crypto/external/bsd/openssh/dist/schnorr.c

   1 /*      $NetBSD: schnorr.c,v 1.1.1.2 2009/12/27 01:07:03 christos Exp $ */
   2 /* $OpenBSD: schnorr.c,v 1.3 2009/03/05 07:18:19 djm Exp $ */
   3 /*
   4  * Copyright (c) 2008 Damien Miller.  All rights reserved.
   5  *
   6  * Permission to use, copy, modify, and distribute this software for any
   7  * purpose with or without fee is hereby granted, provided that the above
   8  * copyright notice and this permission notice appear in all copies.
   9  *
  10  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  11  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  12  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  13  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  14  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  15  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  16  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  17  */
  18
  19 /*
  20  * Implementation of Schnorr signatures / zero-knowledge proofs, based on
  21  * description in:
  22  *
  23  * F. Hao, P. Ryan, "Password Authenticated Key Exchange by Juggling",
  24  * 16th Workshop on Security Protocols, Cambridge, April 2008
  25  *
  26  * http://grouper.ieee.org/groups/1363/Research/contributions/hao-ryan-2008.pdf
  27  */
  28
  29 #include <sys/types.h>
  30
  31 #include <string.h>
  32 #include <stdarg.h>
  33 #include <stdio.h>
  34
  35 #include <openssl/evp.h>
  36 #include <openssl/bn.h>
  37
  38 #include "xmalloc.h"
  39 #include "buffer.h"
  40 #include "log.h"
  41
  42 #include "schnorr.h"
  43
  44 /* #define SCHNORR_DEBUG */             /* Privacy-violating debugging */
  45 /* #define SCHNORR_MAIN */              /* Include main() selftest */
  46
  47 #ifndef SCHNORR_DEBUG
  48 # define SCHNORR_DEBUG_BN(a)
  49 # define SCHNORR_DEBUG_BUF(a)
  50 #else
  51 # define SCHNORR_DEBUG_BN(a)    debug3_bn a
  52 # define SCHNORR_DEBUG_BUF(a)   debug3_buf a
  53 #endif /* SCHNORR_DEBUG */
  54
  55 /*
  56  * Calculate hash component of Schnorr signature H(g || g^v || g^x || id)
  57  * using the hash function defined by "evp_md". Returns signature as
  58  * bignum or NULL on error.
  59  */
  60 static BIGNUM *
  61 schnorr_hash(const BIGNUM *p, const BIGNUM *q, const BIGNUM *g,
  62     const EVP_MD *evp_md, const BIGNUM *g_v, const BIGNUM *g_x,
  63     const u_char *id, u_int idlen)
  64 {
  65         u_char *digest;
  66         u_int digest_len;
  67         BIGNUM *h;
  68         Buffer b;
  69         int success = -1;
  70
  71         if ((h = BN_new()) == NULL) {
  72                 error("%s: BN_new", __func__);
  73                 return NULL;
  74         }
  75
  76         buffer_init(&b);
  77
  78         /* h = H(g || p || q || g^v || g^x || id) */
  79         buffer_put_bignum2(&b, g);
  80         buffer_put_bignum2(&b, p);
  81         buffer_put_bignum2(&b, q);
  82         buffer_put_bignum2(&b, g_v);
  83         buffer_put_bignum2(&b, g_x);
  84         buffer_put_string(&b, id, idlen);
  85
  86         SCHNORR_DEBUG_BUF((buffer_ptr(&b), buffer_len(&b),
  87             "%s: hashblob", __func__));
  88         if (hash_buffer(buffer_ptr(&b), buffer_len(&b), evp_md,
  89             &digest, &digest_len) != 0) {
  90                 error("%s: hash_buffer", __func__);
  91                 goto out;
  92         }
  93         if (BN_bin2bn(digest, (int)digest_len, h) == NULL) {
  94                 error("%s: BN_bin2bn", __func__);
  95                 goto out;
  96         }
  97         success = 0;
  98         SCHNORR_DEBUG_BN((h, "%s: h = ", __func__));
  99  out:
 100         buffer_free(&b);
 101         bzero(digest, digest_len);
 102         xfree(digest);
 103         digest_len = 0;
 104         if (success == 0)
 105                 return h;
 106         BN_clear_free(h);
 107         return NULL;
 108 }
 109
 110 /*
 111  * Generate Schnorr signature to prove knowledge of private value 'x' used
 112  * in public exponent g^x, under group defined by 'grp_p', 'grp_q' and 'grp_g'
 113  * using the hash function "evp_md".
