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  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  57  *
  58  * Portions of the attached software ("Contribution") are developed by
  59  * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
  60  *
  61  * The Contribution is licensed pursuant to the OpenSSL open source
  62  * license provided above.
  63  *
  64  * In addition, Sun covenants to all licensees who provide a reciprocal
  65  * covenant with respect to their own patents if any, not to sue under
  66  * current and future patent claims necessarily infringed by the making,
  67  * using, practicing, selling, offering for sale and/or otherwise
  68  * disposing of the Contribution as delivered hereunder
  69  * (or portions thereof), provided that such covenant shall not apply:
  70  *  1) for code that a licensee deletes from the Contribution;
  71  *  2) separates from the Contribution; or
  72  *  3) for infringements caused by:
  73  *       i) the modification of the Contribution or
  74  *      ii) the combination of the Contribution with other software or
  75  *          devices where such combination causes the infringement.
  76  *
  77  * The elliptic curve binary polynomial software is originally written by
  78  * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
  79  *
  80  */
  81
  82 #include <stdio.h>
  83 #include <stdlib.h>
  84 #include <string.h>
  85 #include <time.h>
  86
  87
  88 #ifdef OPENSSL_NO_EC
  89 int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
  90 #else
  91
  92
  93 #include <openssl/ec.h>
  94 #include <openssl/engine.h>
  95 #include <openssl/err.h>
  96 #include <openssl/obj_mac.h>
  97
  98 #define ABORT do { \
  99         fflush(stdout); \
 100         fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
 101         ERR_print_errors_fp(stderr); \
 102         exit(1); \
 103 } while (0)
 104
 105 #if 0
 106 static void timings(EC_GROUP *group, int multi, BN_CTX *ctx)
 107         {
 108         clock_t clck;
 109         int i, j;
 110         BIGNUM *s;
 111         BIGNUM *r[10], *r0[10];
 112         EC_POINT *P;
 113
 114         s = BN_new();
 115         if (s == NULL) ABORT;
 116
 117         fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group));
 118         if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
 119         fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s));
 120         fflush(stdout);
 121
 122         P = EC_POINT_new(group);
 123         if (P == NULL) ABORT;
 124         EC_POINT_copy(P, EC_GROUP_get0_generator(group));
 125
 126         for (i = 0; i < 10; i++)
 127                 {
 128                 if ((r[i] = BN_new()) == NULL) ABORT;
 129                 if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT;
 130                 if (multi)
 131                         {
 132                         if ((r0[i] = BN_new()) == NULL) ABORT;
 133                         if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT;
 134                         }
 135                 }
 136
 137         clck = clock();
 138         for (i = 0; i < 10; i++)
 139                 {
 140                 for (j = 0; j < 10; j++)
 141                         {
 142                         if (!EC_POINT_mul(group, P, r[i], multi ? P : NULL, multi ? r0[i] : NULL, ctx)) ABORT;
 143                         }
 144                 }
 145         fprintf(stdout, "\n");
 146
 147         clck = clock() - clck;
 148
 149 #ifdef CLOCKS_PER_SEC
 150         /* "To determine the time in seconds, the value returned
 151          * by the clock function should be divided by the value
 152          * of the macro CLOCKS_PER_SEC."
