crypto/jpake/jpake.c

   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 #include <assert.h>
   8
   9 /*
  10  * In the definition, (xa, xb, xc, xd) are Alice's (x1, x2, x3, x4) or
  11  * Bob's (x3, x4, x1, x2). If you see what I mean.
  12  */
  13
  14 typedef struct
  15     {
  16     char *name;  /* Must be unique */
  17     char *peer_name;
  18     BIGNUM *p;
  19     BIGNUM *g;
  20     BIGNUM *q;
  21     BIGNUM *gxc; /* Alice's g^{x3} or Bob's g^{x1} */
  22     BIGNUM *gxd; /* Alice's g^{x4} or Bob's g^{x2} */
  23     } JPAKE_CTX_PUBLIC;
  24
  25 struct JPAKE_CTX
  26     {
  27     JPAKE_CTX_PUBLIC p;
  28     BIGNUM *secret;   /* The shared secret */
  29     BN_CTX *ctx;
  30     BIGNUM *xa;       /* Alice's x1 or Bob's x3 */
  31     BIGNUM *xb;       /* Alice's x2 or Bob's x4 */
  32     BIGNUM *key;      /* The calculated (shared) key */
  33     };
  34
  35 static void JPAKE_ZKP_init(JPAKE_ZKP *zkp)
  36     {
  37     zkp->gr = BN_new();
  38     zkp->b = BN_new();
  39     }
  40
  41 static void JPAKE_ZKP_release(JPAKE_ZKP *zkp)
  42     {
  43     BN_free(zkp->b);
  44     BN_free(zkp->gr);
  45     }
  46
  47 /* Two birds with one stone - make the global name as expected */
  48 #define JPAKE_STEP_PART_init    JPAKE_STEP2_init
  49 #define JPAKE_STEP_PART_release JPAKE_STEP2_release
  50
  51 void JPAKE_STEP_PART_init(JPAKE_STEP_PART *p)
  52     {
  53     p->gx = BN_new();
  54     JPAKE_ZKP_init(&p->zkpx);
  55     }
  56
  57 void JPAKE_STEP_PART_release(JPAKE_STEP_PART *p)
  58     {
  59     JPAKE_ZKP_release(&p->zkpx);
  60     BN_free(p->gx);
  61     }
  62
  63 void JPAKE_STEP1_init(JPAKE_STEP1 *s1)
  64     {
  65     JPAKE_STEP_PART_init(&s1->p1);
  66     JPAKE_STEP_PART_init(&s1->p2);
  67     }
  68
  69 void JPAKE_STEP1_release(JPAKE_STEP1 *s1)
  70     {
  71     JPAKE_STEP_PART_release(&s1->p2);
  72     JPAKE_STEP_PART_release(&s1->p1);
  73     }
  74
  75 static void JPAKE_CTX_init(JPAKE_CTX *ctx, const char *name,
  76                            const char *peer_name, const BIGNUM *p,
  77                            const BIGNUM *g, const BIGNUM *q,
  78                            const BIGNUM *secret)
  79     {
  80     ctx->p.name = OPENSSL_strdup(name);
  81     ctx->p.peer_name = OPENSSL_strdup(peer_name);
  82     ctx->p.p = BN_dup(p);
  83     ctx->p.g = BN_dup(g);
  84     ctx->p.q = BN_dup(q);
  85     ctx->secret = BN_dup(secret);
  86
  87     ctx->p.gxc = BN_new();
  88     ctx->p.gxd = BN_new();
  89
  90     ctx->xa = BN_new();
  91     ctx->xb = BN_new();
  92     ctx->key = BN_new();
  93     ctx->ctx = BN_CTX_new();
  94     }
  95
  96 static void JPAKE_CTX_release(JPAKE_CTX *ctx)
  97     {
  98     BN_CTX_free(ctx->ctx);
  99     BN_clear_free(ctx->key);
 100     BN_clear_free(ctx->xb);
 101     BN_clear_free(ctx->xa);
 102
 103     BN_free(ctx->p.gxd);
 104     BN_free(ctx->p.gxc);
 105