 114  * 'idlen' bytes from 'id' will be included in the signature hash as an anti-
 115  * replay salt.
 116  *
 117  * On success, 0 is returned. The signature values are returned as *e_p
 118  * (g^v mod p) and *r_p (v - xh mod q). The caller must free these values.
 119  * On failure, -1 is returned.
 120  */
 121 int
 122 schnorr_sign(const BIGNUM *grp_p, const BIGNUM *grp_q, const BIGNUM *grp_g,
 123     const EVP_MD *evp_md, const BIGNUM *x, const BIGNUM *g_x,
 124     const u_char *id, u_int idlen, BIGNUM **r_p, BIGNUM **e_p)
 125 {
 126         int success = -1;
 127         BIGNUM *h, *tmp, *v, *g_v, *r;
 128         BN_CTX *bn_ctx;
 129
 130         SCHNORR_DEBUG_BN((x, "%s: x = ", __func__));
 131         SCHNORR_DEBUG_BN((g_x, "%s: g_x = ", __func__));
 132
 133         /* Avoid degenerate cases: g^0 yields a spoofable signature */
 134         if (BN_cmp(g_x, BN_value_one()) <= 0) {
 135                 error("%s: g_x < 1", __func__);
 136                 return -1;
 137         }
 138
 139         h = g_v = r = tmp = v = NULL;
 140         if ((bn_ctx = BN_CTX_new()) == NULL) {
 141                 error("%s: BN_CTX_new", __func__);
 142                 goto out;
 143         }
 144         if ((g_v = BN_new()) == NULL ||
 145             (r = BN_new()) == NULL ||
 146             (tmp = BN_new()) == NULL) {
 147                 error("%s: BN_new", __func__);
 148                 goto out;
 149         }
 150
 151         /*
 152          * v must be a random element of Zq, so 1 <= v < q
 153          * we also exclude v = 1, since g^1 looks dangerous
 154          */
 155         if ((v = bn_rand_range_gt_one(grp_p)) == NULL) {
 156                 error("%s: bn_rand_range2", __func__);
 157                 goto out;
 158         }
 159         SCHNORR_DEBUG_BN((v, "%s: v = ", __func__));
 160
 161         /* g_v = g^v mod p */
 162         if (BN_mod_exp(g_v, grp_g, v, grp_p, bn_ctx) == -1) {
 163                 error("%s: BN_mod_exp (g^v mod p)", __func__);
 164                 goto out;
 165         }
 166         SCHNORR_DEBUG_BN((g_v, "%s: g_v = ", __func__));
 167
 168         /* h = H(g || g^v || g^x || id) */
 169         if ((h = schnorr_hash(grp_p, grp_q, grp_g, evp_md, g_v, g_x,
 170             id, idlen)) == NULL) {
 171                 error("%s: schnorr_hash failed", __func__);
 172                 goto out;
 173         }
 174
 175         /* r = v - xh mod q */
 176         if (BN_mod_mul(tmp, x, h, grp_q, bn_ctx) == -1) {
 177                 error("%s: BN_mod_mul (tmp = xv mod q)", __func__);
 178                 goto out;
 179         }
 180         if (BN_mod_sub(r, v, tmp, grp_q, bn_ctx) == -1) {
 181                 error("%s: BN_mod_mul (r = v - tmp)", __func__);
 182                 goto out;
 183         }
 184         SCHNORR_DEBUG_BN((g_v, "%s: e = ", __func__));
 185         SCHNORR_DEBUG_BN((r, "%s: r = ", __func__));
 186
 187         *e_p = g_v;
 188         *r_p = r;
 189
 190         success = 0;
 191  out:
 192         BN_CTX_free(bn_ctx);
 193         if (h != NULL)
 194                 BN_clear_free(h);
 195         if (v != NULL)
 196                 BN_clear_free(v);
 197         BN_clear_free(tmp);
 198
 199         return success;
 200 }
 201
 202 /*
 203  * Generate Schnorr signature to prove knowledge of private value 'x' used
 204  * in public exponent g^x, under group defined by 'grp_p', 'grp_q' and 'grp_g'
 205  * using a SHA256 hash.
 206  * 'idlen' bytes from 'id' will be included in the signature hash as an anti-
 207  * replay salt.
 208  * On success, 0 is returned and *siglen bytes of signature are returned in
 209  * *sig (caller to free). Returns -1 on failure.