 153          *                                       -- ISO/IEC 9899 */
 154 #       define UNIT "s"
 155 #else
 156         /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
 157          *                            -- cc on NeXTstep/OpenStep */
 158 #       define UNIT "units"
 159 #       define CLOCKS_PER_SEC 1
 160 #endif
 161
 162         fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
 163                 multi ? "s*P+t*Q operations" : "point multiplications",
 164                 (double)clck/CLOCKS_PER_SEC);
 165         fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
 166
 167         EC_POINT_free(P);
 168         BN_free(s);
 169         for (i = 0; i < 10; i++)
 170                 {
 171                 BN_free(r[i]);
 172                 if (multi) BN_free(r0[i]);
 173                 }
 174         }
 175 #endif
 176
 177 void prime_field_tests()
 178         {
 179         BN_CTX *ctx = NULL;
 180         BIGNUM *p, *a, *b;
 181         EC_GROUP *group;
 182         EC_GROUP *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
 183         EC_POINT *P, *Q, *R;
 184         BIGNUM *x, *y, *z;
 185         unsigned char buf[100];
 186         size_t i, len;
 187         int k;
 188
 189 #if 1 /* optional */
 190         ctx = BN_CTX_new();
 191         if (!ctx) ABORT;
 192 #endif
 193
 194         p = BN_new();
 195         a = BN_new();
 196         b = BN_new();
 197         if (!p || !a || !b) ABORT;
 198
 199         if (!BN_hex2bn(&p, "17")) ABORT;
 200         if (!BN_hex2bn(&a, "1")) ABORT;
 201         if (!BN_hex2bn(&b, "1")) ABORT;
 202
 203         group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
 204                                                      * so that the library gets to choose the EC_METHOD */
 205         if (!group) ABORT;
 206
 207         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 208
 209         {
 210                 EC_GROUP *tmp;
 211                 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
 212                 if (!tmp) ABORT;
 213                 if (!EC_GROUP_copy(tmp, group));
 214                 EC_GROUP_free(group);
 215                 group = tmp;
 216         }
 217
 218         if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
 219
 220         fprintf(stdout, "Curve defined by Weierstrass equation\n     y^2 = x^3 + a*x + b  (mod 0x");
 221         BN_print_fp(stdout, p);
 222         fprintf(stdout, ")\n     a = 0x");
 223         BN_print_fp(stdout, a);
 224         fprintf(stdout, "\n     b = 0x");
 225         BN_print_fp(stdout, b);
 226         fprintf(stdout, "\n");
 227
 228         P = EC_POINT_new(group);
 229         Q = EC_POINT_new(group);
 230         R = EC_POINT_new(group);
 231         if (!P || !Q || !R) ABORT;
 232
 233         if (!EC_POINT_set_to_infinity(group, P)) ABORT;
 234         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 235
 236         buf[0] = 0;
 237         if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
 238
 239         if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 240         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 241
 242         x = BN_new();
 243         y = BN_new();
 244         z = BN_new();
 245         if (!x || !y || !z) ABORT;
 246
 247         if (!BN_hex2bn(&x, "D")) ABORT;
 248         if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
 249         if (!EC_POINT_is_on_curve(group, Q, ctx))
 250                 {
 251                 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
 252                 fprintf(stderr, "Point is not on curve: x = 0x");
 253                 BN_print_fp(stderr, x);
 254                 fprintf(stderr, ", y = 0x");
 255                 BN_print_fp(stderr, y);
 256                 fprintf(stderr, "\n");
 257                 ABORT;
 258                 }
 259
 260         fprintf(stdout, "A cyclic subgroup:\n");
 261         k = 100;
 262         do
 263                 {
 264                 if (k-- == 0) ABORT;
 265
 266                 if (EC_POINT_is_at_infinity(group, P))
 267                         fprintf(stdout, "     point at infinity\n");
 268                 else
 269                         {
 270                         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 271
 272                         fprintf(stdout, "     x = 0x");
 273                         BN_print_fp(stdout, x);
 274                         fprintf(stdout, ", y = 0x");
 275                         BN_print_fp(stdout, y);
 276                         fprintf(stdout, "\n");
 277                         }
 278
 279                 if (!EC_POINT_copy(R, P)) ABORT;
 280                 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 281
 282 #if 0 /* optional */
 283                 {
 284                         EC_POINT *points[3];
 285
 286                         points[0] = R;
 287                         points[1] = Q;
 288                         points[2] = P;
 289                         if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
 290                 }
 291 #endif
 292
 293                 }
 294         while (!EC_POINT_is_at_infinity(group, P));
 295
 296         if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
 297         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 298
 299         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
 300         if (len == 0) ABORT;
 301         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 302         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 303         fprintf(stdout, "Generator as octect string, compressed form:\n     ");
 304         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 305
 306         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
 307         if (len == 0) ABORT;
