 | |
| 204 | /* b = r - x*h */ |
| 205 | BN_mod_mul(t, x, h, ctx->p.q, ctx->ctx); |
| 206 | BN_mod_sub(p->zkpx.b, r, t, ctx->p.q, ctx->ctx); |
| 207 | |
| 208 | /* cleanup */ |
| 209 | BN_free(t); |
| 210 | BN_free(h); |
| 211 | BN_free(r); |
| 212 | } |
| 213 | |
| 214 | static int verify_zkp(const JPAKE_STEP_PART *p, const BIGNUM *zkpg, |
| 215 | JPAKE_CTX *ctx) |
| 216 | { |
| 217 | BIGNUM *h = BN_new(); |
| 218 | BIGNUM *t1 = BN_new(); |
| 219 | BIGNUM *t2 = BN_new(); |
| 220 | BIGNUM *t3 = BN_new(); |
| 221 | int ret = 0; |
| 222 | |
| 223 | zkp_hash(h, zkpg, p, ctx->p.peer_name); |
| 224 | |
| 225 | /* t1 = g^b */ |
| 226 | BN_mod_exp(t1, zkpg, p->zkpx.b, ctx->p.p, ctx->ctx); |
| 227 | /* t2 = (g^x)^h = g^{hx} */ |
| 228 | BN_mod_exp(t2, p->gx, h, ctx->p.p, ctx->ctx); |
| 229 | /* t3 = t1 * t2 = g^{hx} * g^b = g^{hx+b} = g^r (allegedly) */ |
| 230 | BN_mod_mul(t3, t1, t2, ctx->p.p, ctx->ctx); |
| 231 | |
| 232 | /* verify t3 == g^r */ |
| 233 | if(BN_cmp(t3, p->zkpx.gr) == 0) |
| 234 | ret = 1; |
| 235 | else |
| 236 | JPAKEerr(JPAKE_F_VERIFY_ZKP, JPAKE_R_ZKP_VERIFY_FAILED); |
| 237 | |
| 238 | /* cleanup */ |
| 239 | BN_free(t3); |
| 240 | BN_free(t2); |
| 241 | BN_free(t1); |
| 242 | BN_free(h); |
| 243 | |
| 244 | return ret; |
| 245 | } |
| 246 | |
| 247 | static void generate_step_part(JPAKE_STEP_PART *p, const BIGNUM *x, |
| 248 | const BIGNUM *g, JPAKE_CTX *ctx) |
| 249 | { |
| 250 | BN_mod_exp(p->gx, g, x, ctx->p.p, ctx->ctx); |
| 251 | generate_zkp(p, x, g, ctx); |
| 252 | } |
| 253 | |
| 254 | /* Generate each party's random numbers. xa is in [0, q), xb is in [1, q). */ |
| 255 | static void genrand(JPAKE_CTX *ctx) |
| 256 | { |
| 257 | BIGNUM *qm1; |
| 258 | |
| 259 | /* xa in [0, q) */ |
| 260 | BN_rand_range(ctx->xa, ctx->p.q); |
| 261 | |
| 262 | /* q-1 */ |
| 263 | qm1 = BN_new(); |
| 264 | BN_copy(qm1, ctx->p.q); |
| 265 | BN_sub_word(qm1, 1); |
| 266 | |
| 267 | /* ... and xb in [0, q-1) */ |
| 268 | BN_rand_range(ctx->xb, qm1); |
| 269 | /* [1, q) */ |
| 270 | BN_add_word(ctx->xb, 1); |
| 271 | |
| 272 | /* cleanup */ |
| 273 | BN_free(qm1); |
| 274 | } |
| 275 | |
| 276 | int JPAKE_STEP1_generate(JPAKE_STEP1 *send, JPAKE_CTX *ctx) |
| 277 | { |
| 278 | genrand(ctx); |
| 279 | generate_step_part(&send->p1, ctx->xa, ctx->p.g, ctx); |
| 280 | generate_step_part(&send->p2, ctx->xb, ctx->p.g, ctx); |
| 281 | |
| 282 | return 1; |
| 283 | } |
| 284 | |
| 285 | /* g^x is a legal value */ |
| 286 | static int is_legal(const BIGNUM *gx, const JPAKE_CTX *ctx) |
| 287 | { |
| 288 | BIGNUM *t; |
| 289 | int res; |
| 290 | |
| 291 | if(BN_is_negative(gx) || BN_is_zero(gx) || BN_cmp(gx, ctx->p.p) >= 0) |
| 292 | return 0; |
| 293 | |
| 294 | t = BN_new(); |
| 295 | BN_mod_exp(t, gx, ctx->p.q, ctx->p.p, ctx->ctx); |
| 296 | res = BN_is_one(t); |
| 297 | BN_free(t); |
| 298 | |
| 299 | return res; |
| 300 | } |
| 301 | |
| 302 | int JPAKE_STEP1_process(JPAKE_CTX *ctx, const JPAKE_STEP1 *received) |
| 303 | { |
| 304 | if(!is_legal(received->p1.gx, ctx)) |
| 305 | { |
| 306 | JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X3_IS_NOT_LEGAL); |
