jpakedemo.c revision 296465
1#include "openssl/bn.h" 2#include "openssl/sha.h" 3#include <assert.h> 4#include <string.h> 5#include <stdlib.h> 6 7/* Copyright (C) 2008 Ben Laurie (ben@links.org) */ 8 9/* 10 * Implement J-PAKE, as described in 11 * http://grouper.ieee.org/groups/1363/Research/contributions/hao-ryan-2008.pdf 12 * 13 * With hints from http://www.cl.cam.ac.uk/~fh240/software/JPAKE2.java. 14 */ 15 16static void showbn(const char *name, const BIGNUM *bn) 17{ 18 fputs(name, stdout); 19 fputs(" = ", stdout); 20 BN_print_fp(stdout, bn); 21 putc('\n', stdout); 22} 23 24typedef struct { 25 BN_CTX *ctx; // Perhaps not the best place for this? 26 BIGNUM *p; 27 BIGNUM *q; 28 BIGNUM *g; 29} JPakeParameters; 30 31static void JPakeParametersInit(JPakeParameters * params) 32{ 33 params->ctx = BN_CTX_new(); 34 35 // For now use p, q, g from Java sample code. Later, generate them. 36 params->p = NULL; 37 BN_hex2bn(¶ms->p, 38 "fd7f53811d75122952df4a9c2eece4e7f611b7523cef4400c31e3f80b6512669455d402251fb593d8d58fabfc5f5ba30f6cb9b556cd7813b801d346ff26660b76b9950a5a49f9fe8047b1022c24fbba9d7feb7c61bf83b57e7c6a8a6150f04fb83f6d3c51ec3023554135a169132f675f3ae2b61d72aeff22203199dd14801c7"); 39 params->q = NULL; 40 BN_hex2bn(¶ms->q, "9760508f15230bccb292b982a2eb840bf0581cf5"); 41 params->g = NULL; 42 BN_hex2bn(¶ms->g, 43 "f7e1a085d69b3ddecbbcab5c36b857b97994afbbfa3aea82f9574c0b3d0782675159578ebad4594fe67107108180b449167123e84c281613b7cf09328cc8a6e13c167a8b547c8d28e0a3ae1e2bb3a675916ea37f0bfa213562f1fb627a01243bcca4f1bea8519089a883dfe15ae59f06928b665e807b552564014c3bfecf492a"); 44 45 showbn("p", params->p); 46 showbn("q", params->q); 47 showbn("g", params->g); 48} 49 50typedef struct { 51 BIGNUM *gr; // g^r (r random) 52 BIGNUM *b; // b = r - x*h, h=hash(g, g^r, g^x, name) 53} JPakeZKP; 54 55typedef struct { 56 BIGNUM *gx; // g^x 57 JPakeZKP zkpx; // ZKP(x) 58} JPakeStep1; 59 60typedef struct { 61 BIGNUM *X; // g^(xa + xc + xd) * xb * s 62 JPakeZKP zkpxbs; // ZKP(xb * s) 63} JPakeStep2; 64 65typedef struct { 66 const char *name; // Must be unique 67 int base; // 1 for Alice, 3 for Bob. Only used for 68 // printing stuff. 69 JPakeStep1 s1c; // Alice's g^x3, ZKP(x3) or Bob's g^x1, 70 // ZKP(x1) 71 JPakeStep1 s1d; // Alice's g^x4, ZKP(x4) or Bob's g^x2, 72 // ZKP(x2) 73 JPakeStep2 s2; // Alice's A, ZKP(x2 * s) or Bob's B, ZKP(x4 74 // * s) 75} JPakeUserPublic; 76 77/* 78 * The user structure. In the definition, (xa, xb, xc, xd) are Alice's 79 * (x1, x2, x3, x4) or Bob's (x3, x4, x1, x2). If you see what I mean. 80 */ 81typedef struct { 82 JPakeUserPublic p; 83 BIGNUM *secret; // The shared secret 84 BIGNUM *key; // The calculated (shared) key 85 BIGNUM *xa; // Alice's x1 or Bob's x3 86 BIGNUM *xb; // Alice's x2 or Bob's x4 87} JPakeUser; 88 89// Generate each party's random numbers. xa is in [0, q), xb is in [1, q). 