 308         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 309         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 310         fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n     ");
 311         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 312
 313         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
 314         if (len == 0) ABORT;
 315         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 316         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 317         fprintf(stdout, "\nGenerator as octect string, hybrid form:\n     ");
 318         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 319
 320         if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
 321         fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n     X = 0x");
 322         BN_print_fp(stdout, x);
 323         fprintf(stdout, ", Y = 0x");
 324         BN_print_fp(stdout, y);
 325         fprintf(stdout, ", Z = 0x");
 326         BN_print_fp(stdout, z);
 327         fprintf(stdout, "\n");
 328
 329         if (!EC_POINT_invert(group, P, ctx)) ABORT;
 330         if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
 331
 332
 333         /* Curve P-192 (FIPS PUB 186-2, App. 6) */
 334
 335         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
 336         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 337         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
 338         if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
 339         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 340
 341         if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
 342         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 343         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 344         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
 345         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 346
 347         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 348         fprintf(stdout, "\nNIST curve P-192 -- Generator:\n     x = 0x");
 349         BN_print_fp(stdout, x);
 350         fprintf(stdout, "\n     y = 0x");
 351         BN_print_fp(stdout, y);
 352         fprintf(stdout, "\n");
 353         /* G_y value taken from the standard: */
 354         if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
 355         if (0 != BN_cmp(y, z)) ABORT;
 356
 357         fprintf(stdout, "verify degree ...");
 358         if (EC_GROUP_get_degree(group) != 192) ABORT;
 359         fprintf(stdout, " ok\n");
 360
 361         fprintf(stdout, "verify group order ...");
 362         fflush(stdout);
 363         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 364         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 365         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 366         fprintf(stdout, ".");
 367         fflush(stdout);
 368         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 369         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 370         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 371         fprintf(stdout, " ok\n");
 372
 373         if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 374         if (!EC_GROUP_copy(P_192, group)) ABORT;
 375
 376
 377         /* Curve P-224 (FIPS PUB 186-2, App. 6) */
 378
 379         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
 380         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 381         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
 382         if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
 383         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 384
 385         if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
 386         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
 387         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 388         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
 389         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 390
 391         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 392         fprintf(stdout, "\nNIST curve P-224 -- Generator:\n     x = 0x");
 393         BN_print_fp(stdout, x);
 394         fprintf(stdout, "\n     y = 0x");
 395         BN_print_fp(stdout, y);
 396         fprintf(stdout, "\n");
 397         /* G_y value taken from the standard: */
 398         if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
 399         if (0 != BN_cmp(y, z)) ABORT;
 400
 401         fprintf(stdout, "verify degree ...");
 402         if (EC_GROUP_get_degree(group) != 224) ABORT;
 403         fprintf(stdout, " ok\n");
 404
 405         fprintf(stdout, "verify group order ...");
 406         fflush(stdout);
 407         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 408         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 409         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 410         fprintf(stdout, ".");
 411         fflush(stdout);
 412         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 413         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 414         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 415         fprintf(stdout, " ok\n");
 416
 417         if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 418         if (!EC_GROUP_copy(P_224, group)) ABORT;
 419
 420
 421         /* Curve P-256 (FIPS PUB 186-2, App. 6) */
 422
 423         if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
 424         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 425         if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
 426         if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
 427         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 428
 429         if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
