crypto/ec/ectest.c

   1 /* crypto/ec/ectest.c */
   2 /*
   3  * Originally written by Bodo Moeller for the OpenSSL project.
   4  */
   5 /* ====================================================================
   6  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
   7  *
   8  * Redistribution and use in source and binary forms, with or without
   9  * modification, are permitted provided that the following conditions
  10  * are met:
  11  *
  12  * 1. Redistributions of source code must retain the above copyright
  13  *    notice, this list of conditions and the following disclaimer.
  14  *
  15  * 2. Redistributions in binary form must reproduce the above copyright
  16  *    notice, this list of conditions and the following disclaimer in
  17  *    the documentation and/or other materials provided with the
  18  *    distribution.
  19  *
  20  * 3. All advertising materials mentioning features or use of this
  21  *    software must display the following acknowledgment:
  22  *    "This product includes software developed by the OpenSSL Project
  23  *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  24  *
  25  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  26  *    endorse or promote products derived from this software without
  27  *    prior written permission. For written permission, please contact
  28  *    openssl-core@openssl.org.
  29  *
  30  * 5. Products derived from this software may not be called "OpenSSL"
  31  *    nor may "OpenSSL" appear in their names without prior written
  32  *    permission of the OpenSSL Project.
  33  *
  34  * 6. Redistributions of any form whatsoever must retain the following
  35  *    acknowledgment:
  36  *    "This product includes software developed by the OpenSSL Project
  37  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  38  *
  39  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  40  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  41  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  42  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  43  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  44  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  45  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  46  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  47  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  48  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  49  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  50  * OF THE POSSIBILITY OF SUCH DAMAGE.
  51  * ====================================================================
  52  *
  53  * This product includes cryptographic software written by Eric Young
  54  * (eay@cryptsoft.com).  This product includes software written by Tim
  55  * Hudson (tjh@cryptsoft.com).
  56  *
  57  */
  58 /* ====================================================================
  59  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  60  *
  61  * Portions of the attached software ("Contribution") are developed by
  62  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
  63  *
  64  * The Contribution is licensed pursuant to the OpenSSL open source
  65  * license provided above.
  66  *
  67  * The elliptic curve binary polynomial software is originally written by
  68  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
  69  *
  70  */
  71
  72 #include <stdio.h>
  73 #include <stdlib.h>
  74 #ifdef FLAT_INC
  75 #include "e_os.h"
  76 #else
  77 #include "../e_os.h"
  78 #endif
  79 #include <string.h>
  80 #include <time.h>
  81
  82
  83 #ifdef OPENSSL_NO_EC
  84 int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
  85 #else
  86
  87
  88 #include <openssl/ec.h>
  89 #ifndef OPENSSL_NO_ENGINE
  90 #include <openssl/engine.h>
  91 #endif
  92 #include <openssl/err.h>
  93 #include <openssl/obj_mac.h>
  94 #include <openssl/objects.h>
  95 #include <openssl/rand.h>
  96 #include <openssl/bn.h>
  97 #include <openssl/opensslconf.h>
  98
  99 #if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12)
 100 /* suppress "too big too optimize" warning */
 101 #pragma warning(disable:4959)
 102 #endif
 103
 104 #define ABORT do { \
 105         fflush(stdout); \
 106         fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
 107         ERR_print_errors_fp(stderr); \
 108         EXIT(1); \
 109 } while (0)
 110
 111 #define TIMING_BASE_PT 0
 112 #define TIMING_RAND_PT 1
 113 #define TIMING_SIMUL 2
 114
 115 #if 0
 116 static void timings(EC_GROUP *group, int type, BN_CTX *ctx)
 117         {
 118         clock_t clck;
 119         int i, j;
 120         BIGNUM *s;
 121         BIGNUM *r[10], *r0[10];
 122         EC_POINT *P;
 123
 124         s = BN_new();
 125         if (s == NULL) ABORT;
 126
 127         fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group));
 128         if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
 129         fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s));
 130         fflush(stdout);
 131
 132         P = EC_POINT_new(group);
 133         if (P == NULL) ABORT;
 134         EC_POINT_copy(P, EC_GROUP_get0_generator(group));
 135
 136         for (i = 0; i < 10; i++)
 137                 {
 138                 if ((r[i] = BN_new()) == NULL) ABORT;
 139                 if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT;
 140                 if (type != TIMING_BASE_PT)
 141                         {
 142                         if ((r0[i] = BN_new()) == NULL) ABORT;
 143                         if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT;
 144                         }
 145                 }
 146
 147         clck = clock();
 148         for (i = 0; i < 10; i++)
 149                 {
 150                 for (j = 0; j < 10; j++)
 151                         {
 152                         if (!EC_POINT_mul(group, P, (type != TIMING_RAND_PT) ? r[i] : NULL,
 153                                 (type != TIMING_BASE_PT) ? P : NULL, (type != TIMING_BASE_PT) ? r0[i] : NULL, ctx)) ABORT;
 154                         }
 155                 }
 156         clck = clock() - clck;
 157
 158         fprintf(stdout, "\n");
 159
 160 #ifdef CLOCKS_PER_SEC
 161         /* "To determine the time in seconds, the value returned
 162          * by the clock function should be divided by the value
 163          * of the macro CLOCKS_PER_SEC."
