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 int JPAKE_STEP1_process(JPAKE_CTX *ctx, const JPAKE_STEP1 *received) 286 { 287 /* verify their ZKP(xc) */ 288 if(!verify_zkp(&received->p1, ctx->p.g, ctx)) 289 { 290 JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X3_FAILED); 291 return 0; 292 } 293 294 /* verify their ZKP(xd) */ 295 if(!verify_zkp(&received->p2, ctx->p.g, ctx)) 296 { 297 JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X4_FAILED); 298 return 0; 299 } 300 301 /* g^xd != 1 */ 302 if(BN_is_one(received->p2.gx)) 303 { 304 JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X4_IS_ONE); 305 return 0; 306 } 307 308 /* Save the bits we need for later */ 309 BN_copy(ctx->p.gxc, received->p1.gx); 310 BN_copy(ctx->p.gxd, received->p2.gx); 311 312 return 1; 313 } 314 315 316 int JPAKE_STEP2_generate(JPAKE_STEP2 *send, JPAKE_CTX *ctx) 317 { 318 BIGNUM *t1 = BN_new(); 319 BIGNUM *t2 = BN_new(); 320 321 /* 322 * X = g^{(xa + xc + xd) * xb * s} 323 * t1 = g^xa 324 */ 325 BN_mod_exp(t1, ctx->p.g, ctx->xa, ctx->p.p, ctx->ctx); 326 /* t2 = t1 * g^{xc} = g^{xa} * g^{xc} = g^{xa + xc} */ 327 BN_mod_mul(t2, t1, ctx->p.gxc, ctx->p.p, ctx->ctx); 328 /* t1 = t2 * g^{xd} = g^{xa + xc + xd} */ 329 BN_mod_mul(t1, t2, ctx->p.gxd, ctx->p.p, ctx->ctx); 330 /* t2 = xb * s */ 331 BN_mod_mul(t2, ctx->xb, ctx->secret, ctx->p.q, ctx->ctx); 332 333 /* 334 * ZKP(xb * s) 335 * XXX: this is kinda funky, because we're using 336 * 337 * g' = g^{xa + xc + xd} 338 * 339 * as the generator, which means X is g'^{xb * s} 340 * X = t1^{t2} = t1^{xb * s} = g^{(xa + xc + xd) * xb * s} 341 */ 342 generate_step_part(send, t2, t1, ctx); 343 344 /* cleanup */ 345 BN_free(t1); 346 BN_free(t2); 347 348 return 1; 349 } 350 351 /* gx = g^{xc + xa + xb} * xd * s */ 352 static int compute_key(JPAKE_CTX *ctx, const BIGNUM *gx) 353 { 354 BIGNUM *t1 = BN_new(); 355 BIGNUM *t2 = BN_new(); 356 BIGNUM *t3 = BN_new(); 357 358 /* 359 * K = (gx/g^{xb * xd * s})^{xb} 360 * = (g^{(xc + xa + xb) * xd * s - xb * xd *s})^{xb} 361 * = (g^{(xa + xc) * xd * s})^{xb} 362 * = g^{(xa + xc) * xb * xd * s} 363 * [which is the same regardless of who calculates it] 364 */ 365 366 /* t1 = (g^{xd})^{xb} = g^{xb * xd} */ 367 BN_mod_exp(t1, ctx->p.gxd, ctx->xb, ctx->p.p, ctx->ctx); 368 /* t2 = -s = q-s */ 369 BN_sub(t2, ctx->p.q, ctx->secret); 370 /* t3 = t1^t2 = g^{-xb * xd * s} */ 371 BN_mod_exp(t3, t1, t2, ctx->p.p, ctx->ctx); 372 /* t1 = gx * t3 = X/g^{xb * xd * s} */ 373 