crypto/openssl-0.9.7d/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 #ifdef FLAT_INC
  59 #include "e_os.h"
  60 #else
  61 #include "../e_os.h"
  62 #endif
  63 #include <string.h>
  64 #include <time.h>
  65
  66
  67 #ifdef OPENSSL_NO_EC
  68 int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
  69 #else
  70
  71
  72 #include <openssl/ec.h>
  73 #ifndef OPENSSL_NO_ENGINE
  74 #include <openssl/engine.h>
  75 #endif
  76 #include <openssl/err.h>
  77
  78 #define ABORT do { \
  79         fflush(stdout); \
  80         fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
  81         ERR_print_errors_fp(stderr); \
  82         EXIT(1); \
  83 } while (0)
  84
  85 #if 0
  86 static void timings(EC_GROUP *group, int multi, BN_CTX *ctx)
  87         {
  88         clock_t clck;
  89         int i, j;
  90         BIGNUM *s, *s0;
  91         EC_POINT *P;
  92
  93         s = BN_new();
  94         s0 = BN_new();
  95         if (s == NULL || s0 == NULL) ABORT;
  96
  97         if (!EC_GROUP_get_curve_GFp(group, s, NULL, NULL, ctx)) ABORT;
  98         fprintf(stdout, "Timings for %d bit prime, ", (int)BN_num_bits(s));
  99         if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
 100         fprintf(stdout, "%d bit scalars ", (int)BN_num_bits(s));
 101         fflush(stdout);
 102
 103         P = EC_POINT_new(group);
 104         if (P == NULL) ABORT;
 105         EC_POINT_copy(P, EC_GROUP_get0_generator(group));
 106
 107         clck = clock();
 108         for (i = 0; i < 10; i++)
 109                 {
 110                 if (!BN_pseudo_rand(s, BN_num_bits(s), 0, 0)) ABORT;
 111                 if (multi)
 112                         {
 113                         if (!BN_pseudo_rand(s0, BN_num_bits(s), 0, 0)) ABORT;
 114                         }
 115                 for (j = 0; j < 10; j++)
 116                         {
 117                         if (!EC_POINT_mul(group, P, s, multi ? P : NULL, multi ? s0 : NULL, ctx)) ABORT;
 118                         }
 119                 fprintf(stdout, ".");
 120                 fflush(stdout);
 121                 }
 122         fprintf(stdout, "\n");
 123
 124         clck = clock() - clck;
 125
 126 #ifdef CLOCKS_PER_SEC
 127         /* "To determine the time in seconds, the value returned
 128          * by the clock function should be divided by the value
 129          * of the macro CLOCKS_PER_SEC."
 130          *                                       -- ISO/IEC 9899 */
 131 #       define UNIT "s"
 132 #else
 133         /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
 134          *                            -- cc on NeXTstep/OpenStep */
 135 #       define UNIT "units"
 136 #       define CLOCKS_PER_SEC 1
 137 #endif
 138
 139         fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
 140                 multi ? "s*P+t*Q operations" : "point multiplications",
 141                 (double)clck/CLOCKS_PER_SEC);
 142         fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
 143
 144         EC_POINT_free(P);
 145         BN_free(s);
 146         BN_free(s0);
 147         }
 148 #endif
 149
 150 int main(int argc, char *argv[])
 151         {
 152         BN_CTX *ctx = NULL;
 153         BIGNUM *p, *a, *b;
 154         EC_GROUP *group;
 155         EC_GROUP *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
 156         EC_POINT *P, *Q, *R;
 157         BIGNUM *x, *y, *z;
 158         unsigned char buf[100];
 159         size_t i, len;
 160         int k;
 161
 162         /* enable memory leak checking unless explicitly disabled */
 163         if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
 164                 {
 165                 CRYPTO_malloc_debug_init();
 166                 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
 167                 }
 168         else
 169                 {
 170                 /* OPENSSL_DEBUG_MEMORY=off */
 171                 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
 172                 }
 173         CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
 174         ERR_load_crypto_strings();
 175
 176 #if 1 /* optional */
 177         ctx = BN_CTX_new();
 178         if (!ctx) ABORT;
 179 #endif
 180
 181         p = BN_new();
 182         a = BN_new();
 183         b = BN_new();
 184         if (!p || !a || !b) ABORT;
 185
 186         if (!BN_hex2bn(&p, "17")) ABORT;
 187         if (!BN_hex2bn(&a, "1")) ABORT;
 188         if (!BN_hex2bn(&b, "1")) ABORT;
 189
 190         group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
 191                                                      * so that the library gets to choose the EC_METHOD */
 192         if (!group) ABORT;
 193
 194         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 195
 196         {
 197                 EC_GROUP *tmp;
 198                 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
 199                 if (!tmp) ABORT;
 200                 if (!EC_GROUP_copy(tmp, group));
 201                 EC_GROUP_free(group);
 202                 group = tmp;
 203         }
 204
 205         if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
 206
 207         fprintf(stdout, "Curve defined by Weierstrass equation\n     y^2 = x^3 + a*x + b  (mod 0x");
 208         BN_print_fp(stdout, p);
 209         fprintf(stdout, ")\n     a = 0x");
 210         BN_print_fp(stdout, a);
 211         fprintf(stdout, "\n     b = 0x");
 212         BN_print_fp(stdout, b);
 213         fprintf(stdout, "\n");
 214
 215         P = EC_POINT_new(group);
 216         Q = EC_POINT_new(group);
 217         R = EC_POINT_new(group);
 218         if (!P || !Q || !R) ABORT;
 219
 220         if (!EC_POINT_set_to_infinity(group, P)) ABORT;
 221         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 222
 223         buf[0] = 0;
 224         if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
 225
 226         if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 227         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 228
 229         x = BN_new();
 230         y = BN_new();
 231         z = BN_new();