90static void genrand(JPakeUser * user, const JPakeParameters * params) 91{ 92 BIGNUM *qm1; 93 94 // xa in [0, q) 95 user->xa = BN_new(); 96 BN_rand_range(user->xa, params->q); 97 98 // q-1 99 qm1 = BN_new(); 100 BN_copy(qm1, params->q); 101 BN_sub_word(qm1, 1); 102 103 // ... and xb in [0, q-1) 104 user->xb = BN_new(); 105 BN_rand_range(user->xb, qm1); 106 // [1, q) 107 BN_add_word(user->xb, 1); 108 109 // cleanup 110 BN_free(qm1); 111 112 // Show 113 printf("x%d", user->p.base); 114 showbn("", user->xa); 115 printf("x%d", user->p.base + 1); 116 showbn("", user->xb); 117} 118 119static void hashlength(SHA_CTX *sha, size_t l) 120{ 121 unsigned char b[2]; 122 123 assert(l <= 0xffff); 124 b[0] = l >> 8; 125 b[1] = l & 0xff; 126 SHA1_Update(sha, b, 2); 127} 128 129static void hashstring(SHA_CTX *sha, const char *string) 130{ 131 size_t l = strlen(string); 132 133 hashlength(sha, l); 134 SHA1_Update(sha, string, l); 135} 136 137static void hashbn(SHA_CTX *sha, const BIGNUM *bn) 138{ 139 size_t l = BN_num_bytes(bn); 140 unsigned char *bin = alloca(l); 141 142 hashlength(sha, l); 143 BN_bn2bin(bn, bin); 144 SHA1_Update(sha, bin, l); 145} 146 147// h=hash(g, g^r, g^x, name) 148static void zkpHash(BIGNUM *h, const JPakeZKP * zkp, const BIGNUM *gx, 149 const JPakeUserPublic * from, 150 const JPakeParameters * params) 151{ 152 unsigned char md[SHA_DIGEST_LENGTH]; 153 SHA_CTX sha; 154 155 // XXX: hash should not allow moving of the boundaries - Java code 156 // is flawed in this respect. Length encoding seems simplest. 157 SHA1_Init(&sha); 158 hashbn(&sha, params->g); 159 hashbn(&sha, zkp->gr); 160 hashbn(&sha, gx); 161 hashstring(&sha, from->name); 162 SHA1_Final(md, &sha); 163 BN_bin2bn(md, SHA_DIGEST_LENGTH, h); 164} 165 166// Prove knowledge of x 167// Note that we don't send g^x because, as it happens, we've always 168// sent it elsewhere. Also note that because of that, we could avoid 169// calculating it here, but we don't, for clarity... 170static void CreateZKP(JPakeZKP * zkp, const BIGNUM *x, const JPakeUser * us, 171 const BIGNUM *zkpg, const JPakeParameters * params, 172 int n, const char *suffix) 173{ 174 BIGNUM *r = BN_new(); 175 BIGNUM *gx = BN_new(); 176 BIGNUM *h = BN_new(); 177 BIGNUM *t = BN_new(); 178 179 // r in [0,q) 180 // XXX: Java chooses r in [0, 2^160) - i.e. distribution not uniform 181 BN_rand_range(r, params->q); 182 // g^r 183 zkp->gr = BN_new(); 184 BN_mod_exp(zkp->gr, zkpg, r, params->p, params->ctx); 185 // g^x 186 BN_mod_exp(gx, zkpg, x, params->p, params->ctx); 187 188 // h=hash... 189 zkpHash(h, zkp, gx, &us->p, params); 190 191 // b = r - x*h 192 BN_mod_mul(t, x, h, params->q, params->ctx); 193 zkp->b = BN_new(); 194 BN_mod_sub(zkp->b, r, t, params->q, params->ctx); 195 196 // show 197 printf(" ZKP(x%d%s)\n", n, suffix); 198 showbn(" zkpg", zkpg); 199 showbn(" g^x", gx); 200 showbn(" g^r", zkp->gr); 201 showbn(" b", zkp->b); 202 203 // cleanup 204 BN_free(t); 205 BN_free(h); 206 BN_free(gx); 207 BN_free(r); 208} 209 210static int VerifyZKP(const JPakeZKP * zkp, BIGNUM *gx, 211 const JPakeUserPublic * them, const BIGNUM *zkpg, 212 const JPakeParameters * params, int n, 213 const char *suffix) 214{ 215 BIGNUM *h = BN_new(); 216 BIGNUM *t1 = BN_new(); 217 BIGNUM *t2 = BN_new(); 218 BIGNUM *t3 = BN_new(); 219 int ret = 0; 220 221 zkpHash(h, zkp, gx, them, params); 222 223 // t1 = g^b 224 BN_mod_exp(t1, zkpg, zkp->b, params->p, params->ctx); 225 // t2 = (g^x)^h = g^{hx} 226 BN_mod_exp(t2, gx, h, params->p, params->ctx); 227 // t3 = t1 * t2 = g^{hx} * g^b = g^{hx+b} = g^r (allegedly) 228 BN_mod_mul(t3, t1, t2, params->p, params->ctx); 229 230 printf(" ZKP(x%d%s)\n", n, suffix); 231 showbn(" zkpg", zkpg); 232 