 210  */
 211 int
 212 schnorr_sign_buf(const BIGNUM *grp_p, const BIGNUM *grp_q, const BIGNUM *grp_g,
 213     const BIGNUM *x, const BIGNUM *g_x, const u_char *id, u_int idlen,
 214     u_char **sig, u_int *siglen)
 215 {
 216         Buffer b;
 217         BIGNUM *r, *e;
 218
 219         if (schnorr_sign(grp_p, grp_q, grp_g, EVP_sha256(),
 220             x, g_x, id, idlen, &r, &e) != 0)
 221                 return -1;
 222
 223         /* Signature is (e, r) */
 224         buffer_init(&b);
 225         /* XXX sigtype-hash as string? */
 226         buffer_put_bignum2(&b, e);
 227         buffer_put_bignum2(&b, r);
 228         *siglen = buffer_len(&b);
 229         *sig = xmalloc(*siglen);
 230         memcpy(*sig, buffer_ptr(&b), *siglen);
 231         SCHNORR_DEBUG_BUF((buffer_ptr(&b), buffer_len(&b),
 232             "%s: sigblob", __func__));
 233         buffer_free(&b);
 234
 235         BN_clear_free(r);
 236         BN_clear_free(e);
 237
 238         return 0;
 239 }
 240
 241 /*
 242  * Verify Schnorr signature { r (v - xh mod q), e (g^v mod p) } against
 243  * public exponent g_x (g^x) under group defined by 'grp_p', 'grp_q' and
 244  * 'grp_g' using hash "evp_md".
 245  * Signature hash will be salted with 'idlen' bytes from 'id'.
 246  * Returns -1 on failure, 0 on incorrect signature or 1 on matching signature.
 247  */
 248 int
 249 schnorr_verify(const BIGNUM *grp_p, const BIGNUM *grp_q, const BIGNUM *grp_g,
 250     const EVP_MD *evp_md, const BIGNUM *g_x, const u_char *id, u_int idlen,
 251     const BIGNUM *r, const BIGNUM *e)
 252 {
 253         int success = -1;
 254         BIGNUM *h, *g_xh, *g_r, *expected;
 255         BN_CTX *bn_ctx;
 256
 257         SCHNORR_DEBUG_BN((g_x, "%s: g_x = ", __func__));
 258
 259         /* Avoid degenerate cases: g^0 yields a spoofable signature */
 260         if (BN_cmp(g_x, BN_value_one()) <= 0) {
 261                 error("%s: g_x < 1", __func__);
 262                 return -1;
 263         }
 264
 265         h = g_xh = g_r = expected = NULL;
 266         if ((bn_ctx = BN_CTX_new()) == NULL) {
 267                 error("%s: BN_CTX_new", __func__);
 268                 goto out;
 269         }
 270         if ((g_xh = BN_new()) == NULL ||
 271             (g_r = BN_new()) == NULL ||
 272             (expected = BN_new()) == NULL) {
 273                 error("%s: BN_new", __func__);
 274                 goto out;
 275         }
 276
 277         SCHNORR_DEBUG_BN((e, "%s: e = ", __func__));
 278         SCHNORR_DEBUG_BN((r, "%s: r = ", __func__));
 279
 280         /* h = H(g || g^v || g^x || id) */
 281         if ((h = schnorr_hash(grp_p, grp_q, grp_g, evp_md, e, g_x,
 282             id, idlen)) == NULL) {
 283                 error("%s: schnorr_hash failed", __func__);
 284                 goto out;
 285         }
 286
 287         /* g_xh = (g^x)^h */
 288         if (BN_mod_exp(g_xh, g_x, h, grp_p, bn_ctx) == -1) {
 289                 error("%s: BN_mod_exp (g_x^h mod p)", __func__);
 290                 goto out;
 291         }
 292         SCHNORR_DEBUG_BN((g_xh, "%s: g_xh = ", __func__));
 293
 294         /* g_r = g^r */
 295         if (BN_mod_exp(g_r, grp_g, r, grp_p, bn_ctx) == -1) {
 296                 error("%s: BN_mod_exp (g_x^h mod p)", __func__);
 297                 goto out;
 298         }
 299         SCHNORR_DEBUG_BN((g_r, "%s: g_r = ", __func__));
 300
 301         /* expected = g^r * g_xh */
 302         if (BN_mod_mul(expected, g_r, g_xh, grp_p, bn_ctx) == -1) {
 303                 error("%s: BN_mod_mul (expected = g_r mod p)", __func__);
 304                 goto out;
 305         }
 306         SCHNORR_DEBUG_BN((expected, "%s: expected = ", __func__));
 307
 308         /* Check e == expected */
 309         success = BN_cmp(expected, e) == 0;
 310  out:
 311         BN_CTX_free(bn_ctx);
 312         if (h != NULL)
 313                 BN_clear_free(h);
 314         BN_clear_free(g_xh);
 315         BN_clear_free(g_r);
 316         BN_clear_free(expected);
 317         return success;
 318 }
 319
 320 /*
 321  * Verify Schnorr signature 'sig' of length 'siglen' against public exponent
 322  * g_x (g^x) under group defined by 'grp_p', 'grp_q' and 'grp_g' using a
 323  * SHA256 hash.
