crypto/ec/ectest.c

   1 /* crypto/ec/ectest.c */
   2 /* ====================================================================
   3  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
   4  *
   5  * Redistribution and use in source and binary forms, with or without
   6  * modification, are permitted provided that the following conditions
   7  * are met:
   8  *
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  *
  12  * 2. Redistributions in binary form must reproduce the above copyright
  13  *    notice, this list of conditions and the following disclaimer in
  14  *    the documentation and/or other materials provided with the
  15  *    distribution.
  16  *
  17  * 3. All advertising materials mentioning features or use of this
  18  *    software must display the following acknowledgment:
  19  *    "This product includes software developed by the OpenSSL Project
  20  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  21  *
  22  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  23  *    endorse or promote products derived from this software without
  24  *    prior written permission. For written permission, please contact
  25  *    openssl-core@openssl.org.
  26  *
  27  * 5. Products derived from this software may not be called "OpenSSL"
  28  *    nor may "OpenSSL" appear in their names without prior written
  29  *    permission of the OpenSSL Project.
  30  *
  31  * 6. Redistributions of any form whatsoever must retain the following
  32  *    acknowledgment:
  33  *    "This product includes software developed by the OpenSSL Project
  34  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  35  *
  36  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  37  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  38  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  39  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  40  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  41  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  42  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  43  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  44  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  45  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  46  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  47  * OF THE POSSIBILITY OF SUCH DAMAGE.
  48  * ====================================================================
  49  *
  50  * This product includes cryptographic software written by Eric Young
  51  * (eay@cryptsoft.com).  This product includes software written by Tim
  52  * Hudson (tjh@cryptsoft.com).
  53  *
  54  */
  55
  56 #include <stdio.h>
  57 #include <stdlib.h>
  58 #include <string.h>
  59 #include <time.h>
  60
  61
  62 #ifdef OPENSSL_NO_EC
  63 int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
  64 #else
  65
  66
  67 #include <openssl/ec.h>
  68 #include <openssl/engine.h>
  69 #include <openssl/err.h>
  70
  71 #define ABORT do { \
  72         fflush(stdout); \
  73         fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
  74         ERR_print_errors_fp(stderr); \
  75         exit(1); \
  76 } while (0)
  77
  78 #if 0
  79 static void timings(EC_GROUP *group, int multi, BN_CTX *ctx)
  80         {
  81         clock_t clck;
  82         int i, j;
  83         BIGNUM *s, *s0;
  84         EC_POINT *P;
  85
  86         s = BN_new();
  87         s0 = BN_new();
  88         if (s == NULL || s0 == NULL) ABORT;
  89
  90         if (!EC_GROUP_get_curve_GFp(group, s, NULL, NULL, ctx)) ABORT;
  91         fprintf(stdout, "Timings for %d bit prime, ", (int)BN_num_bits(s));
  92         if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
  93         fprintf(stdout, "%d bit scalars ", (int)BN_num_bits(s));
  94         fflush(stdout);
  95
  96         P = EC_POINT_new(group);
  97         if (P == NULL) ABORT;
  98         EC_POINT_copy(P, EC_GROUP_get0_generator(group));
  99
 100         clck = clock();
 101         for (i = 0; i < 10; i++)
 102                 {
 103                 if (!BN_pseudo_rand(s, BN_num_bits(s), 0, 0)) ABORT;
 104                 if (multi)
 105                         {
 106                         if (!BN_pseudo_rand(s0, BN_num_bits(s), 0, 0)) ABORT;
 107                         }
 108                 for (j = 0; j < 10; j++)
 109                         {
 110                         if (!EC_POINT_mul(group, P, s, multi ? P : NULL, multi ? s0 : NULL, ctx)) ABORT;
 111                         }
 112                 fprintf(stdout, ".");
 113                 fflush(stdout);
 114                 }
 115         fprintf(stdout, "\n");
 116
 117         clck = clock() - clck;
 118
 119 #ifdef CLOCKS_PER_SEC
 120         /* "To determine the time in seconds, the value returned
 121          * by the clock function should be divided by the value
 122          * of the macro CLOCKS_PER_SEC."