 164          *                                       -- ISO/IEC 9899 */
 165 #       define UNIT "s"
 166 #else
 167         /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
 168          *                            -- cc on NeXTstep/OpenStep */
 169 #       define UNIT "units"
 170 #       define CLOCKS_PER_SEC 1
 171 #endif
 172
 173         if (type == TIMING_BASE_PT) {
 174                 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
 175                         "base point multiplications", (double)clck/CLOCKS_PER_SEC);
 176         } else if (type == TIMING_RAND_PT) {
 177                 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
 178                         "random point multiplications", (double)clck/CLOCKS_PER_SEC);
 179         } else if (type == TIMING_SIMUL) {
 180                 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
 181                         "s*P+t*Q operations", (double)clck/CLOCKS_PER_SEC);
 182         }
 183         fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
 184
 185         EC_POINT_free(P);
 186         BN_free(s);
 187         for (i = 0; i < 10; i++)
 188                 {
 189                 BN_free(r[i]);
 190                 if (type != TIMING_BASE_PT) BN_free(r0[i]);
 191                 }
 192         }
 193 #endif
 194
 195 /* test multiplication with group order, long and negative scalars */
 196 static void group_order_tests(EC_GROUP *group)
 197         {
 198         BIGNUM *n1, *n2, *order;
 199         EC_POINT *P = EC_POINT_new(group);
 200         EC_POINT *Q = EC_POINT_new(group);
 201         BN_CTX *ctx = BN_CTX_new();
 202         int i;
 203
 204         n1 = BN_new(); n2 = BN_new(); order = BN_new();
 205         fprintf(stdout, "verify group order ...");
 206         fflush(stdout);
 207         if (!EC_GROUP_get_order(group, order, ctx)) ABORT;
 208         if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT;
 209         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 210         fprintf(stdout, ".");
 211         fflush(stdout);
 212         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 213         if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT;
 214         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 215         fprintf(stdout, " ok\n");
 216         fprintf(stdout, "long/negative scalar tests ");
 217         for (i = 1; i <= 2; i++)
 218                 {
 219                 const BIGNUM *scalars[6];
 220                 const EC_POINT *points[6];
 221
 222                 fprintf(stdout, i == 1 ?
 223                         "allowing precomputation ... " :
 224                         "without precomputation ... ");
 225                 if (!BN_set_word(n1, i)) ABORT;
 226                 /* If i == 1, P will be the predefined generator for which
 227                  * EC_GROUP_precompute_mult has set up precomputation. */
 228                 if (!EC_POINT_mul(group, P, n1, NULL, NULL, ctx)) ABORT;
 229
 230                 if (!BN_one(n1)) ABORT;
 231                 /* n1 = 1 - order */
 232                 if (!BN_sub(n1, n1, order)) ABORT;
 233                 if (!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT;
 234                 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
 235
 236                 /* n2 = 1 + order */
 237                 if (!BN_add(n2, order, BN_value_one())) ABORT;
 238                 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
 239                 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
 240
 241                 /* n2 = (1 - order) * (1 + order) = 1 - order^2 */
 242                 if (!BN_mul(n2, n1, n2, ctx)) ABORT;
 243                 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
 244                 if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
 245
 246                 /* n2 = order^2 - 1 */
 247                 BN_set_negative(n2, 0);
 248                 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
 249                 /* Add P to verify the result. */
 250                 if (!EC_POINT_add(group, Q, Q, P, ctx)) ABORT;
 251                 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 252
 253                 /* Exercise EC_POINTs_mul, including corner cases. */
 254                 scalars[0] = n1; points[0] = Q; /* => infinity */
 255                 scalars[1] = n2; points[1] = P; /* => -P */
 256                 scalars[2] = n1; points[2] = Q; /* => infinity */
 257                 scalars[3] = n2; points[3] = Q; /* => infinity */
 258                 scalars[4] = n1; points[4] = P; /* => P */
 259                 scalars[5] = n2; points[5] = Q; /* => infinity */
 260                 if (!EC_POINTs_mul(group, Q, NULL, 5, points, scalars, ctx)) ABORT;
 261                 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 262                 }
 263         fprintf(stdout, "ok\n");
 264
 265         EC_POINT_free(P);
 266         EC_POINT_free(Q);
 267         BN_free(n1);
 268         BN_free(n2);
 269         BN_free(order);
 270         BN_CTX_free(ctx);
 271         }
 272
 273 static void prime_field_tests(void)
 274         {
 275         BN_CTX *ctx = NULL;
 276         BIGNUM *p, *a, *b;
 277         EC_GROUP *group;
 278         EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
 279         EC_POINT *P, *Q, *R;
 280         BIGNUM *x, *y, *z;
 281         unsigned char buf[100];
 282         size_t i, len;
 283         int k;
 284
 285 #if 1 /* optional */
 286         ctx = BN_CTX_new();
 287         if (!ctx) ABORT;
 288 #endif
 289
 290         p = BN_new();
 291         a = BN_new();
 292         b = BN_new();
 293         if (!p || !a || !b) ABORT;
 294
 295         if (!BN_hex2bn(&p, "17")) ABORT;
 296         if (!BN_hex2bn(&a, "1")) ABORT;
 297         if (!BN_hex2bn(&b, "1")) ABORT;
 298
 299         group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
 300                                                      * so that the library gets to choose the EC_METHOD */
 301         if (!group) ABORT;
 302
 303         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 304
 305         {
 306                 EC_GROUP *tmp;
 307                 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
 308                 if (!tmp) ABORT;
 309                 if (!EC_GROUP_copy(tmp, group)) ABORT;
 310                 EC_GROUP_free(group);
 311                 group = tmp;
 312         }
 313
 314         if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
 315
 316         fprintf(stdout, "Curve defined by Weierstrass equation\n     y^2 = x^3 + a*x + b  (mod 0x");
 317         BN_print_fp(stdout, p);
 318         fprintf(stdout, ")\n     a = 0x");
 319         BN_print_fp(stdout, a);
 320         fprintf(stdout, "\n     b = 0x");
 321         BN_print_fp(stdout, b);
 322         fprintf(stdout, "\n");
 323
 324         P = EC_POINT_new(group);
 325         Q = EC_POINT_new(group);
 326         R = EC_POINT_new(group);
 327         if (!P || !Q || !R) ABORT;
 328
 329         if (!EC_POINT_set_to_infinity(group, P)) ABORT;
 330         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 331
 332         buf[0] = 0;
 333         if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
 334
 335         if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 336         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 337
 338         x = BN_new();
 339         y = BN_new();
 340         z = BN_new();
 341         if (!x || !y || !z) ABORT;
 342
 343         if (!BN_hex2bn(&x, "D")) ABORT;
 344         if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
 345         if (!EC_POINT_is_on_curve(group, Q, ctx))
 346                 {
 347                 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
 348                 fprintf(stderr, "Point is not on curve: x = 0x");
 349                 BN_print_fp(stderr, x);
 350                 fprintf(stderr, ", y = 0x");
 351                 BN_print_fp(stderr, y);
 352                 fprintf(stderr, "\n");
 353                 ABORT;
 354                 }
 355
 356         fprintf(stdout, "A cyclic subgroup:\n");
 357         k = 100;
 358         do
 359                 {
 360                 if (k-- == 0) ABORT;
 361
 362                 if (EC_POINT_is_at_infinity(group, P))
 363                         fprintf(stdout, "     point at infinity\n");
 364                 else