 106     BN_clear_free(ctx->secret);
 107     BN_free(ctx->p.q);
 108     BN_free(ctx->p.g);
 109     BN_free(ctx->p.p);
 110     OPENSSL_free(ctx->p.peer_name);
 111     OPENSSL_free(ctx->p.name);
 112
 113     memset(ctx, '\0', sizeof *ctx);
 114     }
 115
 116 JPAKE_CTX *JPAKE_CTX_new(const char *name, const char *peer_name,
 117                          const BIGNUM *p, const BIGNUM *g, const BIGNUM *q,
 118                          const BIGNUM *secret)
 119     {
 120     JPAKE_CTX *ctx = OPENSSL_malloc(sizeof *ctx);
 121
 122     JPAKE_CTX_init(ctx, name, peer_name, p, g, q, secret);
 123
 124     return ctx;
 125     }
 126
 127 void JPAKE_CTX_free(JPAKE_CTX *ctx)
 128     {
 129     JPAKE_CTX_release(ctx);
 130     OPENSSL_free(ctx);
 131     }
 132
 133 static void hashlength(SHA_CTX *sha, size_t l)
 134     {
 135     unsigned char b[2];
 136
 137     assert(l <= 0xffff);
 138     b[0] = l >> 8;
 139     b[1] = l&0xff;
 140     SHA1_Update(sha, b, 2);
 141     }
 142
 143 static void hashstring(SHA_CTX *sha, const char *string)
 144     {
 145     size_t l = strlen(string);
 146
 147     hashlength(sha, l);
 148     SHA1_Update(sha, string, l);
 149     }
 150
 151 static void hashbn(SHA_CTX *sha, const BIGNUM *bn)
 152     {
 153     size_t l = BN_num_bytes(bn);
 154     unsigned char *bin = OPENSSL_malloc(l);
 155
 156     hashlength(sha, l);
 157     BN_bn2bin(bn, bin);
 158     SHA1_Update(sha, bin, l);
 159     OPENSSL_free(bin);
 160     }
 161
 162 /* h=hash(g, g^r, g^x, name) */
 163 static void zkp_hash(BIGNUM *h, const BIGNUM *zkpg, const JPAKE_STEP_PART *p,
 164                      const char *proof_name)
 165     {
 166     unsigned char md[SHA_DIGEST_LENGTH];
 167     SHA_CTX sha;
 168
 169    /*
 170     * XXX: hash should not allow moving of the boundaries - Java code
 171     * is flawed in this respect. Length encoding seems simplest.
 172     */
 173     SHA1_Init(&sha);
 174     hashbn(&sha, zkpg);
 175     assert(!BN_is_zero(p->zkpx.gr));
 176     hashbn(&sha, p->zkpx.gr);
 177     hashbn(&sha, p->gx);
 178     hashstring(&sha, proof_name);
 179     SHA1_Final(md, &sha);
 180     BN_bin2bn(md, SHA_DIGEST_LENGTH, h);
 181     }
 182
 183 /*
 184  * Prove knowledge of x
 185  * Note that p->gx has already been calculated
 186  */
 187 static void generate_zkp(JPAKE_STEP_PART *p, const BIGNUM *x,
 188                          const BIGNUM *zkpg, JPAKE_CTX *ctx)
 189     {
 190     BIGNUM *r = BN_new();
 191     BIGNUM *h = BN_new();
 192     BIGNUM *t = BN_new();
 193
 194    /*-
 195     * r in [0,q)
 196     * XXX: Java chooses r in [0, 2^160) - i.e. distribution not uniform
 197     */
 198     BN_rand_range(r, ctx->p.q);
 199    /* g^r */
 200     BN_mod_exp(p->zkpx.gr, zkpg, r, ctx->p.p, ctx->ctx);
 201
 202    /* h=hash... */
 203     zkp_hash(h, zkpg, p, ctx->p.name);
 204
 205    /* b = r - x*h */
 206     BN_mod_mul(t, x, h, ctx->p.q, ctx->ctx);