BN_mod_mul(t1, gx, t3, ctx->p.p, ctx->ctx); 374 /* K = t1^{xb} */ 375 BN_mod_exp(ctx->key, t1, ctx->xb, ctx->p.p, ctx->ctx); 376 377 /* cleanup */ 378 BN_free(t3); 379 BN_free(t2); 380 BN_free(t1); 381 382 return 1; 383 } 384 385 int JPAKE_STEP2_process(JPAKE_CTX *ctx, const JPAKE_STEP2 *received) 386 { 387 BIGNUM *t1 = BN_new(); 388 BIGNUM *t2 = BN_new(); 389 int ret = 0; 390 391 /* 392 * g' = g^{xc + xa + xb} [from our POV] 393 * t1 = xa + xb 394 */ 395 BN_mod_add(t1, ctx->xa, ctx->xb, ctx->p.q, ctx->ctx); 396 /* t2 = g^{t1} = g^{xa+xb} */ 397 BN_mod_exp(t2, ctx->p.g, t1, ctx->p.p, ctx->ctx); 398 /* t1 = g^{xc} * t2 = g^{xc + xa + xb} */ 399 BN_mod_mul(t1, ctx->p.gxc, t2, ctx->p.p, ctx->ctx); 400 401 if(verify_zkp(received, t1, ctx)) 402 ret = 1; 403 else 404 JPAKEerr(JPAKE_F_JPAKE_STEP2_PROCESS, JPAKE_R_VERIFY_B_FAILED); 405 406 compute_key(ctx, received->gx); 407 408 /* cleanup */ 409 BN_free(t2); 410 BN_free(t1); 411 412 return ret; 413 } 414 415 static void quickhashbn(unsigned char *md, const BIGNUM *bn) 416 { 417 SHA_CTX sha; 418 419 SHA1_Init(&sha); 420 hashbn(&sha, bn); 421 SHA1_Final(md, &sha); 422 } 423 424 void JPAKE_STEP3A_init(JPAKE_STEP3A *s3a) 425 {} 426 427 int JPAKE_STEP3A_generate(JPAKE_STEP3A *send, JPAKE_CTX *ctx) 428 { 429 quickhashbn(send->hhk, ctx->key); 430 SHA1(send->hhk, sizeof send->hhk, send->hhk); 431 432 return 1; 433 } 434 435 int JPAKE_STEP3A_process(JPAKE_CTX *ctx, const JPAKE_STEP3A *received) 436 { 437 unsigned char hhk[SHA_DIGEST_LENGTH]; 438 439 quickhashbn(hhk, ctx->key); 440 SHA1(hhk, sizeof hhk, hhk); 441 if(memcmp(hhk, received->hhk, sizeof hhk)) 442 { 443 JPAKEerr(JPAKE_F_JPAKE_STEP3A_PROCESS, JPAKE_R_HASH_OF_HASH_OF_KEY_MISMATCH); 444 return 0; 445 } 446 return 1; 447 } 448 449 void JPAKE_STEP3A_release(JPAKE_STEP3A *s3a) 450 {} 451 452 void JPAKE_STEP3B_init(JPAKE_STEP3B *s3b) 453 {} 454 455 int JPAKE_STEP3B_generate(JPAKE_STEP3B *send, JPAKE_CTX *ctx) 456 { 457 quickhashbn(send->hk, ctx->key); 458 459 return 1; 460 } 461 462 int JPAKE_STEP3B_process(JPAKE_CTX *ctx, const JPAKE_STEP3B *received) 463 { 464 unsigned char hk[SHA_DIGEST_LENGTH]; 465 466 quickhashbn(hk, ctx->key); 467 if(memcmp(hk, received->hk, sizeof hk)) 468 { 469 JPAKEerr(JPAKE_F_JPAKE_STEP3B_PROCESS, JPAKE_R_HASH_OF_KEY_MISMATCH); 470 return 0; 471 } 472 return 1; 473 } 474 475 void JPAKE_STEP3B_release(JPAKE_STEP3B *s3b) 476 {} 477 478 const BIGNUM *JPAKE_get_shared_key(JPAKE_CTX *ctx) 479 { 480 return ctx->key; 481 } 482 483