 365                         {
 366                         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 367
 368                         fprintf(stdout, "     x = 0x");
 369                         BN_print_fp(stdout, x);
 370                         fprintf(stdout, ", y = 0x");
 371                         BN_print_fp(stdout, y);
 372                         fprintf(stdout, "\n");
 373                         }
 374
 375                 if (!EC_POINT_copy(R, P)) ABORT;
 376                 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 377
 378 #if 0 /* optional */
 379                 {
 380                         EC_POINT *points[3];
 381
 382                         points[0] = R;
 383                         points[1] = Q;
 384                         points[2] = P;
 385                         if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
 386                 }
 387 #endif
 388
 389                 }
 390         while (!EC_POINT_is_at_infinity(group, P));
 391
 392         if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
 393         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 394
 395         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
 396         if (len == 0) ABORT;
 397         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 398         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 399         fprintf(stdout, "Generator as octet string, compressed form:\n     ");
 400         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 401
 402         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
 403         if (len == 0) ABORT;
 404         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 405         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 406         fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n     ");
 407         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 408
 409         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
 410         if (len == 0) ABORT;
 411         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 412         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 413         fprintf(stdout, "\nGenerator as octet string, hybrid form:\n     ");
 414         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 415
 416         if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
 417         fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n     X = 0x");
 418         BN_print_fp(stdout, x);
 419         fprintf(stdout, ", Y = 0x");
 420         BN_print_fp(stdout, y);
 421         fprintf(stdout, ", Z = 0x");
 422         BN_print_fp(stdout, z);
 423         fprintf(stdout, "\n");
 424
 425         if (!EC_POINT_invert(group, P, ctx)) ABORT;
 426         if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
 427
 428
 429         /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000)
 430          * -- not a NIST curve, but commonly used */
 431
 432         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT;
 433         if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
 434         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT;
 435         if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT;
 436         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 437
 438         if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT;
 439         if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
 440         if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 441         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 442         if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) ABORT;
 443         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 444
 445         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 446         fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n     x = 0x");
 447         BN_print_fp(stdout, x);
 448         fprintf(stdout, "\n     y = 0x");
 449         BN_print_fp(stdout, y);
 450         fprintf(stdout, "\n");
 451         /* G_y value taken from the standard: */
 452         if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
 453         if (0 != BN_cmp(y, z)) ABORT;
 454
 455         fprintf(stdout, "verify degree ...");
 456         if (EC_GROUP_get_degree(group) != 160) ABORT;
 457         fprintf(stdout, " ok\n");
 458
 459         group_order_tests(group);
 460
 461         if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 462         if (!EC_GROUP_copy(P_160, group)) ABORT;
 463
 464
 465         /* Curve P-192 (FIPS PUB 186-2, App. 6) */
 466
 467         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
 468         if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
 469         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
 470         if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
 471         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 472
 473         if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
 474         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 475         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 476         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
 477         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 478
 479         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 480         fprintf(stdout, "\nNIST curve P-192 -- Generator:\n     x = 0x");
 481         BN_print_fp(stdout, x);
 482         fprintf(stdout, "\n     y = 0x");
 483         BN_print_fp(stdout, y);
 484         fprintf(stdout, "\n");
 485         /* G_y value taken from the standard: */
 486         if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
 487         if (0 != BN_cmp(y, z)) ABORT;
 488
 489         fprintf(stdout, "verify degree ...");
 490         if (EC_GROUP_get_degree(group) != 192) ABORT;
 491         fprintf(stdout, " ok\n");
 492
 493         group_order_tests(group);
 494
 495         if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 496         if (!EC_GROUP_copy(P_192, group)) ABORT;
 497
 498
 499         /* Curve P-224 (FIPS PUB 186-2, App. 6) */
 500
 501         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
 502         if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
 503         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
 504         if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
 505         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 506
 507         if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
 508         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
 509         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 510         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
 511         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 512
 513         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 514         fprintf(stdout, "\nNIST curve P-224 -- Generator:\n     x = 0x");
 515         BN_print_fp(stdout, x);
 516         fprintf(stdout, "\n     y = 0x");
 517         BN_print_fp(stdout, y);
 518         fprintf(stdout, "\n");
 519         /* G_y value taken from the standard: */
 520         if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
 521         if (0 != BN_cmp(y, z)) ABORT;
 522
 523         fprintf(stdout, "verify degree ...");
 524         if (EC_GROUP_get_degree(group) != 224) ABORT;
 525         fprintf(stdout, " ok\n");
 526
 527         group_order_tests(group);
 528
 529         if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 530         if (!EC_GROUP_copy(P_224, group)) ABORT;
 531
 532
 533         /* Curve P-256 (FIPS PUB 186-2, App. 6) */
 534
 535         if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
 536         if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
 537         if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
 538         if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
 539         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 540
 541         if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
 542         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 543         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 544         if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
 545                 "84F3B9CAC2FC632551")) ABORT;
 546         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 547