 207     BN_mod_sub(p->zkpx.b, r, t, ctx->p.q, ctx->ctx);
 208
 209    /* cleanup */
 210     BN_free(t);
 211     BN_free(h);
 212     BN_free(r);
 213     }
 214
 215 static int verify_zkp(const JPAKE_STEP_PART *p, const BIGNUM *zkpg,
 216                       JPAKE_CTX *ctx)
 217     {
 218     BIGNUM *h = BN_new();
 219     BIGNUM *t1 = BN_new();
 220     BIGNUM *t2 = BN_new();
 221     BIGNUM *t3 = BN_new();
 222     int ret = 0;
 223
 224     zkp_hash(h, zkpg, p, ctx->p.peer_name);
 225
 226    /* t1 = g^b */
 227     BN_mod_exp(t1, zkpg, p->zkpx.b, ctx->p.p, ctx->ctx);
 228    /* t2 = (g^x)^h = g^{hx} */
 229     BN_mod_exp(t2, p->gx, h, ctx->p.p, ctx->ctx);
 230    /* t3 = t1 * t2 = g^{hx} * g^b = g^{hx+b} = g^r (allegedly) */
 231     BN_mod_mul(t3, t1, t2, ctx->p.p, ctx->ctx);
 232
 233    /* verify t3 == g^r */
 234     if(BN_cmp(t3, p->zkpx.gr) == 0)
 235         ret = 1;
 236     else
 237         JPAKEerr(JPAKE_F_VERIFY_ZKP, JPAKE_R_ZKP_VERIFY_FAILED);
 238
 239    /* cleanup */
 240     BN_free(t3);
 241     BN_free(t2);
 242     BN_free(t1);
 243     BN_free(h);
 244
 245     return ret;
 246     }
 247
 248 static void generate_step_part(JPAKE_STEP_PART *p, const BIGNUM *x,
 249                                const BIGNUM *g, JPAKE_CTX *ctx)
 250     {
 251     BN_mod_exp(p->gx, g, x, ctx->p.p, ctx->ctx);
 252     generate_zkp(p, x, g, ctx);
 253     }
 254
 255 /* Generate each party's random numbers. xa is in [0, q), xb is in [1, q). */
 256 static void genrand(JPAKE_CTX *ctx)
 257     {
 258     BIGNUM *qm1;
 259
 260    /* xa in [0, q) */
 261     BN_rand_range(ctx->xa, ctx->p.q);
 262
 263    /* q-1 */
 264     qm1 = BN_new();
 265     BN_copy(qm1, ctx->p.q);
 266     BN_sub_word(qm1, 1);
 267
 268    /* ... and xb in [0, q-1) */
 269     BN_rand_range(ctx->xb, qm1);
 270    /* [1, q) */
 271     BN_add_word(ctx->xb, 1);
 272
 273    /* cleanup */
 274     BN_free(qm1);
 275     }
 276
 277 int JPAKE_STEP1_generate(JPAKE_STEP1 *send, JPAKE_CTX *ctx)
 278     {
 279     genrand(ctx);
 280     generate_step_part(&send->p1, ctx->xa, ctx->p.g, ctx);
 281     generate_step_part(&send->p2, ctx->xb, ctx->p.g, ctx);
 282
 283     return 1;
 284     }
 285
 286 /* g^x is a legal value */
 287 static int is_legal(const BIGNUM *gx, const JPAKE_CTX *ctx)
 288     {
 289     BIGNUM *t;
 290     int res;
 291
 292     if(BN_is_negative(gx) || BN_is_zero(gx) || BN_cmp(gx, ctx->p.p) >= 0)
 293         return 0;
 294
 295     t = BN_new();
 296     BN_mod_exp(t, gx, ctx->p.q, ctx->p.p, ctx->ctx);
 297     res = BN_is_one(t);
 298     BN_free(t);
 299
 300     return res;
 301     }
 302
 303 int JPAKE_STEP1_process(JPAKE_CTX *ctx, const JPAKE_STEP1 *received)
 304     {
 305     if(!is_legal(received->p1.gx, ctx))
 306         {
 307         JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X3_IS_NOT_LEGAL);
 308         return 0;
 309         }
 310