 123          *                                       -- ISO/IEC 9899 */
 124 #       define UNIT "s"
 125 #else
 126         /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
 127          *                            -- cc on NeXTstep/OpenStep */
 128 #       define UNIT "units"
 129 #       define CLOCKS_PER_SEC 1
 130 #endif
 131
 132         fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
 133                 multi ? "s*P+t*Q operations" : "point multiplications",
 134                 (double)clck/CLOCKS_PER_SEC);
 135         fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
 136
 137         EC_POINT_free(P);
 138         BN_free(s);
 139         BN_free(s0);
 140         }
 141 #endif
 142
 143 int main(int argc, char *argv[])
 144         {
 145         BN_CTX *ctx = NULL;
 146         BIGNUM *p, *a, *b;
 147         EC_GROUP *group;
 148         EC_GROUP *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
 149         EC_POINT *P, *Q, *R;
 150         BIGNUM *x, *y, *z;
 151         unsigned char buf[100];
 152         size_t i, len;
 153         int k;
 154
 155         /* enable memory leak checking unless explicitly disabled */
 156         if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
 157                 {
 158                 CRYPTO_malloc_debug_init();
 159                 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
 160                 }
 161         else
 162                 {
 163                 /* OPENSSL_DEBUG_MEMORY=off */
 164                 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
 165                 }
 166         CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
 167         ERR_load_crypto_strings();
 168
 169 #if 1 /* optional */
 170         ctx = BN_CTX_new();
 171         if (!ctx) ABORT;
 172 #endif
 173
 174         p = BN_new();
 175         a = BN_new();
 176         b = BN_new();
 177         if (!p || !a || !b) ABORT;
 178
 179         if (!BN_hex2bn(&p, "17")) ABORT;
 180         if (!BN_hex2bn(&a, "1")) ABORT;
 181         if (!BN_hex2bn(&b, "1")) ABORT;
 182
 183         group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
 184                                                      * so that the library gets to choose the EC_METHOD */
 185         if (!group) ABORT;
 186
 187         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 188
 189         {
 190                 EC_GROUP *tmp;
 191                 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
 192                 if (!tmp) ABORT;
 193                 if (!EC_GROUP_copy(tmp, group));
 194                 EC_GROUP_free(group);
 195                 group = tmp;
 196         }
 197
 198         if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
 199
 200         fprintf(stdout, "Curve defined by Weierstrass equation\n     y^2 = x^3 + a*x + b  (mod 0x");
 201         BN_print_fp(stdout, p);
 202         fprintf(stdout, ")\n     a = 0x");
 203         BN_print_fp(stdout, a);
 204         fprintf(stdout, "\n     b = 0x");
 205         BN_print_fp(stdout, b);
 206         fprintf(stdout, "\n");
 207
 208         P = EC_POINT_new(group);
 209         Q = EC_POINT_new(group);
 210         R = EC_POINT_new(group);
 211         if (!P || !Q || !R) ABORT;
 212
 213         if (!EC_POINT_set_to_infinity(group, P)) ABORT;
 214         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 215
 216         buf[0] = 0;
 217         if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
 218
 219         if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 220         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 221
 222         x = BN_new();
 223         y = BN_new();
 224         z = BN_new();
 225         if (!x || !y || !z) ABORT;
 226
 227         if (!BN_hex2bn(&x, "D")) ABORT;
 228         if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
 229         if (!EC_POINT_is_on_curve(group, Q, ctx))
 230                 {
 231                 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
 232                 fprintf(stderr, "Point is not on curve: x = 0x");
 233                 BN_print_fp(stderr, x);
 234                 fprintf(stderr, ", y = 0x");
 235                 BN_print_fp(stderr, y);
 236                 fprintf(stderr, "\n");
 237                 ABORT;
 238                 }
 239
 240         fprintf(stdout, "A cyclic subgroup:\n");
 241         k = 100;
 242         do
 243                 {
 244                 if (k-- == 0) ABORT;
 245
 246                 if (EC_POINT_is_at_infinity(group, P))
 247                         fprintf(stdout, "     point at infinity\n");
 248                 else
 249                         {
 250                         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 251
 252                         fprintf(stdout, "     x = 0x");
 253                         BN_print_fp(stdout, x);
 254                         fprintf(stdout, ", y = 0x");
 255                         BN_print_fp(stdout, y);
 256                         fprintf(stdout, "\n");
 257                         }
 258
 259                 if (!EC_POINT_copy(R, P)) ABORT;
 260                 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 261
 262 #if 0 /* optional */
 263                 {
 264                         EC_POINT *points[3];
 265
 266                         points[0] = R;
 267                         points[1] = Q;
 268                         points[2] = P;
 269                         if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
 270                 }
 271 #endif
 272
 273                 }
 274         while (!EC_POINT_is_at_infinity(group, P));
 275
 276         if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
 277         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 278
 279         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
 280         if (len == 0) ABORT;
 281         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 282         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 283         fprintf(stdout, "Generator as octect string, compressed form:\n     ");
 284         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 285
 286         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
 287         if (len == 0) ABORT;
 288         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 289         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 290         fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n     ");
 291         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 292
 293         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
 294         if (len == 0) ABORT;
 295         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 296         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 297         fprintf(stdout, "\nGenerator as octect string, hybrid form:\n     ");
 298         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 299
 300         if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
 301         fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n     X = 0x");
 302         BN_print_fp(stdout, x);
 303         fprintf(stdout, ", Y = 0x");
 304         BN_print_fp(stdout, y);
 305         fprintf(stdout, ", Z = 0x");
 306         BN_print_fp(stdout, z);
 307         fprintf(stdout, "\n");
 308
 309         if (!EC_POINT_invert(group, P, ctx)) ABORT;
 310         if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