 548         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 549         fprintf(stdout, "\nNIST curve P-256 -- Generator:\n     x = 0x");
 550         BN_print_fp(stdout, x);
 551         fprintf(stdout, "\n     y = 0x");
 552         BN_print_fp(stdout, y);
 553         fprintf(stdout, "\n");
 554         /* G_y value taken from the standard: */
 555         if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
 556         if (0 != BN_cmp(y, z)) ABORT;
 557
 558         fprintf(stdout, "verify degree ...");
 559         if (EC_GROUP_get_degree(group) != 256) ABORT;
 560         fprintf(stdout, " ok\n");
 561
 562         group_order_tests(group);
 563
 564         if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 565         if (!EC_GROUP_copy(P_256, group)) ABORT;
 566
 567
 568         /* Curve P-384 (FIPS PUB 186-2, App. 6) */
 569
 570         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 571                 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
 572         if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
 573         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 574                 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
 575         if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
 576                 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
 577         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 578
 579         if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
 580                 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
 581         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 582         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 583         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 584                 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
 585         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 586
 587         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 588         fprintf(stdout, "\nNIST curve P-384 -- Generator:\n     x = 0x");
 589         BN_print_fp(stdout, x);
 590         fprintf(stdout, "\n     y = 0x");
 591         BN_print_fp(stdout, y);
 592         fprintf(stdout, "\n");
 593         /* G_y value taken from the standard: */
 594         if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
 595                 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
 596         if (0 != BN_cmp(y, z)) ABORT;
 597
 598         fprintf(stdout, "verify degree ...");
 599         if (EC_GROUP_get_degree(group) != 384) ABORT;
 600         fprintf(stdout, " ok\n");
 601
 602         group_order_tests(group);
 603
 604         if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 605         if (!EC_GROUP_copy(P_384, group)) ABORT;
 606
 607
 608         /* Curve P-521 (FIPS PUB 186-2, App. 6) */
 609
 610         if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 611                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 612                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
 613         if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
 614         if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 615                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 616                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
 617         if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
 618                 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
 619                 "DF883D2C34F1EF451FD46B503F00")) ABORT;
 620         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 621
 622         if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
 623                 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
 624                 "3C1856A429BF97E7E31C2E5BD66")) ABORT;
 625         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
 626         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 627         if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 628                 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
 629                 "C9B8899C47AEBB6FB71E91386409")) ABORT;
 630         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 631
 632         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 633         fprintf(stdout, "\nNIST curve P-521 -- Generator:\n     x = 0x");
 634         BN_print_fp(stdout, x);
 635         fprintf(stdout, "\n     y = 0x");
 636         BN_print_fp(stdout, y);
 637         fprintf(stdout, "\n");
 638         /* G_y value taken from the standard: */
 639         if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
 640                 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
 641                 "7086A272C24088BE94769FD16650")) ABORT;
 642         if (0 != BN_cmp(y, z)) ABORT;
 643
 644         fprintf(stdout, "verify degree ...");
 645         if (EC_GROUP_get_degree(group) != 521) ABORT;
 646         fprintf(stdout, " ok\n");
 647
 648         group_order_tests(group);
 649
 650         if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 651         if (!EC_GROUP_copy(P_521, group)) ABORT;
 652
 653
 654         /* more tests using the last curve */
 655
 656         if (!EC_POINT_copy(Q, P)) ABORT;
 657         if (EC_POINT_is_at_infinity(group, Q)) ABORT;
 658         if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
 659         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 660         if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
 661
 662         if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
 663         if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
 664         if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
 665
 666         {
 667                 const EC_POINT *points[4];
 668                 const BIGNUM *scalars[4];
 669                 BIGNUM scalar3;
 670
 671                 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
 672                 points[0] = Q;
 673                 points[1] = Q;
 674                 points[2] = Q;
 675                 points[3] = Q;
 676
 677                 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 678                 if (!BN_add(y, z, BN_value_one())) ABORT;
 679                 if (BN_is_odd(y)) ABORT;
 680                 if (!BN_rshift1(y, y)) ABORT;
 681                 scalars[0] = y; /* (group order + 1)/2,  so  y*Q + y*Q = Q */
 682                 scalars[1] = y;
 683
 684                 fprintf(stdout, "combined multiplication ...");
 685                 fflush(stdout);
 686
 687                 /* z is still the group order */
 688                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
 689                 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
 690                 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
 691                 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
 692
 693                 fprintf(stdout, ".");
 694                 fflush(stdout);
 695
 696                 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
 697                 if (!BN_add(z, z, y)) ABORT;
 698                 BN_set_negative(z, 1);
 699                 scalars[0] = y;
 700                 scalars[1] = z; /* z = -(order + y) */
 701
 702                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
 703                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 704
 705                 fprintf(stdout, ".");
 706                 fflush(stdout);
 707
 708                 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
 709                 if (!BN_add(z, x, y)) ABORT;
 710                 BN_set_negative(z, 1);
 711                 scalars[0] = x;
 712                 scalars[1] = y;
 713                 scalars[2] = z; /* z = -(x+y) */
 714
 715                 BN_init(&scalar3);
 716                 BN_zero(&scalar3);
 717                 scalars[3] = &scalar3;
 718
 719                 if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx)) ABORT;
 720                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 721
 722                 fprintf(stdout, " ok\n\n");
 723
 724                 BN_free(&scalar3);
 725         }
 726
 727
 728 #if 0
 729         timings(P_160, TIMING_BASE_PT, ctx);
 730         timings(P_160, TIMING_RAND_PT, ctx);
 731         timings(P_160, TIMING_SIMUL, ctx);
 732         timings(P_192, TIMING_BASE_PT, ctx);