 430         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 431         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 432         if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
 433                 "84F3B9CAC2FC632551")) ABORT;
 434         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 435
 436         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 437         fprintf(stdout, "\nNIST curve P-256 -- Generator:\n     x = 0x");
 438         BN_print_fp(stdout, x);
 439         fprintf(stdout, "\n     y = 0x");
 440         BN_print_fp(stdout, y);
 441         fprintf(stdout, "\n");
 442         /* G_y value taken from the standard: */
 443         if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
 444         if (0 != BN_cmp(y, z)) ABORT;
 445
 446         fprintf(stdout, "verify degree ...");
 447         if (EC_GROUP_get_degree(group) != 256) ABORT;
 448         fprintf(stdout, " ok\n");
 449
 450         fprintf(stdout, "verify group order ...");
 451         fflush(stdout);
 452         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 453         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 454         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 455         fprintf(stdout, ".");
 456         fflush(stdout);
 457         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 458         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 459         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 460         fprintf(stdout, " ok\n");
 461
 462         if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 463         if (!EC_GROUP_copy(P_256, group)) ABORT;
 464
 465
 466         /* Curve P-384 (FIPS PUB 186-2, App. 6) */
 467
 468         if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 469                 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
 470         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 471         if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 472                 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
 473         if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
 474                 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
 475         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 476
 477         if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
 478                 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
 479         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
 480         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 481         if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 482                 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
 483         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 484
 485         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 486         fprintf(stdout, "\nNIST curve P-384 -- Generator:\n     x = 0x");
 487         BN_print_fp(stdout, x);
 488         fprintf(stdout, "\n     y = 0x");
 489         BN_print_fp(stdout, y);
 490         fprintf(stdout, "\n");
 491         /* G_y value taken from the standard: */
 492         if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
 493                 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
 494         if (0 != BN_cmp(y, z)) ABORT;
 495
 496         fprintf(stdout, "verify degree ...");
 497         if (EC_GROUP_get_degree(group) != 384) ABORT;
 498         fprintf(stdout, " ok\n");
 499
 500         fprintf(stdout, "verify group order ...");
 501         fflush(stdout);
 502         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 503         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 504         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 505         fprintf(stdout, ".");
 506         fflush(stdout);
 507         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 508         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 509         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 510         fprintf(stdout, " ok\n");
 511
 512         if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 513         if (!EC_GROUP_copy(P_384, group)) ABORT;
 514
 515
 516         /* Curve P-521 (FIPS PUB 186-2, App. 6) */
 517
 518         if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 519                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 520                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
 521         if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
 522         if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 523                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 524                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
 525         if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
 526                 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
 527                 "DF883D2C34F1EF451FD46B503F00")) ABORT;
 528         if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
 529
 530         if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
 531                 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
 532                 "3C1856A429BF97E7E31C2E5BD66")) ABORT;
 533         if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
 534         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 535         if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
 536                 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
 537                 "C9B8899C47AEBB6FB71E91386409")) ABORT;
 538         if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
 539
 540         if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
 541         fprintf(stdout, "\nNIST curve P-521 -- Generator:\n     x = 0x");
 542         BN_print_fp(stdout, x);
 543         fprintf(stdout, "\n     y = 0x");