 324  * Signature hash will be salted with 'idlen' bytes from 'id'.
 325  * Returns -1 on failure, 0 on incorrect signature or 1 on matching signature.
 326  */
 327 int
 328 schnorr_verify_buf(const BIGNUM *grp_p, const BIGNUM *grp_q,
 329     const BIGNUM *grp_g,
 330     const BIGNUM *g_x, const u_char *id, u_int idlen,
 331     const u_char *sig, u_int siglen)
 332 {
 333         Buffer b;
 334         int ret = -1;
 335         u_int rlen;
 336         BIGNUM *r, *e;
 337
 338         e = r = NULL;
 339         if ((e = BN_new()) == NULL ||
 340             (r = BN_new()) == NULL) {
 341                 error("%s: BN_new", __func__);
 342                 goto out;
 343         }
 344
 345         /* Extract g^v and r from signature blob */
 346         buffer_init(&b);
 347         buffer_append(&b, sig, siglen);
 348         SCHNORR_DEBUG_BUF((buffer_ptr(&b), buffer_len(&b),
 349             "%s: sigblob", __func__));
 350         buffer_get_bignum2(&b, e);
 351         buffer_get_bignum2(&b, r);
 352         rlen = buffer_len(&b);
 353         buffer_free(&b);
 354         if (rlen != 0) {
 355                 error("%s: remaining bytes in signature %d", __func__, rlen);
 356                 goto out;
 357         }
 358
 359         ret = schnorr_verify(grp_p, grp_q, grp_g, EVP_sha256(),
 360             g_x, id, idlen, r, e);
 361  out:
 362         BN_clear_free(e);
 363         BN_clear_free(r);
 364
 365         return ret;
 366 }
 367
 368 /* Helper functions */
 369
 370 /*
 371  * Generate uniformly distributed random number in range (1, high).
 372  * Return number on success, NULL on failure.
 373  */
 374 BIGNUM *
 375 bn_rand_range_gt_one(const BIGNUM *high)
 376 {
 377         BIGNUM *r, *tmp;
 378         int success = -1;
 379
 380         if ((tmp = BN_new()) == NULL) {
 381                 error("%s: BN_new", __func__);
 382                 return NULL;
 383         }
 384         if ((r = BN_new()) == NULL) {
 385                 error("%s: BN_new failed", __func__);
 386                 goto out;
 387         }
 388         if (BN_set_word(tmp, 2) != 1) {
 389                 error("%s: BN_set_word(tmp, 2)", __func__);
 390                 goto out;
 391         }
 392         if (BN_sub(tmp, high, tmp) == -1) {
 393                 error("%s: BN_sub failed (tmp = high - 2)", __func__);
 394                 goto out;
 395         }
 396         if (BN_rand_range(r, tmp) == -1) {
 397                 error("%s: BN_rand_range failed", __func__);
 398                 goto out;
 399         }
 400         if (BN_set_word(tmp, 2) != 1) {
 401                 error("%s: BN_set_word(tmp, 2)", __func__);
 402                 goto out;
 403         }
 404         if (BN_add(r, r, tmp) == -1) {
 405                 error("%s: BN_add failed (r = r + 2)", __func__);
 406                 goto out;
 407         }
 408         success = 0;
 409  out:
 410         BN_clear_free(tmp);
 411         if (success == 0)
 412                 return r;
 413         BN_clear_free(r);
 414         return NULL;
 415 }
 416
 417 /*
 418  * Hash contents of buffer 'b' with hash 'md'. Returns 0 on success,
 419  * with digest via 'digestp' (caller to free) and length via 'lenp'.
 420  * Returns -1 on failure.