 232         if (!x || !y || !z) ABORT;
 233
 234         if (!BN_hex2bn(&x, "D")) ABORT;
 235         if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
 236         if (!EC_POINT_is_on_curve(group, Q, ctx))
 237                 {
 238                 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
 239                 fprintf(stderr, "Point is not on curve: x = 0x");
 240                 BN_print_fp(stderr, x);
 241                 fprintf(stderr, ", y = 0x");
 242                 BN_print_fp(stderr, y);
 243                 fprintf(stderr, "\n");
 244                 ABORT;
 245                 }
 246
 247         fprintf(stdout, "A cyclic subgroup:\n");
 248         k = 100;
 249         do
 250                 {
 251                 if (k-- == 0) ABORT;
 252
 253                 if (EC_POINT_is_at_infinity(group, P))
 254                         fprintf(stdout, "     point at infinity\n");
 255                 else
 256                         {
 257                         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 258
 259                         fprintf(stdout, "     x = 0x");
 260                         BN_print_fp(stdout, x);
 261                         fprintf(stdout, ", y = 0x");
 262                         BN_print_fp(stdout, y);
 263                         fprintf(stdout, "\n");
 264                         }
 265
 266                 if (!EC_POINT_copy(R, P)) ABORT;
 267                 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 268
 269 #if 0 /* optional */
 270                 {
 271                         EC_POINT *points[3];
 272
 273                         points[0] = R;
 274                         points[1] = Q;
 275                         points[2] = P;
 276                         if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
 277                 }
 278 #endif
 279
 280                 }
 281         while (!EC_POINT_is_at_infinity(group, P));
 282
 283         if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
 284         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 285
 286         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, 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, "Generator as octect string, compressed form:\n     ");
 291         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 292
 293         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, 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, uncompressed form:\n     ");
 298         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 299
 300         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
 301         if (len == 0) ABORT;
 302         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 303         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 304         fprintf(stdout, "\nGenerator as octect string, hybrid form:\n     ");
 305         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 306
 307         if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
 308         fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n     X = 0x");
 309         BN_print_fp(stdout, x);
 310         fprintf(stdout, ", Y = 0x");
 311         BN_print_fp(stdout, y);
 312         fprintf(stdout, ", Z = 0x");
 313         BN_print_fp(stdout, z);
 314         fprintf(stdout, "\n");
 315
 316         if (!EC_POINT_invert(group, P, ctx)) ABORT;
 317         if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
 318
 319
 320         /* Curve P-192 (FIPS PUB 186-2, App. 6) */
 321
 322         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
 323         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 324         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
 325         if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
 326         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 327
 328         if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
 329         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 330         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 331         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
 332         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 333
 334         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 335         fprintf(stdout, "\nNIST curve P-192 -- Generator:\n     x = 0x");
 336         BN_print_fp(stdout, x);
 337         fprintf(stdout, "\n     y = 0x");
 338         BN_print_fp(stdout, y);
 339         fprintf(stdout, "\n");
 340         /* G_y value taken from the standard: */
 341         if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
 342         if (0 != BN_cmp(y, z)) ABORT;
 343
 344         fprintf(stdout, "verify group order ...");
 345         fflush(stdout);
 346         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 347         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 348         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 349         fprintf(stdout, ".");
 350         fflush(stdout);
 351         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 352         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 353         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 354         fprintf(stdout, " ok\n");
 355
 356         if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 357         if (!EC_GROUP_copy(P_192, group)) ABORT;
 358
 359
 360         /* Curve P-224 (FIPS PUB 186-2, App. 6) */
 361
 362         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
 363         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 364         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
 365         if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
 366         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 367
 368         if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
 369         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
 370         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 371         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
 372         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 373