 311
 312
 313         /* Curve P-192 (FIPS PUB 186-2, App. 6) */
 314
 315         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
 316         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 317         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
 318         if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
 319         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 320
 321         if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
 322         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 323         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 324         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
 325         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 326
 327         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 328         fprintf(stdout, "\nNIST curve P-192 -- Generator:\n     x = 0x");
 329         BN_print_fp(stdout, x);
 330         fprintf(stdout, "\n     y = 0x");
 331         BN_print_fp(stdout, y);
 332         fprintf(stdout, "\n");
 333         /* G_y value taken from the standard: */
 334         if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
 335         if (0 != BN_cmp(y, z)) ABORT;
 336
 337         fprintf(stdout, "verify group order ...");
 338         fflush(stdout);
 339         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 340         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 341         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 342         fprintf(stdout, ".");
 343         fflush(stdout);
 344         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 345         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 346         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 347         fprintf(stdout, " ok\n");
 348
 349         if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 350         if (!EC_GROUP_copy(P_192, group)) ABORT;
 351
 352
 353         /* Curve P-224 (FIPS PUB 186-2, App. 6) */
 354
 355         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
 356         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 357         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
 358         if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
 359         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 360
 361         if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
 362         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
 363         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 364         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
 365         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 366
 367         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 368         fprintf(stdout, "\nNIST curve P-224 -- Generator:\n     x = 0x");
 369         BN_print_fp(stdout, x);
 370         fprintf(stdout, "\n     y = 0x");
 371         BN_print_fp(stdout, y);
 372         fprintf(stdout, "\n");
 373         /* G_y value taken from the standard: */
 374         if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
 375         if (0 != BN_cmp(y, z)) ABORT;
 376
 377         fprintf(stdout, "verify group order ...");
 378         fflush(stdout);
 379         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 380         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 381         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 382         fprintf(stdout, ".");
 383         fflush(stdout);
 384         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 385         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 386         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 387         fprintf(stdout, " ok\n");
 388
 389         if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 390         if (!EC_GROUP_copy(P_224, group)) ABORT;
 391
 392
 393         /* Curve P-256 (FIPS PUB 186-2, App. 6) */
 394
 395         if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
 396         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 397         if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
 398         if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
 399         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 400
 401         if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
 402         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 403         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 404         if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
 405                 "84F3B9CAC2FC632551")) ABORT;
 406         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 407
 408         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 409         fprintf(stdout, "\nNIST curve P-256 -- Generator:\n     x = 0x");
 410         BN_print_fp(stdout, x);
 411         fprintf(stdout, "\n     y = 0x");
 412         BN_print_fp(stdout, y);
 413         fprintf(stdout, "\n");
 414         /* G_y value taken from the standard: */
 415         if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
 416         if (0 != BN_cmp(y, z)) ABORT;
 417
 418         fprintf(stdout, "verify group order ...");
 419         fflush(stdout);
 420         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 421         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 422         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 423         fprintf(stdout, ".");
 424         fflush(stdout);
 425         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 426         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 427         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 428         fprintf(stdout, " ok\n");
 429
 430         if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 431         if (!EC_GROUP_copy(P_256, group)) ABORT;
 432
 433
 434         /* Curve P-384 (FIPS PUB 186-2, App. 6) */
 435
 436         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 437                 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
 438         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 439         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 440                 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
 441         if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
 442                 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
 443         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 444
 445         if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
 446                 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
 447         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 448         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 449         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 450                 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
 451         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 452
 453         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 454         fprintf(stdout, "\nNIST curve P-384 -- Generator:\n     x = 0x");
 455         BN_print_fp(stdout, x);
 456         fprintf(stdout, "\n     y = 0x");
 457         BN_print_fp(stdout, y);
 458         fprintf(stdout, "\n");
 459         /* G_y value taken from the standard: */
 460         if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
 461                 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