 421  */
 422 int
 423 hash_buffer(const u_char *buf, u_int len, const EVP_MD *md,
 424     u_char **digestp, u_int *lenp)
 425 {
 426         u_char digest[EVP_MAX_MD_SIZE];
 427         u_int digest_len;
 428         EVP_MD_CTX evp_md_ctx;
 429         int success = -1;
 430
 431         EVP_MD_CTX_init(&evp_md_ctx);
 432
 433         if (EVP_DigestInit_ex(&evp_md_ctx, md, NULL) != 1) {
 434                 error("%s: EVP_DigestInit_ex", __func__);
 435                 goto out;
 436         }
 437         if (EVP_DigestUpdate(&evp_md_ctx, buf, len) != 1) {
 438                 error("%s: EVP_DigestUpdate", __func__);
 439                 goto out;
 440         }
 441         if (EVP_DigestFinal_ex(&evp_md_ctx, digest, &digest_len) != 1) {
 442                 error("%s: EVP_DigestFinal_ex", __func__);
 443                 goto out;
 444         }
 445         *digestp = xmalloc(digest_len);
 446         *lenp = digest_len;
 447         memcpy(*digestp, digest, *lenp);
 448         success = 0;
 449  out:
 450         EVP_MD_CTX_cleanup(&evp_md_ctx);
 451         bzero(digest, sizeof(digest));
 452         digest_len = 0;
 453         return success;
 454 }
 455
 456 /* print formatted string followed by bignum */
 457 void
 458 debug3_bn(const BIGNUM *n, const char *fmt, ...)
 459 {
 460         char *out, *h;
 461         va_list args;
 462
 463         out = NULL;
 464         va_start(args, fmt);
 465         vasprintf(&out, fmt, args);
 466         va_end(args);
 467         if (out == NULL)
 468                 fatal("%s: vasprintf failed", __func__);
 469
 470         if (n == NULL)
 471                 debug3("%s(null)", out);
 472         else {
 473                 h = BN_bn2hex(n);
 474                 debug3("%s0x%s", out, h);
 475                 free(h);
 476         }
 477         free(out);
 478 }
 479
 480 /* print formatted string followed by buffer contents in hex */
 481 void
 482 debug3_buf(const u_char *buf, u_int len, const char *fmt, ...)
 483 {
 484         char *out, h[65];
 485         u_int i, j;
 486         va_list args;
 487
 488         out = NULL;
 489         va_start(args, fmt);
 490         vasprintf(&out, fmt, args);
 491         va_end(args);
 492         if (out == NULL)
 493                 fatal("%s: vasprintf failed", __func__);
 494
 495         debug3("%s length %u%s", out, len, buf == NULL ? " (null)" : "");
 496         free(out);
 497         if (buf == NULL)
 498                 return;
 499
 500         *h = '\0';
 501         for (i = j = 0; i < len; i++) {
 502                 snprintf(h + j, sizeof(h) - j, "%02x", buf[i]);
 503                 j += 2;
 504                 if (j >= sizeof(h) - 1 || i == len - 1) {
 505                         debug3("    %s", h);
 506                         *h = '\0';
 507                         j = 0;
 508                 }
 509         }
 510 }
 511
 512 /*
 513  * Construct a MODP group from hex strings p (which must be a safe
 514  * prime) and g, automatically calculating subgroup q as (p / 2)
 515  */
 516 struct modp_group *
 517 modp_group_from_g_and_safe_p(const char *grp_g, const char *grp_p)
 518 {
 519         struct modp_group *ret;
 520
 521         ret = xmalloc(sizeof(*ret));
 522         ret->p = ret->q = ret->g = NULL;
 523         if (BN_hex2bn(&ret->p, grp_p) == 0 ||
 524             BN_hex2bn(&ret->g, grp_g) == 0)
 525                 fatal("%s: BN_hex2bn", __func__);
 526         /* Subgroup order is p/2 (p is a safe prime) */
 527         if ((ret->q = BN_new()) == NULL)
 528                 fatal("%s: BN_new", __func__);
 529         if (BN_rshift1(ret->q, ret->p) != 1)
 530                 fatal("%s: BN_rshift1", __func__);
 531
 532         return ret;
 533 }
 534
 535 void
 536 modp_group_free(struct modp_group *grp)
 537 {
 538         if (grp->g != NULL)
 539                 BN_clear_free(grp->g);
 540         if (grp->p != NULL)