 733         timings(P_192, TIMING_RAND_PT, ctx);
 734         timings(P_192, TIMING_SIMUL, ctx);
 735         timings(P_224, TIMING_BASE_PT, ctx);
 736         timings(P_224, TIMING_RAND_PT, ctx);
 737         timings(P_224, TIMING_SIMUL, ctx);
 738         timings(P_256, TIMING_BASE_PT, ctx);
 739         timings(P_256, TIMING_RAND_PT, ctx);
 740         timings(P_256, TIMING_SIMUL, ctx);
 741         timings(P_384, TIMING_BASE_PT, ctx);
 742         timings(P_384, TIMING_RAND_PT, ctx);
 743         timings(P_384, TIMING_SIMUL, ctx);
 744         timings(P_521, TIMING_BASE_PT, ctx);
 745         timings(P_521, TIMING_RAND_PT, ctx);
 746         timings(P_521, TIMING_SIMUL, ctx);
 747 #endif
 748
 749
 750         if (ctx)
 751                 BN_CTX_free(ctx);
 752         BN_free(p); BN_free(a); BN_free(b);
 753         EC_GROUP_free(group);
 754         EC_POINT_free(P);
 755         EC_POINT_free(Q);
 756         EC_POINT_free(R);
 757         BN_free(x); BN_free(y); BN_free(z);
 758
 759         if (P_160) EC_GROUP_free(P_160);
 760         if (P_192) EC_GROUP_free(P_192);
 761         if (P_224) EC_GROUP_free(P_224);
 762         if (P_256) EC_GROUP_free(P_256);
 763         if (P_384) EC_GROUP_free(P_384);
 764         if (P_521) EC_GROUP_free(P_521);
 765
 766         }
 767
 768 /* Change test based on whether binary point compression is enabled or not. */
 769 #ifdef OPENSSL_EC_BIN_PT_COMP
 770 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
 771         if (!BN_hex2bn(&x, _x)) ABORT; \
 772         if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
 773         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
 774         if (!BN_hex2bn(&z, _order)) ABORT; \
 775         if (!BN_hex2bn(&cof, _cof)) ABORT; \
 776         if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
 777         if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
 778         fprintf(stdout, "\n%s -- Generator:\n     x = 0x", _name); \
 779         BN_print_fp(stdout, x); \
 780         fprintf(stdout, "\n     y = 0x"); \
 781         BN_print_fp(stdout, y); \
 782         fprintf(stdout, "\n"); \
 783         /* G_y value taken from the standard: */ \
 784         if (!BN_hex2bn(&z, _y)) ABORT; \
 785         if (0 != BN_cmp(y, z)) ABORT;
 786 #else
 787 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
 788         if (!BN_hex2bn(&x, _x)) ABORT; \
 789         if (!BN_hex2bn(&y, _y)) ABORT; \
 790         if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
 791         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
 792         if (!BN_hex2bn(&z, _order)) ABORT; \
 793         if (!BN_hex2bn(&cof, _cof)) ABORT; \
 794         if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
 795         fprintf(stdout, "\n%s -- Generator:\n     x = 0x", _name); \
 796         BN_print_fp(stdout, x); \
 797         fprintf(stdout, "\n     y = 0x"); \
 798         BN_print_fp(stdout, y); \
 799         fprintf(stdout, "\n");
 800 #endif
 801
 802 #define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
 803         if (!BN_hex2bn(&p, _p)) ABORT; \
 804         if (!BN_hex2bn(&a, _a)) ABORT; \
 805         if (!BN_hex2bn(&b, _b)) ABORT; \
 806         if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
 807         CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
 808         fprintf(stdout, "verify degree ..."); \
 809         if (EC_GROUP_get_degree(group) != _degree) ABORT; \
 810         fprintf(stdout, " ok\n"); \
 811         group_order_tests(group); \
 812         if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
 813         if (!EC_GROUP_copy(_variable, group)) ABORT; \
 814
 815 #ifndef OPENSSL_NO_EC2M
 816
 817 static void char2_field_tests(void)
 818         {
 819         BN_CTX *ctx = NULL;
 820         BIGNUM *p, *a, *b;
 821         EC_GROUP *group;
 822         EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL;
 823         EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL;
 824         EC_POINT *P, *Q, *R;
 825         BIGNUM *x, *y, *z, *cof;
 826         unsigned char buf[100];
 827         size_t i, len;
 828         int k;
 829
 830 #if 1 /* optional */
 831         ctx = BN_CTX_new();
 832         if (!ctx) ABORT;
 833 #endif
 834
 835         p = BN_new();
 836         a = BN_new();
 837         b = BN_new();
 838         if (!p || !a || !b) ABORT;
 839
 840         if (!BN_hex2bn(&p, "13")) ABORT;
 841         if (!BN_hex2bn(&a, "3")) ABORT;
 842         if (!BN_hex2bn(&b, "1")) ABORT;
 843
 844         group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m
 845                                                         * so that the library gets to choose the EC_METHOD */
 846         if (!group) ABORT;
 847         if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT;
 848
 849         {
 850                 EC_GROUP *tmp;
 851                 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
 852                 if (!tmp) ABORT;
 853                 if (!EC_GROUP_copy(tmp, group)) ABORT;
 854                 EC_GROUP_free(group);
 855                 group = tmp;
 856         }
 857
 858         if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT;
 859
 860         fprintf(stdout, "Curve defined by Weierstrass equation\n     y^2 + x*y = x^3 + a*x^2 + b  (mod 0x");
 861         BN_print_fp(stdout, p);
 862         fprintf(stdout, ")\n     a = 0x");
 863         BN_print_fp(stdout, a);
 864         fprintf(stdout, "\n     b = 0x");
 865         BN_print_fp(stdout, b);
 866         fprintf(stdout, "\n(0x... means binary polynomial)\n");
 867
 868         P = EC_POINT_new(group);
 869         Q = EC_POINT_new(group);
 870         R = EC_POINT_new(group);
 871         if (!P || !Q || !R) ABORT;
 872
 873         if (!EC_POINT_set_to_infinity(group, P)) ABORT;
 874         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 875
 876         buf[0] = 0;
 877         if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
 878
 879         if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 880         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 881
 882         x = BN_new();
 883         y = BN_new();
 884         z = BN_new();
 885         cof = BN_new();
 886         if (!x || !y || !z || !cof) ABORT;
 887
 888         if (!BN_hex2bn(&x, "6")) ABORT;
 889 /* Change test based on whether binary point compression is enabled or not. */
 890 #ifdef OPENSSL_EC_BIN_PT_COMP
 891         if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT;
 892 #else
 893         if (!BN_hex2bn(&y, "8")) ABORT;
 894         if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
 895 #endif
 896         if (!EC_POINT_is_on_curve(group, Q, ctx))
 897                 {
 898 /* Change test based on whether binary point compression is enabled or not. */
 899 #ifdef OPENSSL_EC_BIN_PT_COMP
 900                 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
 901 #endif
 902                 fprintf(stderr, "Point is not on curve: x = 0x");
 903                 BN_print_fp(stderr, x);
 904                 fprintf(stderr, ", y = 0x");
 905                 BN_print_fp(stderr, y);
 906                 fprintf(stderr, "\n");
 907                 ABORT;
 908                 }
 909
 910         fprintf(stdout, "A cyclic subgroup:\n");
 911         k = 100;
 912         do
 913                 {
 914                 if (k-- == 0) ABORT;
 915
 916                 if (EC_POINT_is_at_infinity(group, P))
 917                         fprintf(stdout, "     point at infinity\n");
 918                 else
 919                         {
 920                         if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT;
 921
 922                         fprintf(stdout, "     x = 0x");
 923                         BN_print_fp(stdout, x);
 924                         fprintf(stdout, ", y = 0x");
 925                         BN_print_fp(stdout, y);
 926                         fprintf(stdout, "\n");
 927                         }
 928
 929                 if (!EC_POINT_copy(R, P)) ABORT;
 930                 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 931                 }
 932         while (!EC_POINT_is_at_infinity(group, P));
 933
 934         if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
 935         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 936
 937 /* Change test based on whether binary point compression is enabled or not. */