 544         BN_print_fp(stdout, y);
 545         fprintf(stdout, "\n");
 546         /* G_y value taken from the standard: */
 547         if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
 548                 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
 549                 "7086A272C24088BE94769FD16650")) ABORT;
 550         if (0 != BN_cmp(y, z)) ABORT;
 551
 552         fprintf(stdout, "verify degree ...");
 553         if (EC_GROUP_get_degree(group) != 521) ABORT;
 554         fprintf(stdout, " ok\n");
 555
 556         fprintf(stdout, "verify group order ...");
 557         fflush(stdout);
 558         if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
 559         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 560         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 561         fprintf(stdout, ".");
 562         fflush(stdout);
 563         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
 564         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
 565         if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
 566         fprintf(stdout, " ok\n");
 567
 568         if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
 569         if (!EC_GROUP_copy(P_521, group)) ABORT;
 570
 571
 572         /* more tests using the last curve */
 573
 574         if (!EC_POINT_copy(Q, P)) ABORT;
 575         if (EC_POINT_is_at_infinity(group, Q)) ABORT;
 576         if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
 577         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
 578         if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
 579
 580         if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
 581         if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
 582         if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
 583
 584         {
 585                 const EC_POINT *points[3];
 586                 const BIGNUM *scalars[3];
 587
 588                 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
 589                 points[0] = Q;
 590                 points[1] = Q;
 591                 points[2] = Q;
 592
 593                 if (!BN_add(y, z, BN_value_one())) ABORT;
 594                 if (BN_is_odd(y)) ABORT;
 595                 if (!BN_rshift1(y, y)) ABORT;
 596                 scalars[0] = y; /* (group order + 1)/2,  so  y*Q + y*Q = Q */
 597                 scalars[1] = y;
 598
 599                 fprintf(stdout, "combined multiplication ...");
 600                 fflush(stdout);
 601
 602                 /* z is still the group order */
 603                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
 604                 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
 605                 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
 606                 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
 607
 608                 fprintf(stdout, ".");
 609                 fflush(stdout);
 610
 611                 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
 612                 if (!BN_add(z, z, y)) ABORT;
 613                 z->neg = 1;
 614                 scalars[0] = y;
 615                 scalars[1] = z; /* z = -(order + y) */
 616
 617                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
 618                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 619
 620                 fprintf(stdout, ".");
 621                 fflush(stdout);
 622
 623                 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
 624                 if (!BN_add(z, x, y)) ABORT;
 625                 z->neg = 1;
 626                 scalars[0] = x;
 627                 scalars[1] = y;
 628                 scalars[2] = z; /* z = -(x+y) */
 629
 630                 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
 631                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 632
 633                 fprintf(stdout, " ok\n\n");
 634         }
 635
 636
 637 #if 0
 638         timings(P_192, 0, ctx);
 639         timings(P_192, 1, ctx);
 640         timings(P_224, 0, ctx);
 641         timings(P_224, 1, ctx);
 642         timings(P_256, 0, ctx);
 643         timings(P_256, 1, ctx);
 644         timings(P_384, 0, ctx);
 645         timings(P_384, 1, ctx);
 646         timings(P_521, 0, ctx);
 647         timings(P_521, 1, ctx);
 648 #endif
 649
 650
 651         if (ctx)
 652                 BN_CTX_free(ctx);
 653         BN_free(p); BN_free(a); BN_free(b);
 654         EC_GROUP_free(group);
 655         EC_POINT_free(P);
 656         EC_POINT_free(Q);
 657         EC_POINT_free(R);
 658         BN_free(x); BN_free(y); BN_free(z);
 659
 660         if (P_192) EC_GROUP_free(P_192);
 661         if (P_224) EC_GROUP_free(P_224);
 662         if (P_256) EC_GROUP_free(P_256);
 663         if (P_384) EC_GROUP_free(P_384);
 664         if (P_521) EC_GROUP_free(P_521);
 665
 666         }
 667
 668 /* Change test based on whether binary point compression is enabled or not. */
 669 #ifdef OPENSSL_EC_BIN_PT_COMP
 670 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
 671         if (!BN_hex2bn(&x, _x)) ABORT; \
 672         if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
 673         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
 674         if (!BN_hex2bn(&z, _order)) ABORT; \
 675         if (!BN_hex2bn(&cof, _cof)) ABORT; \
 676         if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
 677         if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
 678         fprintf(stdout, "\n%s -- Generator:\n     x = 0x", _name); \
 679         BN_print_fp(stdout, x); \
 680         fprintf(stdout, "\n     y = 0x"); \
 681         BN_print_fp(stdout, y); \
 682         fprintf(stdout, "\n"); \
 683         /* G_y value taken from the standard: */ \