| 307 | return 0; |
| 308 | } |
| 309 | |
| 310 | if(!is_legal(received->p2.gx, ctx)) |
| 311 | { |
| 312 | JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X4_IS_NOT_LEGAL); |
| 313 | return 0; |
| 314 | } |
| 315 | |
| 316 | /* verify their ZKP(xc) */ |
| 317 | if(!verify_zkp(&received->p1, ctx->p.g, ctx)) |
| 318 | { |
| 319 | JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X3_FAILED); |
| 320 | return 0; |
| 321 | } |
| 322 | |
| 323 | /* verify their ZKP(xd) */ |
| 324 | if(!verify_zkp(&received->p2, ctx->p.g, ctx)) |
| 325 | { |
| 326 | JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X4_FAILED); |
| 327 | return 0; |
| 328 | } |
| 329 | |
| 330 | /* g^xd != 1 */ |
| 331 | if(BN_is_one(received->p2.gx)) |
| 332 | { |
| 333 | JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X4_IS_ONE); |
| 334 | return 0; |
| 335 | } |
| 336 | |
| 337 | /* Save the bits we need for later */ |
| 338 | BN_copy(ctx->p.gxc, received->p1.gx); |
| 339 | BN_copy(ctx->p.gxd, received->p2.gx); |
| 340 | |
| 341 | return 1; |
| 342 | } |
| 343 | |
| 344 | |
| 345 | int JPAKE_STEP2_generate(JPAKE_STEP2 *send, JPAKE_CTX *ctx) |
| 346 | { |
| 347 | BIGNUM *t1 = BN_new(); |
| 348 | BIGNUM *t2 = BN_new(); |
| 349 | |
| 350 | /* |
| 351 | * X = g^{(xa + xc + xd) * xb * s} |
| 352 | * t1 = g^xa |
| 353 | */ |
| 354 | BN_mod_exp(t1, ctx->p.g, ctx->xa, ctx->p.p, ctx->ctx); |
| 355 | /* t2 = t1 * g^{xc} = g^{xa} * g^{xc} = g^{xa + xc} */ |
| 356 | BN_mod_mul(t2, t1, ctx->p.gxc, ctx->p.p, ctx->ctx); |
| 357 | /* t1 = t2 * g^{xd} = g^{xa + xc + xd} */ |
| 358 | BN_mod_mul(t1, t2, ctx->p.gxd, ctx->p.p, ctx->ctx); |
| 359 | /* t2 = xb * s */ |
| 360 | BN_mod_mul(t2, ctx->xb, ctx->secret, ctx->p.q, ctx->ctx); |
| 361 | |
| 362 | /* |
| 363 | * ZKP(xb * s) |
| 364 | * XXX: this is kinda funky, because we're using |
| 365 | * |
| 366 | * g' = g^{xa + xc + xd} |
| 367 | * |
| 368 | * as the generator, which means X is g'^{xb * s} |
| 369 | * X = t1^{t2} = t1^{xb * s} = g^{(xa + xc + xd) * xb * s} |
| 370 | */ |
| 371 | generate_step_part(send, t2, t1, ctx); |
| 372 | |
| 373 | /* cleanup */ |
| 374 | BN_free(t1); |
| 375 | BN_free(t2); |
| 376 | |
| 377 | return 1; |
| 378 | } |
| 379 | |
| 380 | /* gx = g^{xc + xa + xb} * xd * s */ |
| 381 | static int compute_key(JPAKE_CTX *ctx, const BIGNUM *gx) |
| 382 | { |
| 383 | BIGNUM *t1 = BN_new(); |
| 384 | BIGNUM *t2 = BN_new(); |
| 385 | BIGNUM *t3 = BN_new(); |
| 386 | |
| 387 | /* |
| 388 | * K = (gx/g^{xb * xd * s})^{xb} |
| 389 | * = (g^{(xc + xa + xb) * xd * s - xb * xd *s})^{xb} |
| 390 | * = (g^{(xa + xc) * xd * s})^{xb} |
| 391 | * = g^{(xa + xc) * xb * xd * s} |
| 392 | * [which is the same regardless of who calculates it] |
| 393 | */ |
| 394 | |
| 395 | /* t1 = (g^{xd})^{xb} = g^{xb * xd} */ |
| 396 | BN_mod_exp(t1, ctx->p.gxd, ctx->xb, ctx->p.p, ctx->ctx); |
| 397 | /* t2 = -s = q-s */ |
| 398 | BN_sub(t2, ctx->p.q, ctx->secret); |
| 399 | /* t3 = t1^t2 = g^{-xb * xd * s} */ |
| 400 | BN_mod_exp(t3, t1, t2, ctx->p.p, ctx->ctx); |
| 401 | /* t1 = gx * t3 = X/g^{xb * xd * s} */ |
| 402 | BN_mod_mul(t1, gx, t3, ctx->p.p, ctx->ctx); |