 541                 BN_clear_free(grp->p);
 542         if (grp->q != NULL)
 543                 BN_clear_free(grp->q);
 544         bzero(grp, sizeof(*grp));
 545         xfree(grp);
 546 }
 547
 548 /* main() function for self-test */
 549
 550 #ifdef SCHNORR_MAIN
 551 static void
 552 schnorr_selftest_one(const BIGNUM *grp_p, const BIGNUM *grp_q,
 553     const BIGNUM *grp_g, const BIGNUM *x)
 554 {
 555         BIGNUM *g_x;
 556         u_char *sig;
 557         u_int siglen;
 558         BN_CTX *bn_ctx;
 559
 560         if ((bn_ctx = BN_CTX_new()) == NULL)
 561                 fatal("%s: BN_CTX_new", __func__);
 562         if ((g_x = BN_new()) == NULL)
 563                 fatal("%s: BN_new", __func__);
 564
 565         if (BN_mod_exp(g_x, grp_g, x, grp_p, bn_ctx) == -1)
 566                 fatal("%s: g_x", __func__);
 567         if (schnorr_sign_buf(grp_p, grp_q, grp_g, x, g_x, "junk", 4,
 568             &sig, &siglen))
 569                 fatal("%s: schnorr_sign", __func__);
 570         if (schnorr_verify_buf(grp_p, grp_q, grp_g, g_x, "junk", 4,
 571             sig, siglen) != 1)
 572                 fatal("%s: verify fail", __func__);
 573         if (schnorr_verify_buf(grp_p, grp_q, grp_g, g_x, "JUNK", 4,
 574             sig, siglen) != 0)
 575                 fatal("%s: verify should have failed (bad ID)", __func__);
 576         sig[4] ^= 1;
 577         if (schnorr_verify_buf(grp_p, grp_q, grp_g, g_x, "junk", 4,
 578             sig, siglen) != 0)
 579                 fatal("%s: verify should have failed (bit error)", __func__);
 580         xfree(sig);
 581         BN_free(g_x);
 582         BN_CTX_free(bn_ctx);
 583 }
 584
 585 static void
 586 schnorr_selftest(void)
 587 {
 588         BIGNUM *x;
 589         struct modp_group *grp;
 590         u_int i;
 591         char *hh;
 592
 593         grp = jpake_default_group();
 594         if ((x = BN_new()) == NULL)
 595                 fatal("%s: BN_new", __func__);
 596         SCHNORR_DEBUG_BN((grp->p, "%s: grp->p = ", __func__));
 597         SCHNORR_DEBUG_BN((grp->q, "%s: grp->q = ", __func__));
 598         SCHNORR_DEBUG_BN((grp->g, "%s: grp->g = ", __func__));
 599
 600         /* [1, 20) */
 601         for (i = 1; i < 20; i++) {
 602                 printf("x = %u\n", i);
 603                 fflush(stdout);
 604                 if (BN_set_word(x, i) != 1)
 605                         fatal("%s: set x word", __func__);
 606                 schnorr_selftest_one(grp->p, grp->q, grp->g, x);
 607         }
 608
 609         /* 100 x random [0, p) */
 610         for (i = 0; i < 100; i++) {
 611                 if (BN_rand_range(x, grp->p) != 1)
 612                         fatal("%s: BN_rand_range", __func__);
 613                 hh = BN_bn2hex(x);
 614                 printf("x = (random) 0x%s\n", hh);
 615                 free(hh);
 616                 fflush(stdout);
 617                 schnorr_selftest_one(grp->p, grp->q, grp->g, x);
 618         }
 619
 620         /* [q-20, q) */
 621         if (BN_set_word(x, 20) != 1)
 622                 fatal("%s: BN_set_word (x = 20)", __func__);
 623         if (BN_sub(x, grp->q, x) != 1)
 624                 fatal("%s: BN_sub (q - x)", __func__);
 625         for (i = 0; i < 19; i++) {
 626                 hh = BN_bn2hex(x);
 627                 printf("x = (q - %d) 0x%s\n", 20 - i, hh);
 628                 free(hh);
 629                 fflush(stdout);
 630                 schnorr_selftest_one(grp->p, grp->q, grp->g, x);
 631                 if (BN_add(x, x, BN_value_one()) != 1)
 632                         fatal("%s: BN_add (x + 1)", __func__);
 633         }
 634         BN_free(x);
 635 }
 636
 637 int
 638 main(int argc, char **argv)
 639 {
 640         log_init(argv[0], SYSLOG_LEVEL_DEBUG3, SYSLOG_FACILITY_USER, 1);
 641
 642         schnorr_selftest();
 643         return 0;
 644 }
 645 #endif
 646