 684         if (!BN_hex2bn(&z, _y)) ABORT; \
 685         if (0 != BN_cmp(y, z)) ABORT;
 686 #else
 687 #define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
 688         if (!BN_hex2bn(&x, _x)) ABORT; \
 689         if (!BN_hex2bn(&y, _y)) ABORT; \
 690         if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
 691         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
 692         if (!BN_hex2bn(&z, _order)) ABORT; \
 693         if (!BN_hex2bn(&cof, _cof)) ABORT; \
 694         if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
 695         fprintf(stdout, "\n%s -- Generator:\n     x = 0x", _name); \
 696         BN_print_fp(stdout, x); \
 697         fprintf(stdout, "\n     y = 0x"); \
 698         BN_print_fp(stdout, y); \
 699         fprintf(stdout, "\n");
 700 #endif
 701
 702 #define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
 703         if (!BN_hex2bn(&p, _p)) ABORT; \
 704         if (!BN_hex2bn(&a, _a)) ABORT; \
 705         if (!BN_hex2bn(&b, _b)) ABORT; \
 706         if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
 707         CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
 708         fprintf(stdout, "verify degree ..."); \
 709         if (EC_GROUP_get_degree(group) != _degree) ABORT; \
 710         fprintf(stdout, " ok\n"); \
 711         fprintf(stdout, "verify group order ..."); \
 712         fflush(stdout); \
 713         if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \
 714         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
 715         if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
 716         fprintf(stdout, "."); \
 717         fflush(stdout); \
 718         if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; \
 719         if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \
 720         if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
 721         fprintf(stdout, " ok\n"); \
 722         if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
 723         if (!EC_GROUP_copy(_variable, group)) ABORT;
 724
 725 void char2_field_tests()
 726         {
 727         BN_CTX *ctx = NULL;
 728         BIGNUM *p, *a, *b;
 729         EC_GROUP *group;
 730         EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL;
 731         EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL;
 732         EC_POINT *P, *Q, *R;
 733         BIGNUM *x, *y, *z, *cof;
 734         unsigned char buf[100];
 735         size_t i, len;
 736         int k;
 737
 738 #if 1 /* optional */
 739         ctx = BN_CTX_new();
 740         if (!ctx) ABORT;
 741 #endif
 742
 743         p = BN_new();
 744         a = BN_new();
 745         b = BN_new();
 746         if (!p || !a || !b) ABORT;
 747
 748         if (!BN_hex2bn(&p, "13")) ABORT;
 749         if (!BN_hex2bn(&a, "3")) ABORT;
 750         if (!BN_hex2bn(&b, "1")) ABORT;
 751
 752         group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GFp
 753                                                      * so that the library gets to choose the EC_METHOD */
 754         if (!group) ABORT;
 755         if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT;
 756
 757         {
 758                 EC_GROUP *tmp;
 759                 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
 760                 if (!tmp) ABORT;
 761                 if (!EC_GROUP_copy(tmp, group));
 762                 EC_GROUP_free(group);
 763                 group = tmp;
 764         }
 765
 766         if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT;
 767
 768         fprintf(stdout, "Curve defined by Weierstrass equation\n     y^2 + x*y = x^3 + a*x^2 + b  (mod 0x");
 769         BN_print_fp(stdout, p);
 770         fprintf(stdout, ")\n     a = 0x");
 771         BN_print_fp(stdout, a);
 772         fprintf(stdout, "\n     b = 0x");
 773         BN_print_fp(stdout, b);
 774         fprintf(stdout, "\n");
 775
 776         P = EC_POINT_new(group);
 777         Q = EC_POINT_new(group);
 778         R = EC_POINT_new(group);
 779         if (!P || !Q || !R) ABORT;
 780
 781         if (!EC_POINT_set_to_infinity(group, P)) ABORT;
 782         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 783
 784         buf[0] = 0;
 785         if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
 786
 787         if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 788         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 789
 790         x = BN_new();
 791         y = BN_new();
 792         z = BN_new();
 793         cof = BN_new();
 794         if (!x || !y || !z || !cof) ABORT;
 795
 796         if (!BN_hex2bn(&x, "6")) ABORT;
 797 /* Change test based on whether binary point compression is enabled or not. */
 798 #ifdef OPENSSL_EC_BIN_PT_COMP
 799         if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT;
 800 #else
 801         if (!BN_hex2bn(&y, "8")) ABORT;
 802         if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
 803 #endif
 804         if (!EC_POINT_is_on_curve(group, Q, ctx))
 805                 {
 806 /* Change test based on whether binary point compression is enabled or not. */
 807 #ifdef OPENSSL_EC_BIN_PT_COMP
 808                 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
 809 #endif
 810                 fprintf(stderr, "Point is not on curve: x = 0x");
 811                 BN_print_fp(stderr, x);
 812                 fprintf(stderr, ", y = 0x");
 813                 BN_print_fp(stderr, y);
 814                 fprintf(stderr, "\n");
 815                 ABORT;
 816                 }
 817
 818         fprintf(stdout, "A cyclic subgroup:\n");
 819         k = 100;
 820         do
 821                 {
 822                 if (k-- == 0) ABORT;
 823
 824                 if (EC_POINT_is_at_infinity(group, P))