 311     if(!is_legal(received->p2.gx, ctx))
 312         {
 313         JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X4_IS_NOT_LEGAL);
 314         return 0;
 315         }
 316
 317
 318     /* verify their ZKP(xc) */
 319     if(!verify_zkp(&received->p1, ctx->p.g, ctx))
 320         {
 321         JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X3_FAILED);
 322         return 0;
 323         }
 324
 325     /* verify their ZKP(xd) */
 326     if(!verify_zkp(&received->p2, ctx->p.g, ctx))
 327         {
 328         JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X4_FAILED);
 329         return 0;
 330         }
 331
 332     /* g^xd != 1 */
 333     if(BN_is_one(received->p2.gx))
 334         {
 335         JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X4_IS_ONE);
 336         return 0;
 337         }
 338
 339    /* Save the bits we need for later */
 340     BN_copy(ctx->p.gxc, received->p1.gx);
 341     BN_copy(ctx->p.gxd, received->p2.gx);
 342
 343     return 1;
 344     }
 345
 346
 347 int JPAKE_STEP2_generate(JPAKE_STEP2 *send, JPAKE_CTX *ctx)
 348     {
 349     BIGNUM *t1 = BN_new();
 350     BIGNUM *t2 = BN_new();
 351
 352    /*-
 353     * X = g^{(xa + xc + xd) * xb * s}
 354     * t1 = g^xa
 355     */
 356     BN_mod_exp(t1, ctx->p.g, ctx->xa, ctx->p.p, ctx->ctx);
 357    /* t2 = t1 * g^{xc} = g^{xa} * g^{xc} = g^{xa + xc} */
 358     BN_mod_mul(t2, t1, ctx->p.gxc, ctx->p.p, ctx->ctx);
 359    /* t1 = t2 * g^{xd} = g^{xa + xc + xd} */
 360     BN_mod_mul(t1, t2, ctx->p.gxd, ctx->p.p, ctx->ctx);
 361    /* t2 = xb * s */
 362     BN_mod_mul(t2, ctx->xb, ctx->secret, ctx->p.q, ctx->ctx);
 363
 364    /*-
 365     * ZKP(xb * s)
 366     * XXX: this is kinda funky, because we're using
 367     *
 368     * g' = g^{xa + xc + xd}
 369     *
 370     * as the generator, which means X is g'^{xb * s}
 371     * X = t1^{t2} = t1^{xb * s} = g^{(xa + xc + xd) * xb * s}
 372     */
 373     generate_step_part(send, t2, t1, ctx);
 374
 375    /* cleanup */
 376     BN_free(t1);
 377     BN_free(t2);
 378
 379     return 1;
 380     }
 381
 382 /* gx = g^{xc + xa + xb} * xd * s */
 383 static int compute_key(JPAKE_CTX *ctx, const BIGNUM *gx)
 384     {
 385     BIGNUM *t1 = BN_new();
 386     BIGNUM *t2 = BN_new();
 387     BIGNUM *t3 = BN_new();
 388
 389    /*-
 390     * K = (gx/g^{xb * xd * s})^{xb}
 391     *   = (g^{(xc + xa + xb) * xd * s - xb * xd *s})^{xb}
 392     *   = (g^{(xa + xc) * xd * s})^{xb}
 393     *   = g^{(xa + xc) * xb * xd * s}
 394     * [which is the same regardless of who calculates it]
 395     */
 396
 397    /* t1 = (g^{xd})^{xb} = g^{xb * xd} */
 398     BN_mod_exp(t1, ctx->p.gxd, ctx->xb, ctx->p.p, ctx->ctx);
 399    /* t2 = -s = q-s */
 400     BN_sub(t2, ctx->p.q, ctx->secret);
 401    /* t3 = t1^t2 = g^{-xb * xd * s} */
 402     BN_mod_exp(t3, t1, t2, ctx->p.p, ctx->ctx);
 403    /* t1 = gx * t3 = X/g^{xb * xd * s} */