 462         if (0 != BN_cmp(y, z)) ABORT;
 463
 464         fprintf(stdout, "verify group order ...");
 465         fflush(stdout);
 466         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 467         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 468         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 469         fprintf(stdout, ".");
 470         fflush(stdout);
 471         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 472         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 473         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 474         fprintf(stdout, " ok\n");
 475
 476         if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 477         if (!EC_GROUP_copy(P_384, group)) ABORT;
 478
 479
 480         /* Curve P-521 (FIPS PUB 186-2, App. 6) */
 481
 482         if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 483                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 484                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
 485         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 486         if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 487                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 488                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
 489         if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
 490                 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
 491                 "DF883D2C34F1EF451FD46B503F00")) ABORT;
 492         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 493
 494         if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
 495                 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
 496                 "3C1856A429BF97E7E31C2E5BD66")) ABORT;
 497         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
 498         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 499         if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 500                 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
 501                 "C9B8899C47AEBB6FB71E91386409")) ABORT;
 502         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 503
 504         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 505         fprintf(stdout, "\nNIST curve P-521 -- Generator:\n     x = 0x");
 506         BN_print_fp(stdout, x);
 507         fprintf(stdout, "\n     y = 0x");
 508         BN_print_fp(stdout, y);
 509         fprintf(stdout, "\n");
 510         /* G_y value taken from the standard: */
 511         if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
 512                 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
 513                 "7086A272C24088BE94769FD16650")) ABORT;
 514         if (0 != BN_cmp(y, z)) ABORT;
 515
 516         fprintf(stdout, "verify group order ...");
 517         fflush(stdout);
 518         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 519         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 520         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 521         fprintf(stdout, ".");
 522         fflush(stdout);
 523         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 524         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 525         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 526         fprintf(stdout, " ok\n");
 527
 528         if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 529         if (!EC_GROUP_copy(P_521, group)) ABORT;
 530
 531
 532         /* more tests using the last curve */
 533
 534         if (!EC_POINT_copy(Q, P)) ABORT;
 535         if (EC_POINT_is_at_infinity(group, Q)) ABORT;
 536         if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
 537         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 538         if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
 539
 540         if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
 541         if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
 542         if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
 543
 544         {
 545                 const EC_POINT *points[3];
 546                 const BIGNUM *scalars[3];
 547
 548                 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
 549                 points[0] = Q;
 550                 points[1] = Q;
 551                 points[2] = Q;
 552
 553                 if (!BN_add(y, z, BN_value_one())) ABORT;
 554                 if (BN_is_odd(y)) ABORT;
 555                 if (!BN_rshift1(y, y)) ABORT;
 556                 scalars[0] = y; /* (group order + 1)/2,  so  y*Q + y*Q = Q */
 557                 scalars[1] = y;
 558
 559                 fprintf(stdout, "combined multiplication ...");
 560                 fflush(stdout);
 561
 562                 /* z is still the group order */
 563                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
 564                 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
 565                 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
 566                 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
 567
 568                 fprintf(stdout, ".");
 569                 fflush(stdout);
 570
 571                 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
 572                 if (!BN_add(z, z, y)) ABORT;
 573                 z->neg = 1;
 574                 scalars[0] = y;
 575                 scalars[1] = z; /* z = -(order + y) */
 576
 577                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
 578                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 579
 580                 fprintf(stdout, ".");
 581                 fflush(stdout);
 582
 583                 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
 584                 if (!BN_add(z, x, y)) ABORT;
 585                 z->neg = 1;
 586                 scalars[0] = x;
 587                 scalars[1] = y;
 588                 scalars[2] = z; /* z = -(x+y) */
 589
 590                 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
 591                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 592
 593                 fprintf(stdout, " ok\n\n");
 594         }
 595
 596
 597 #if 0
 598         timings(P_192, 0, ctx);
 599         timings(P_192, 1, ctx);
 600         timings(P_224, 0, ctx);
 601         timings(P_224, 1, ctx);
 602         timings(P_256, 0, ctx);
 603         timings(P_256, 1, ctx);
 604         timings(P_384, 0, ctx);
 605         timings(P_384, 1, ctx);
 606         timings(P_521, 0, ctx);
 607         timings(P_521, 1, ctx);
 608 #endif
 609
 610
 611         if (ctx)
 612                 BN_CTX_free(ctx);
 613         BN_free(p); BN_free(a); BN_free(b);
 614         EC_GROUP_free(group);
 615         EC_POINT_free(P);
 616         EC_POINT_free(Q);
 617         EC_POINT_free(R);
 618         BN_free(x); BN_free(y); BN_free(z);
 619
 620         if (P_192) EC_GROUP_free(P_192);
 621         if (P_224) EC_GROUP_free(P_224);
 622         if (P_256) EC_GROUP_free(P_256);
 623         if (P_384) EC_GROUP_free(P_384);
 624         if (P_521) EC_GROUP_free(P_521);
 625
 626         ENGINE_cleanup();
 627         CRYPTO_cleanup_all_ex_data();
 628         ERR_free_strings();
 629         ERR_remove_state(0);
 630         CRYPTO_mem_leaks_fp(stderr);
 631
 632         return 0;
 633         }
 634 #endif