 825                         fprintf(stdout, "     point at infinity\n");
 826                 else
 827                         {
 828                         if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT;
 829
 830                         fprintf(stdout, "     x = 0x");
 831                         BN_print_fp(stdout, x);
 832                         fprintf(stdout, ", y = 0x");
 833                         BN_print_fp(stdout, y);
 834                         fprintf(stdout, "\n");
 835                         }
 836
 837                 if (!EC_POINT_copy(R, P)) ABORT;
 838                 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
 839                 }
 840         while (!EC_POINT_is_at_infinity(group, P));
 841
 842         if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
 843         if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 844
 845 /* Change test based on whether binary point compression is enabled or not. */
 846 #ifdef OPENSSL_EC_BIN_PT_COMP
 847         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
 848         if (len == 0) ABORT;
 849         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 850         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 851         fprintf(stdout, "Generator as octet string, compressed form:\n     ");
 852         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 853 #endif
 854
 855         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
 856         if (len == 0) ABORT;
 857         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 858         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 859         fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n     ");
 860         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 861
 862 /* Change test based on whether binary point compression is enabled or not. */
 863 #ifdef OPENSSL_EC_BIN_PT_COMP
 864         len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
 865         if (len == 0) ABORT;
 866         if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
 867         if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
 868         fprintf(stdout, "\nGenerator as octet string, hybrid form:\n     ");
 869         for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
 870 #endif
 871
 872         fprintf(stdout, "\n");
 873
 874         if (!EC_POINT_invert(group, P, ctx)) ABORT;
 875         if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
 876
 877
 878         /* Curve K-163 (FIPS PUB 186-2, App. 6) */
 879         CHAR2_CURVE_TEST
 880                 (
 881                 "NIST curve K-163",
 882                 "0800000000000000000000000000000000000000C9",
 883                 "1",
 884                 "1",
 885                 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
 886                 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
 887                 1,
 888                 "04000000000000000000020108A2E0CC0D99F8A5EF",
 889                 "2",
 890                 163,
 891                 C2_K163
 892                 );
 893
 894         /* Curve B-163 (FIPS PUB 186-2, App. 6) */
 895         CHAR2_CURVE_TEST
 896                 (
 897                 "NIST curve B-163",
 898                 "0800000000000000000000000000000000000000C9",
 899                 "1",
 900                 "020A601907B8C953CA1481EB10512F78744A3205FD",
 901                 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
 902                 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
 903                 1,
 904                 "040000000000000000000292FE77E70C12A4234C33",
 905                 "2",
 906                 163,
 907                 C2_B163
 908                 );
 909
 910         /* Curve K-233 (FIPS PUB 186-2, App. 6) */
 911         CHAR2_CURVE_TEST
 912                 (
 913                 "NIST curve K-233",
 914                 "020000000000000000000000000000000000000004000000000000000001",
 915                 "0",
 916                 "1",
 917                 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
 918                 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
 919                 0,
 920                 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
 921                 "4",
 922                 233,
 923                 C2_K233
 924                 );
 925
 926         /* Curve B-233 (FIPS PUB 186-2, App. 6) */
 927         CHAR2_CURVE_TEST
 928                 (
 929                 "NIST curve B-233",
 930                 "020000000000000000000000000000000000000004000000000000000001",
 931                 "000000000000000000000000000000000000000000000000000000000001",
 932                 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
 933                 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
 934                 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
 935                 1,
 936                 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
 937                 "2",
 938                 233,
 939                 C2_B233
 940                 );
 941
 942         /* Curve K-283 (FIPS PUB 186-2, App. 6) */
 943         CHAR2_CURVE_TEST
 944                 (
 945                 "NIST curve K-283",
 946                 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
 947                 "0",
 948                 "1",
 949                 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
 950                 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
 951                 0,
 952                 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
 953                 "4",
 954                 283,
 955                 C2_K283
 956                 );
 957
 958         /* Curve B-283 (FIPS PUB 186-2, App. 6) */
 959         CHAR2_CURVE_TEST