showbn(" g^r'", t3); 233 234 // verify t3 == g^r 235 if (BN_cmp(t3, zkp->gr) == 0) 236 ret = 1; 237 238 // cleanup 239 BN_free(t3); 240 BN_free(t2); 241 BN_free(t1); 242 BN_free(h); 243 244 if (ret) 245 puts(" OK"); 246 else 247 puts(" FAIL"); 248 249 return ret; 250} 251 252static void sendstep1_substep(JPakeStep1 * s1, const BIGNUM *x, 253 const JPakeUser * us, 254 const JPakeParameters * params, int n) 255{ 256 s1->gx = BN_new(); 257 BN_mod_exp(s1->gx, params->g, x, params->p, params->ctx); 258 printf(" g^{x%d}", n); 259 showbn("", s1->gx); 260 261 CreateZKP(&s1->zkpx, x, us, params->g, params, n, ""); 262} 263 264static void sendstep1(const JPakeUser * us, JPakeUserPublic * them, 265 const JPakeParameters * params) 266{ 267 printf("\n%s sends %s:\n\n", us->p.name, them->name); 268 269 // from's g^xa (which becomes to's g^xc) and ZKP(xa) 270 sendstep1_substep(&them->s1c, us->xa, us, params, us->p.base); 271 // from's g^xb (which becomes to's g^xd) and ZKP(xb) 272 sendstep1_substep(&them->s1d, us->xb, us, params, us->p.base + 1); 273} 274 275static int verifystep1(const JPakeUser * us, const JPakeUserPublic * them, 276 const JPakeParameters * params) 277{ 278 printf("\n%s verifies %s:\n\n", us->p.name, them->name); 279 280 // verify their ZKP(xc) 281 if (!VerifyZKP(&us->p.s1c.zkpx, us->p.s1c.gx, them, params->g, params, 282 them->base, "")) 283 return 0; 284 285 // verify their ZKP(xd) 286 if (!VerifyZKP(&us->p.s1d.zkpx, us->p.s1d.gx, them, params->g, params, 287 them->base + 1, "")) 288 return 0; 289 290 // g^xd != 1 291 printf(" g^{x%d} != 1: ", them->base + 1); 292 if (BN_is_one(us->p.s1d.gx)) { 293 puts("FAIL"); 294 return 0; 295 } 296 puts("OK"); 297 298 return 1; 299} 300 301static void sendstep2(const JPakeUser * us, JPakeUserPublic * them, 302 const JPakeParameters * params) 303{ 304 BIGNUM *t1 = BN_new(); 305 BIGNUM *t2 = BN_new(); 306 307 printf("\n%s sends %s:\n\n", us->p.name, them->name); 308 309 // X = g^{(xa + xc + xd) * xb * s} 310 // t1 = g^xa 311 BN_mod_exp(t1, params->g, us->xa, params->p, params->ctx); 312 // t2 = t1 * g^{xc} = g^{xa} * g^{xc} = g^{xa + xc} 313 BN_mod_mul(t2, t1, us->p.s1c.gx, params->p, params->ctx); 314 // t1 = t2 * g^{xd} = g^{xa + xc + xd} 315 BN_mod_mul(t1, t2, us->p.s1d.gx, params->p, params->ctx); 316 // t2 = xb * s 317 BN_mod_mul(t2, us->xb, us->secret, params->q, params->ctx); 318 // X = t1^{t2} = t1^{xb * s} = g^{(xa + xc + xd) * xb * s} 319 them->s2.X = BN_new(); 320 BN_mod_exp(them->s2.X, t1, t2, params->p, params->ctx); 321 322 // Show 323 printf(" g^{(x%d + x%d + x%d) * x%d * s)", us->p.base, them->base, 324 them->base + 1, us->p.base + 1); 325 showbn("", them->s2.X); 326 327 // ZKP(xb * s) 328 // XXX: this is kinda funky, because we're using 329 // 330 // g' = g^{xa + xc + xd} 331 // 332 // as the generator, which means X is g'^{xb * s} 333 CreateZKP(&them->s2.zkpxbs, t2, us, t1, params, us->p.base + 1, " * s"); 334 335 // cleanup 336 BN_free(t1); 337 BN_free(t2); 338} 339 340static int verifystep2(const JPakeUser * us, const JPakeUserPublic * them, 341 const JPakeParameters * params) 342{ 343 BIGNUM *t1 = BN_new(); 344 BIGNUM *t2 = BN_new(); 345 int ret = 0; 346 347 printf("\n%s verifies %s:\n\n", us->p.name, them->name); 348 349 // g' = g^{xc + xa + xb} [from our