 938 #ifdef OPENSSL_EC_BIN_PT_COMP
 939         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
 940         if (len == 0) ABORT;
 941         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 942         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 943         fprintf(stdout, "Generator as octet string, compressed form:\n     ");
 944         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 945 #endif
 946
 947         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
 948         if (len == 0) ABORT;
 949         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 950         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 951         fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n     ");
 952         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 953
 954 /* Change test based on whether binary point compression is enabled or not. */
 955 #ifdef OPENSSL_EC_BIN_PT_COMP
 956         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
 957         if (len == 0) ABORT;
 958         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 959         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 960         fprintf(stdout, "\nGenerator as octet string, hybrid form:\n     ");
 961         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 962 #endif
 963
 964         fprintf(stdout, "\n");
 965
 966         if (!EC_POINT_invert(group, P, ctx)) ABORT;
 967         if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
 968
 969
 970         /* Curve K-163 (FIPS PUB 186-2, App. 6) */
 971         CHAR2_CURVE_TEST
 972                 (
 973                 "NIST curve K-163",
 974                 "0800000000000000000000000000000000000000C9",
 975                 "1",
 976                 "1",
 977                 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
 978                 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
 979                 1,
 980                 "04000000000000000000020108A2E0CC0D99F8A5EF",
 981                 "2",
 982                 163,
 983                 C2_K163
 984                 );
 985
 986         /* Curve B-163 (FIPS PUB 186-2, App. 6) */
 987         CHAR2_CURVE_TEST
 988                 (
 989                 "NIST curve B-163",
 990                 "0800000000000000000000000000000000000000C9",
 991                 "1",
 992                 "020A601907B8C953CA1481EB10512F78744A3205FD",
 993                 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
 994                 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
 995                 1,
 996                 "040000000000000000000292FE77E70C12A4234C33",
 997                 "2",
 998                 163,
 999                 C2_B163
1000                 );
1001
1002         /* Curve K-233 (FIPS PUB 186-2, App. 6) */
1003         CHAR2_CURVE_TEST
1004                 (
1005                 "NIST curve K-233",
1006                 "020000000000000000000000000000000000000004000000000000000001",
1007                 "0",
1008                 "1",
1009                 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
1010                 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
1011                 0,
1012                 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
1013                 "4",
1014                 233,
1015                 C2_K233
1016                 );
1017
1018         /* Curve B-233 (FIPS PUB 186-2, App. 6) */
1019         CHAR2_CURVE_TEST
1020                 (
1021                 "NIST curve B-233",
1022                 "020000000000000000000000000000000000000004000000000000000001",
1023                 "000000000000000000000000000000000000000000000000000000000001",
1024                 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1025                 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1026                 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1027                 1,
1028                 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1029                 "2",
1030                 233,
1031                 C2_B233
1032                 );
1033
1034         /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1035         CHAR2_CURVE_TEST
1036                 (
1037                 "NIST curve K-283",
1038                 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1039                 "0",
1040                 "1",
1041                 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1042                 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1043                 0,
1044                 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1045                 "4",
1046                 283,
1047                 C2_K283
1048                 );
1049
1050         /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1051         CHAR2_CURVE_TEST
1052                 (
1053                 "NIST curve B-283",
1054                 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1055                 "000000000000000000000000000000000000000000000000000000000000000000000001",
1056                 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1057                 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1058                 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1059                 1,
1060                 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1061                 "2",
1062                 283,
1063                 C2_B283
1064                 );
1065
1066         /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1067         CHAR2_CURVE_TEST
1068                 (
1069                 "NIST curve K-409",
1070                 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1071                 "0",
1072                 "1",
1073                 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1074                 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1075                 1,
1076                 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1077                 "4",
1078                 409,
1079                 C2_K409
1080                 );
1081
1082         /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1083         CHAR2_CURVE_TEST
1084                 (
1085                 "NIST curve B-409",
1086                 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1087                 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1088                 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1089                 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1090                 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1091                 1,
1092                 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1093                 "2",
1094                 409,
1095                 C2_B409
1096                 );
1097
1098         /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1099         CHAR2_CURVE_TEST
1100                 (
1101                 "NIST curve K-571",
1102                 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1103                 "0",
1104                 "1",
1105                 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1106                 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1107                 0,
1108                 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1109                 "4",
1110                 571,
1111                 C2_K571
1112                 );
1113
1114         /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1115         CHAR2_CURVE_TEST
1116                 (
1117                 "NIST curve B-571",
1118                 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1119                 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1120                 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1121                 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1122                 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1123                 1,
1124                 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1125                 "2",
1126                 571,
1127                 C2_B571
1128                 );
1129
1130         /* more tests using the last curve */
1131
1132         if (!EC_POINT_copy(Q, P)) ABORT;