 374         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 375         fprintf(stdout, "\nNIST curve P-224 -- Generator:\n     x = 0x");
 376         BN_print_fp(stdout, x);
 377         fprintf(stdout, "\n     y = 0x");
 378         BN_print_fp(stdout, y);
 379         fprintf(stdout, "\n");
 380         /* G_y value taken from the standard: */
 381         if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
 382         if (0 != BN_cmp(y, z)) ABORT;
 383
 384         fprintf(stdout, "verify group order ...");
 385         fflush(stdout);
 386         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 387         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 388         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 389         fprintf(stdout, ".");
 390         fflush(stdout);
 391         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 392         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 393         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 394         fprintf(stdout, " ok\n");
 395
 396         if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 397         if (!EC_GROUP_copy(P_224, group)) ABORT;
 398
 399
 400         /* Curve P-256 (FIPS PUB 186-2, App. 6) */
 401
 402         if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
 403         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 404         if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
 405         if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
 406         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 407
 408         if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
 409         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 410         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 411         if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
 412                 "84F3B9CAC2FC632551")) ABORT;
 413         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 414
 415         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 416         fprintf(stdout, "\nNIST curve P-256 -- Generator:\n     x = 0x");
 417         BN_print_fp(stdout, x);
 418         fprintf(stdout, "\n     y = 0x");
 419         BN_print_fp(stdout, y);
 420         fprintf(stdout, "\n");
 421         /* G_y value taken from the standard: */
 422         if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
 423         if (0 != BN_cmp(y, z)) ABORT;
 424
 425         fprintf(stdout, "verify group order ...");
 426         fflush(stdout);
 427         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 428         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 429         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 430         fprintf(stdout, ".");
 431         fflush(stdout);
 432         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 433         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 434         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 435         fprintf(stdout, " ok\n");
 436
 437         if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 438         if (!EC_GROUP_copy(P_256, group)) ABORT;
 439
 440
 441         /* Curve P-384 (FIPS PUB 186-2, App. 6) */
 442
 443         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 444                 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
 445         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 446         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 447                 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
 448         if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
 449                 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
 450         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 451
 452         if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
 453                 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
 454         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 455         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 456         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 457                 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
 458         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 459
 460         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 461         fprintf(stdout, "\nNIST curve P-384 -- Generator:\n     x = 0x");
 462         BN_print_fp(stdout, x);
 463         fprintf(stdout, "\n     y = 0x");
 464         BN_print_fp(stdout, y);
 465         fprintf(stdout, "\n");
 466         /* G_y value taken from the standard: */
 467         if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
 468                 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
 469         if (0 != BN_cmp(y, z)) ABORT;
 470
 471         fprintf(stdout, "verify group order ...");
 472         fflush(stdout);
 473         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 474         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 475         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 476         fprintf(stdout, ".");
 477         fflush(stdout);
 478         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 479         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 480         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 481         fprintf(stdout, " ok\n");
 482
 483         if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 484         if (!EC_GROUP_copy(P_384, group)) ABORT;
 485
 486
 487         /* Curve P-521 (FIPS PUB 186-2, App. 6) */
 488
 489         if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 490                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 491                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
 492         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 493         if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 494                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 495                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