| 403 | /* K = t1^{xb} */ |
| 404 | BN_mod_exp(ctx->key, t1, ctx->xb, ctx->p.p, ctx->ctx); |
| 405 | |
| 406 | /* cleanup */ |
| 407 | BN_free(t3); |
| 408 | BN_free(t2); |
| 409 | BN_free(t1); |
| 410 | |
| 411 | return 1; |
| 412 | } |
| 413 | |
| 414 | int JPAKE_STEP2_process(JPAKE_CTX *ctx, const JPAKE_STEP2 *received) |
| 415 | { |
| 416 | BIGNUM *t1 = BN_new(); |
| 417 | BIGNUM *t2 = BN_new(); |
| 418 | int ret = 0; |
| 419 | |
| 420 | /* |
| 421 | * g' = g^{xc + xa + xb} [from our POV] |
| 422 | * t1 = xa + xb |
| 423 | */ |
| 424 | BN_mod_add(t1, ctx->xa, ctx->xb, ctx->p.q, ctx->ctx); |
| 425 | /* t2 = g^{t1} = g^{xa+xb} */ |
| 426 | BN_mod_exp(t2, ctx->p.g, t1, ctx->p.p, ctx->ctx); |
| 427 | /* t1 = g^{xc} * t2 = g^{xc + xa + xb} */ |
| 428 | BN_mod_mul(t1, ctx->p.gxc, t2, ctx->p.p, ctx->ctx); |
| 429 | |
| 430 | if(verify_zkp(received, t1, ctx)) |
| 431 | ret = 1; |
| 432 | else |
| 433 | JPAKEerr(JPAKE_F_JPAKE_STEP2_PROCESS, JPAKE_R_VERIFY_B_FAILED); |
| 434 | |
| 435 | compute_key(ctx, received->gx); |
| 436 | |
| 437 | /* cleanup */ |
| 438 | BN_free(t2); |
| 439 | BN_free(t1); |
| 440 | |
| 441 | return ret; |
| 442 | } |
| 443 | |
| 444 | static void quickhashbn(unsigned char *md, const BIGNUM *bn) |
| 445 | { |
| 446 | SHA_CTX sha; |
| 447 | |
| 448 | SHA1_Init(&sha); |
| 449 | hashbn(&sha, bn); |
| 450 | SHA1_Final(md, &sha); |
| 451 | } |
| 452 | |
| 453 | void JPAKE_STEP3A_init(JPAKE_STEP3A *s3a) |
| 454 | {} |
| 455 | |
| 456 | int JPAKE_STEP3A_generate(JPAKE_STEP3A *send, JPAKE_CTX *ctx) |
| 457 | { |
| 458 | quickhashbn(send->hhk, ctx->key); |
| 459 | SHA1(send->hhk, sizeof send->hhk, send->hhk); |
| 460 | |
| 461 | return 1; |
| 462 | } |
| 463 | |
| 464 | int JPAKE_STEP3A_process(JPAKE_CTX *ctx, const JPAKE_STEP3A *received) |
| 465 | { |
| 466 | unsigned char hhk[SHA_DIGEST_LENGTH]; |
| 467 | |
| 468 | quickhashbn(hhk, ctx->key); |
| 469 | SHA1(hhk, sizeof hhk, hhk); |
| 470 | if(memcmp(hhk, received->hhk, sizeof hhk)) |
| 471 | { |
| 472 | JPAKEerr(JPAKE_F_JPAKE_STEP3A_PROCESS, JPAKE_R_HASH_OF_HASH_OF_KEY_MISMATCH); |
| 473 | return 0; |
| 474 | } |
| 475 | return 1; |
| 476 | } |
| 477 | |
| 478 | void JPAKE_STEP3A_release(JPAKE_STEP3A *s3a) |
| 479 | {} |
| 480 | |
| 481 | void JPAKE_STEP3B_init(JPAKE_STEP3B *s3b) |
| 482 | {} |
| 483 | |
| 484 | int JPAKE_STEP3B_generate(JPAKE_STEP3B *send, JPAKE_CTX *ctx) |
| 485 | { |
| 486 | quickhashbn(send->hk, ctx->key); |
| 487 | |
| 488 | return 1; |
| 489 | } |
| 490 | |
| 491 | int JPAKE_STEP3B_process(JPAKE_CTX *ctx, const JPAKE_STEP3B *received) |
| 492 | { |
| 493 | unsigned char hk[SHA_DIGEST_LENGTH]; |
| 494 | |
| 495 | quickhashbn(hk, ctx->key); |
| 496 | if(memcmp(hk, received->hk, sizeof hk)) |
| 497 | { |
| 498 | JPAKEerr(JPAKE_F_JPAKE_STEP3B_PROCESS, JPAKE_R_HASH_OF_KEY_MISMATCH); |
| 499 | return 0; |
| 500 | } |
| 501 | return 1; |
| 502 | } |
| 503 | |
| 504 | void JPAKE_STEP3B_release(JPAKE_STEP3B *s3b) |
| 505 | {} |
| 506 | |
| 507 | const BIGNUM *JPAKE_get_shared_key(JPAKE_CTX *ctx) |
| 508 | { |
| 509 | return ctx->key; |
| 510 | } |
| 511 | |