 404     BN_mod_mul(t1, gx, t3, ctx->p.p, ctx->ctx);
 405    /* K = t1^{xb} */
 406     BN_mod_exp(ctx->key, t1, ctx->xb, ctx->p.p, ctx->ctx);
 407
 408    /* cleanup */
 409     BN_free(t3);
 410     BN_free(t2);
 411     BN_free(t1);
 412
 413     return 1;
 414     }
 415
 416 int JPAKE_STEP2_process(JPAKE_CTX *ctx, const JPAKE_STEP2 *received)
 417     {
 418     BIGNUM *t1 = BN_new();
 419     BIGNUM *t2 = BN_new();
 420     int ret = 0;
 421
 422    /*-
 423     * g' = g^{xc + xa + xb} [from our POV]
 424     * t1 = xa + xb
 425     */
 426     BN_mod_add(t1, ctx->xa, ctx->xb, ctx->p.q, ctx->ctx);
 427    /* t2 = g^{t1} = g^{xa+xb} */
 428     BN_mod_exp(t2, ctx->p.g, t1, ctx->p.p, ctx->ctx);
 429    /* t1 = g^{xc} * t2 = g^{xc + xa + xb} */
 430     BN_mod_mul(t1, ctx->p.gxc, t2, ctx->p.p, ctx->ctx);
 431
 432     if(verify_zkp(received, t1, ctx))
 433         ret = 1;
 434     else
 435         JPAKEerr(JPAKE_F_JPAKE_STEP2_PROCESS, JPAKE_R_VERIFY_B_FAILED);
 436
 437     compute_key(ctx, received->gx);
 438
 439    /* cleanup */
 440     BN_free(t2);
 441     BN_free(t1);
 442
 443     return ret;
 444     }
 445
 446 static void quickhashbn(unsigned char *md, const BIGNUM *bn)
 447     {
 448     SHA_CTX sha;
 449
 450     SHA1_Init(&sha);
 451     hashbn(&sha, bn);
 452     SHA1_Final(md, &sha);
 453     }
 454
 455 void JPAKE_STEP3A_init(JPAKE_STEP3A *s3a)
 456     {}
 457
 458 int JPAKE_STEP3A_generate(JPAKE_STEP3A *send, JPAKE_CTX *ctx)
 459     {
 460     quickhashbn(send->hhk, ctx->key);
 461     SHA1(send->hhk, sizeof send->hhk, send->hhk);
 462
 463     return 1;
 464     }
 465
 466 int JPAKE_STEP3A_process(JPAKE_CTX *ctx, const JPAKE_STEP3A *received)
 467     {
 468     unsigned char hhk[SHA_DIGEST_LENGTH];
 469
 470     quickhashbn(hhk, ctx->key);
 471     SHA1(hhk, sizeof hhk, hhk);
 472     if(memcmp(hhk, received->hhk, sizeof hhk))
 473         {
 474         JPAKEerr(JPAKE_F_JPAKE_STEP3A_PROCESS, JPAKE_R_HASH_OF_HASH_OF_KEY_MISMATCH);
 475         return 0;
 476         }
 477     return 1;
 478     }
 479
 480 void JPAKE_STEP3A_release(JPAKE_STEP3A *s3a)
 481     {}
 482
 483 void JPAKE_STEP3B_init(JPAKE_STEP3B *s3b)
 484     {}
 485
 486 int JPAKE_STEP3B_generate(JPAKE_STEP3B *send, JPAKE_CTX *ctx)
 487     {
 488     quickhashbn(send->hk, ctx->key);
 489
 490     return 1;
 491     }
 492
 493 int JPAKE_STEP3B_process(JPAKE_CTX *ctx, const JPAKE_STEP3B *received)
 494     {
 495     unsigned char hk[SHA_DIGEST_LENGTH];
 496
 497     quickhashbn(hk, ctx->key);
 498     if(memcmp(hk, received->hk, sizeof hk))
 499         {
 500         JPAKEerr(JPAKE_F_JPAKE_STEP3B_PROCESS, JPAKE_R_HASH_OF_KEY_MISMATCH);
 501         return 0;
 502         }
 503     return 1;
 504     }
 505
 506 void JPAKE_STEP3B_release(JPAKE_STEP3B *s3b)
 507     {}
 508
 509 const BIGNUM *JPAKE_get_shared_key(JPAKE_CTX *ctx)
 510     {
 511     return ctx->key;
 512     }
 513