 496         if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
 497                 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
 498                 "DF883D2C34F1EF451FD46B503F00")) ABORT;
 499         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 500
 501         if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
 502                 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
 503                 "3C1856A429BF97E7E31C2E5BD66")) ABORT;
 504         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
 505         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 506         if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 507                 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
 508                 "C9B8899C47AEBB6FB71E91386409")) ABORT;
 509         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 510
 511         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 512         fprintf(stdout, "\nNIST curve P-521 -- Generator:\n     x = 0x");
 513         BN_print_fp(stdout, x);
 514         fprintf(stdout, "\n     y = 0x");
 515         BN_print_fp(stdout, y);
 516         fprintf(stdout, "\n");
 517         /* G_y value taken from the standard: */
 518         if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
 519                 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
 520                 "7086A272C24088BE94769FD16650")) ABORT;
 521         if (0 != BN_cmp(y, z)) ABORT;
 522
 523         fprintf(stdout, "verify group order ...");
 524         fflush(stdout);
 525         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 526         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 527         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 528         fprintf(stdout, ".");
 529         fflush(stdout);
 530         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 531         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 532         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 533         fprintf(stdout, " ok\n");
 534
 535         if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 536         if (!EC_GROUP_copy(P_521, group)) ABORT;
 537
 538
 539         /* more tests using the last curve */
 540
 541         if (!EC_POINT_copy(Q, P)) ABORT;
 542         if (EC_POINT_is_at_infinity(group, Q)) ABORT;
 543         if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
 544         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 545         if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
 546
 547         if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
 548         if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
 549         if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
 550
 551         {
 552                 const EC_POINT *points[3];
 553                 const BIGNUM *scalars[3];
 554
 555                 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
 556                 points[0] = Q;
 557                 points[1] = Q;
 558                 points[2] = Q;
 559
 560                 if (!BN_add(y, z, BN_value_one())) ABORT;
 561                 if (BN_is_odd(y)) ABORT;
 562                 if (!BN_rshift1(y, y)) ABORT;
 563                 scalars[0] = y; /* (group order + 1)/2,  so  y*Q + y*Q = Q */
 564                 scalars[1] = y;
 565
 566                 fprintf(stdout, "combined multiplication ...");
 567                 fflush(stdout);
 568
 569                 /* z is still the group order */
 570                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
 571                 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
 572                 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
 573                 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
 574
 575                 fprintf(stdout, ".");
 576                 fflush(stdout);
 577
 578                 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
 579                 if (!BN_add(z, z, y)) ABORT;
 580                 z->neg = 1;
 581                 scalars[0] = y;
 582                 scalars[1] = z; /* z = -(order + y) */
 583
 584                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
 585                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 586
 587                 fprintf(stdout, ".");
 588                 fflush(stdout);
 589
 590                 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
 591                 if (!BN_add(z, x, y)) ABORT;
 592                 z->neg = 1;
 593                 scalars[0] = x;
 594                 scalars[1] = y;
 595                 scalars[2] = z; /* z = -(x+y) */
 596
 597                 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
 598                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 599
 600                 fprintf(stdout, " ok\n\n");
 601         }
 602
 603
 604 #if 0
 605         timings(P_192, 0, ctx);
 606         timings(P_192, 1, ctx);
 607         timings(P_224, 0, ctx);
 608         timings(P_224, 1, ctx);
 609         timings(P_256, 0, ctx);
 610         timings(P_256, 1, ctx);
 611         timings(P_384, 0, ctx);
 612         timings(P_384, 1, ctx);
 613         timings(P_521, 0, ctx);
 614         timings(P_521, 1, ctx);
 615 #endif
 616
 617
 618         if (ctx)
 619                 BN_CTX_free(ctx);
 620         BN_free(p); BN_free(a); BN_free(b);
 621         EC_GROUP_free(group);
 622         EC_POINT_free(P);
 623         EC_POINT_free(Q);
 624         EC_POINT_free(R);
 625         BN_free(x); BN_free(y); BN_free(z);
 626
 627         if (P_192) EC_GROUP_free(P_192);
 628         if (P_224) EC_GROUP_free(P_224);
 629         if (P_256) EC_GROUP_free(P_256);
 630         if (P_384) EC_GROUP_free(P_384);
 631         if (P_521) EC_GROUP_free(P_521);
 632
 633 #ifndef OPENSSL_NO_ENGINE
 634         ENGINE_cleanup();
 635 #endif
 636         CRYPTO_cleanup_all_ex_data();
 637         ERR_free_strings();
 638         ERR_remove_state(0);
 639         CRYPTO_mem_leaks_fp(stderr);
 640
 641         return 0;
 642         }
 643 #endif