POV] 350 // t1 = xa + xb 351 BN_mod_add(t1, us->xa, us->xb, params->q, params->ctx); 352 // t2 = g^{t1} = g^{xa+xb} 353 BN_mod_exp(t2, params->g, t1, params->p, params->ctx); 354 // t1 = g^{xc} * t2 = g^{xc + xa + xb} 355 BN_mod_mul(t1, us->p.s1c.gx, t2, params->p, params->ctx); 356 357 if (VerifyZKP 358 (&us->p.s2.zkpxbs, us->p.s2.X, them, t1, params, them->base + 1, 359 " * s")) 360 ret = 1; 361 362 // cleanup 363 BN_free(t2); 364 BN_free(t1); 365 366 return ret; 367} 368 369static void computekey(JPakeUser * us, const JPakeParameters * params) 370{ 371 BIGNUM *t1 = BN_new(); 372 BIGNUM *t2 = BN_new(); 373 BIGNUM *t3 = BN_new(); 374 375 printf("\n%s calculates the shared key:\n\n", us->p.name); 376 377 // K = (X/g^{xb * xd * s})^{xb} 378 // = (g^{(xc + xa + xb) * xd * s - xb * xd *s})^{xb} 379 // = (g^{(xa + xc) * xd * s})^{xb} 380 // = g^{(xa + xc) * xb * xd * s} 381 // [which is the same regardless of who calculates it] 382 383 // t1 = (g^{xd})^{xb} = g^{xb * xd} 384 BN_mod_exp(t1, us->p.s1d.gx, us->xb, params->p, params->ctx); 385 // t2 = -s = q-s 386 BN_sub(t2, params->q, us->secret); 387 // t3 = t1^t2 = g^{-xb * xd * s} 388 BN_mod_exp(t3, t1, t2, params->p, params->ctx); 389 // t1 = X * t3 = X/g^{xb * xd * s} 390 BN_mod_mul(t1, us->p.s2.X, t3, params->p, params->ctx); 391 // K = t1^{xb} 392 us->key = BN_new(); 393 BN_mod_exp(us->key, t1, us->xb, params->p, params->ctx); 394 395 // show 396 showbn(" K", us->key); 397 398 // cleanup 399 BN_free(t3); 400 BN_free(t2); 401 BN_free(t1); 402} 403 404int main(int argc, char **argv) 405{ 406 JPakeParameters params; 407 JPakeUser alice, bob; 408 409 alice.p.name = "Alice"; 410 alice.p.base = 1; 411 bob.p.name = "Bob"; 412 bob.p.base = 3; 413 414 JPakeParametersInit(¶ms); 415 416 // Shared secret 417 alice.secret = BN_new(); 418 BN_rand(alice.secret, 32, -1, 0); 419 bob.secret = alice.secret; 420 showbn("secret", alice.secret); 421 422 assert(BN_cmp(alice.secret, params.q) < 0); 423 424 // Alice's x1, x2 425 genrand(&alice, ¶ms); 426 427 // Bob's x3, x4 428 genrand(&bob, ¶ms); 429 430 // Now send stuff to each other... 431 sendstep1(&alice, &bob.p, ¶ms); 432 sendstep1(&bob, &alice.p, ¶ms); 433 434 // And verify what each other sent 435 if (!verifystep1(&alice, &bob.p, ¶ms)) 436 return 1; 437 if (!verifystep1(&bob, &alice.p, ¶ms)) 438 return 2; 439 440 // Second send 441 sendstep2(&alice, &bob.p, ¶ms); 442 sendstep2(&bob, &alice.p, ¶ms); 443 444 // And second verify 445 if (!verifystep2(&alice, &bob.p, ¶ms)) 446 return 3; 447 if (!verifystep2(&bob, &alice.p, ¶ms)) 448 return 4; 449 450 // Compute common key 451 computekey(&alice, ¶ms); 452 computekey(&bob, ¶ms); 453 454 // Confirm the common key is identical 455 // XXX: if the two secrets are not the same, everything works up 456 // to this point, so the only way to detect a failure is by the 457 // difference in the calculated keys. 458 // Since we're all the same code, just compare them directly. In a 459 // real system, Alice sends Bob H(H(K)), Bob checks it, then sends 460 // back H(K), which Alice checks, or something equivalent. 461 puts("\nAlice and Bob check keys are the same:"); 462 if (BN_cmp(alice.key, bob.key) == 0) 463 puts(" OK"); 464 else { 465 puts(" FAIL"); 466 return 5; 467 } 468 469 return 0; 470} 471