1133         if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1134         if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
1135         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
1136         if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
1137
1138         if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
1139         if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
1140         if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
1141
1142         {
1143                 const EC_POINT *points[3];
1144                 const BIGNUM *scalars[3];
1145
1146                 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1147                 points[0] = Q;
1148                 points[1] = Q;
1149                 points[2] = Q;
1150
1151                 if (!BN_add(y, z, BN_value_one())) ABORT;
1152                 if (BN_is_odd(y)) ABORT;
1153                 if (!BN_rshift1(y, y)) ABORT;
1154                 scalars[0] = y; /* (group order + 1)/2,  so  y*Q + y*Q = Q */
1155                 scalars[1] = y;
1156
1157                 fprintf(stdout, "combined multiplication ...");
1158                 fflush(stdout);
1159
1160                 /* z is still the group order */
1161                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1162                 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
1163                 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
1164                 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
1165
1166                 fprintf(stdout, ".");
1167                 fflush(stdout);
1168
1169                 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
1170                 if (!BN_add(z, z, y)) ABORT;
1171                 BN_set_negative(z, 1);
1172                 scalars[0] = y;
1173                 scalars[1] = z; /* z = -(order + y) */
1174
1175                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1176                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1177
1178                 fprintf(stdout, ".");
1179                 fflush(stdout);
1180
1181                 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
1182                 if (!BN_add(z, x, y)) ABORT;
1183                 BN_set_negative(z, 1);
1184                 scalars[0] = x;
1185                 scalars[1] = y;
1186                 scalars[2] = z; /* z = -(x+y) */
1187
1188                 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
1189                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1190
1191                 fprintf(stdout, " ok\n\n");
1192         }
1193
1194
1195 #if 0
1196         timings(C2_K163, TIMING_BASE_PT, ctx);
1197         timings(C2_K163, TIMING_RAND_PT, ctx);
1198         timings(C2_K163, TIMING_SIMUL, ctx);
1199         timings(C2_B163, TIMING_BASE_PT, ctx);
1200         timings(C2_B163, TIMING_RAND_PT, ctx);
1201         timings(C2_B163, TIMING_SIMUL, ctx);
1202         timings(C2_K233, TIMING_BASE_PT, ctx);
1203         timings(C2_K233, TIMING_RAND_PT, ctx);
1204         timings(C2_K233, TIMING_SIMUL, ctx);
1205         timings(C2_B233, TIMING_BASE_PT, ctx);
1206         timings(C2_B233, TIMING_RAND_PT, ctx);
1207         timings(C2_B233, TIMING_SIMUL, ctx);
1208         timings(C2_K283, TIMING_BASE_PT, ctx);
1209         timings(C2_K283, TIMING_RAND_PT, ctx);
1210         timings(C2_K283, TIMING_SIMUL, ctx);
1211         timings(C2_B283, TIMING_BASE_PT, ctx);
1212         timings(C2_B283, TIMING_RAND_PT, ctx);
1213         timings(C2_B283, TIMING_SIMUL, ctx);
1214         timings(C2_K409, TIMING_BASE_PT, ctx);
1215         timings(C2_K409, TIMING_RAND_PT, ctx);
1216         timings(C2_K409, TIMING_SIMUL, ctx);
1217         timings(C2_B409, TIMING_BASE_PT, ctx);
1218         timings(C2_B409, TIMING_RAND_PT, ctx);
1219         timings(C2_B409, TIMING_SIMUL, ctx);
1220         timings(C2_K571, TIMING_BASE_PT, ctx);
1221         timings(C2_K571, TIMING_RAND_PT, ctx);
1222         timings(C2_K571, TIMING_SIMUL, ctx);
1223         timings(C2_B571, TIMING_BASE_PT, ctx);
1224         timings(C2_B571, TIMING_RAND_PT, ctx);
1225         timings(C2_B571, TIMING_SIMUL, ctx);
1226 #endif
1227
1228
1229         if (ctx)
1230                 BN_CTX_free(ctx);
1231         BN_free(p); BN_free(a); BN_free(b);
1232         EC_GROUP_free(group);
1233         EC_POINT_free(P);
1234         EC_POINT_free(Q);
1235         EC_POINT_free(R);
1236         BN_free(x); BN_free(y); BN_free(z); BN_free(cof);
1237
1238         if (C2_K163) EC_GROUP_free(C2_K163);
1239         if (C2_B163) EC_GROUP_free(C2_B163);
1240         if (C2_K233) EC_GROUP_free(C2_K233);
1241         if (C2_B233) EC_GROUP_free(C2_B233);
1242         if (C2_K283) EC_GROUP_free(C2_K283);
1243         if (C2_B283) EC_GROUP_free(C2_B283);
1244         if (C2_K409) EC_GROUP_free(C2_K409);
1245         if (C2_B409) EC_GROUP_free(C2_B409);
1246         if (C2_K571) EC_GROUP_free(C2_K571);
1247         if (C2_B571) EC_GROUP_free(C2_B571);
1248
1249         }
1250 #endif
1251
1252 static void internal_curve_test(void)
1253         {
1254         EC_builtin_curve *curves = NULL;
1255         size_t crv_len = 0, n = 0;
1256         int    ok = 1;
1257
1258         crv_len = EC_get_builtin_curves(NULL, 0);
1259
1260         curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len);
1261
1262         if (curves == NULL)
1263                 return;
1264
1265         if (!EC_get_builtin_curves(curves, crv_len))
1266                 {
1267                 OPENSSL_free(curves);
1268                 return;
1269                 }
1270
1271         fprintf(stdout, "testing internal curves: ");
1272
1273         for (n = 0; n < crv_len; n++)
1274                 {
1275                 EC_GROUP *group = NULL;
1276                 int nid = curves[n].nid;
1277                 if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL)
1278                         {
1279                         ok = 0;
1280                         fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with"
1281                                 " curve %s\n", OBJ_nid2sn(nid));
1282                         /* try next curve */
1283                         continue;
1284                         }
1285                 if (!EC_GROUP_check(group, NULL))
1286                         {
1287                         ok = 0;
1288                         fprintf(stdout, "\nEC_GROUP_check() failed with"
1289                                 " curve %s\n", OBJ_nid2sn(nid));
1290                         EC_GROUP_free(group);
1291                         /* try the next curve */
1292                         continue;
1293                         }
1294                 fprintf(stdout, ".");
1295                 fflush(stdout);
1296                 EC_GROUP_free(group);
1297                 }
1298         if (ok)
1299                 fprintf(stdout, " ok\n\n");
1300         else
1301                 {
1302                 fprintf(stdout, " failed\n\n");
1303                 ABORT;
1304                 }
1305         OPENSSL_free(curves);
1306         return;
1307         }
1308
1309 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1310 /* nistp_test_params contains magic numbers for testing our optimized
1311  * implementations of several NIST curves with characteristic > 3. */
1312 struct nistp_test_params
1313         {
1314         const EC_METHOD* (*meth) ();
1315         int degree;
1316         /* Qx, Qy and D are taken from
1317          * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
1318          * Otherwise, values are standard curve parameters from FIPS 180-3 */
1319         const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d;
1320         };
1321
1322 static const struct nistp_test_params nistp_tests_params[] =
1323         {
1324                 {
1325                 /* P-224 */
1326                 EC_GFp_nistp224_method,
1327                 224,
1328                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", /* p */
1329                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", /* a */
1330                 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", /* b */
1331                 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E", /* Qx */
1332                 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555", /* Qy */
1333                 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", /* Gx */
1334                 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34", /* Gy */
1335                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", /* order */
1336                 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8", /* d */
1337                 },
1338                 {
1339                 /* P-256 */
1340                 EC_GFp_nistp256_method,
1341                 256,
1342                 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", /* p */
1343                 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", /* a */
1344                 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", /* b */
1345                 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19", /* Qx */
1346                 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09", /* Qy */
1347                 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", /* Gx */
1348                 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", /* Gy */
1349                 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", /* order */
1350                 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96", /* d */
1351                 },
1352                 {
1353                 /* P-521 */
1354                 EC_GFp_nistp521_method,
1355                 521,
1356                 "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", /* p */
1357                 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc", /* a */
1358                 "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", /* b */
1359                 "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4", /* Qx */
1360                 "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e", /* Qy */
1361                 "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", /* Gx */
1362                 "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", /* Gy */
1363                 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409", /* order */
1364                 "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722", /* d */
1365                 },
1366         };
1367
1368 void nistp_single_test(const struct nistp_test_params *test)
1369         {
1370         BN_CTX *ctx;
1371         BIGNUM *p, *a, *b, *x, *y, *n, *m, *order;
1372         EC_GROUP *NISTP;
1373         EC_POINT *G, *P, *Q, *Q_CHECK;
1374
1375         fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n", test->degree);
1376         ctx = BN_CTX_new();
1377         p = BN_new();
1378         a = BN_new();
1379         b = BN_new();
1380         x = BN_new(); y = BN_new();
1381         m = BN_new(); n = BN_new(); order = BN_new();
1382
1383         NISTP = EC_GROUP_new(test->meth());
1384         if(!NISTP) ABORT;
1385         if (!BN_hex2bn(&p, test->p)) ABORT;
1386         if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
1387         if (!BN_hex2bn(&a, test->a)) ABORT;
1388         if (!BN_hex2bn(&b, test->b)) ABORT;
1389         if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx)) ABORT;
1390         G = EC_POINT_new(NISTP);
1391         P = EC_POINT_new(NISTP);
1392         Q = EC_POINT_new(NISTP);
1393         Q_CHECK = EC_POINT_new(NISTP);
1394         if(!BN_hex2bn(&x, test->Qx)) ABORT;
1395         if(!BN_hex2bn(&y, test->Qy)) ABORT;
1396         if(!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx)) ABORT;
1397         if (!BN_hex2bn(&x, test->Gx)) ABORT;
1398         if (!BN_hex2bn(&y, test->Gy)) ABORT;
1399         if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx)) ABORT;
1400         if (!BN_hex2bn(&order, test->order)) ABORT;
1401         if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT;
1402
1403         fprintf(stdout, "verify degree ... ");
1404         if (EC_GROUP_get_degree(NISTP) != test->degree) ABORT;
1405         fprintf(stdout, "ok\n");
1406
1407         fprintf(stdout, "NIST test vectors ... ");
1408         if (!BN_hex2bn(&n, test->d)) ABORT;
1409         /* fixed point multiplication */
1410         EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1411         if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
1412         /* random point multiplication */
1413         EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1414         if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
1415
1416         /* set generator to P = 2*G, where G is the standard generator */
1417         if (!EC_POINT_dbl(NISTP, P, G, ctx)) ABORT;
1418         if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one())) ABORT;
1419         /* set the scalar to m=n/2, where n is the NIST test scalar */
1420         if (!BN_rshift(m, n, 1)) ABORT;
1421
1422         /* test the non-standard generator */
1423         /* fixed point multiplication */
1424         EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1425         if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
1426         /* random point multiplication */
1427         EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1428         if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
1429
1430         /* now repeat all tests with precomputation */
1431         if (!EC_GROUP_precompute_mult(NISTP, ctx)) ABORT;
1432
1433         /* fixed point multiplication */
1434         EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1435         if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
1436         /* random point multiplication */
1437         EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1438         if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
1439
1440         /* reset generator */
1441         if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT;
1442         /* fixed point multiplication */
1443         EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1444         if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
1445         /* random point multiplication */
1446         EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1447         if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
1448
1449         fprintf(stdout, "ok\n");
1450         group_order_tests(NISTP);
1451 #if 0
1452         timings(NISTP, TIMING_BASE_PT, ctx);
1453         timings(NISTP, TIMING_RAND_PT, ctx);
1454 #endif
1455         EC_GROUP_free(NISTP);
1456         EC_POINT_free(G);
1457         EC_POINT_free(P);
1458         EC_POINT_free(Q);
1459         EC_POINT_free(Q_CHECK);
1460         BN_free(n);
1461         BN_free(m);
1462         BN_free(p);
1463         BN_free(a);
1464         BN_free(b);
1465         BN_free(x);
1466         BN_free(y);
1467         BN_free(order);
1468         BN_CTX_free(ctx);
1469         }
1470
1471 void nistp_tests()
1472         {
1473         unsigned i;
1474
1475         for (i = 0; i < sizeof(nistp_tests_params) / sizeof(struct nistp_test_params); i++)
1476                 {
1477                 nistp_single_test(&nistp_tests_params[i]);
1478                 }
1479         }
1480 #endif
1481
1482 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
1483
1484 int main(int argc, char *argv[])
1485         {
1486
1487         /* enable memory leak checking unless explicitly disabled */
1488         if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
1489                 {
1490                 CRYPTO_malloc_debug_init();
1491                 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
1492                 }
1493         else
1494                 {
1495                 /* OPENSSL_DEBUG_MEMORY=off */
1496                 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1497                 }
1498         CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
1499         ERR_load_crypto_strings();
1500
1501         RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
1502
1503         prime_field_tests();
1504         puts("");
1505 #ifndef OPENSSL_NO_EC2M
1506         char2_field_tests();
1507 #endif
1508 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1509         nistp_tests();
1510 #endif
1511         /* test the internal curves */
1512         internal_curve_test();
1513
1514 #ifndef OPENSSL_NO_ENGINE
1515         ENGINE_cleanup();
1516 #endif
1517         CRYPTO_cleanup_all_ex_data();
1518         ERR_free_strings();
1519         ERR_remove_thread_state(NULL);
1520         CRYPTO_mem_leaks_fp(stderr);
1521
1522         return 0;
1523         }
1524 #endif