 960                 (
 961                 "NIST curve B-283",
 962                 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
 963                 "000000000000000000000000000000000000000000000000000000000000000000000001",
 964                 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
 965                 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
 966                 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
 967                 1,
 968                 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
 969                 "2",
 970                 283,
 971                 C2_B283
 972                 );
 973
 974         /* Curve K-409 (FIPS PUB 186-2, App. 6) */
 975         CHAR2_CURVE_TEST
 976                 (
 977                 "NIST curve K-409",
 978                 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
 979                 "0",
 980                 "1",
 981                 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
 982                 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
 983                 1,
 984                 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
 985                 "4",
 986                 409,
 987                 C2_K409
 988                 );
 989
 990         /* Curve B-409 (FIPS PUB 186-2, App. 6) */
 991         CHAR2_CURVE_TEST
 992                 (
 993                 "NIST curve B-409",
 994                 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
 995                 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
 996                 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
 997                 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
 998                 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
 999                 1,
1000                 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1001                 "2",
1002                 409,
1003                 C2_B409
1004                 );
1005
1006         /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1007         CHAR2_CURVE_TEST
1008                 (
1009                 "NIST curve K-571",
1010                 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1011                 "0",
1012                 "1",
1013                 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1014                 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1015                 0,
1016                 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1017                 "4",
1018                 571,
1019                 C2_K571
1020                 );
1021
1022         /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1023         CHAR2_CURVE_TEST
1024                 (
1025                 "NIST curve B-571",
1026                 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1027                 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1028                 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1029                 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1030                 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1031                 1,
1032                 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1033                 "2",
1034                 571,
1035                 C2_B571
1036                 );
1037
1038         /* more tests using the last curve */
1039
1040         if (!EC_POINT_copy(Q, P)) ABORT;
1041         if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1042         if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
1043         if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
1044         if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
1045
1046         if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
1047         if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
1048         if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
1049
1050         {
1051                 const EC_POINT *points[3];
1052                 const BIGNUM *scalars[3];
1053
1054                 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
1055                 points[0] = Q;
1056                 points[1] = Q;
1057                 points[2] = Q;
1058
1059                 if (!BN_add(y, z, BN_value_one())) ABORT;
1060                 if (BN_is_odd(y)) ABORT;
1061                 if (!BN_rshift1(y, y)) ABORT;
1062                 scalars[0] = y; /* (group order + 1)/2,  so  y*Q + y*Q = Q */
1063                 scalars[1] = y;
1064
1065                 fprintf(stdout, "combined multiplication ...");
1066                 fflush(stdout);
1067
1068                 /* z is still the group order */
1069                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1070                 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
1071                 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
1072                 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
1073
1074                 fprintf(stdout, ".");
1075                 fflush(stdout);
1076
1077                 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
1078                 if (!BN_add(z, z, y)) ABORT;
1079                 z->neg = 1;
1080                 scalars[0] = y;
1081                 scalars[1] = z; /* z = -(order + y) */
1082
1083                 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
1084                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1085
1086                 fprintf(stdout, ".");
1087                 fflush(stdout);
1088
1089                 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
1090                 if (!BN_add(z, x, y)) ABORT;
1091                 z->neg = 1;
1092                 scalars[0] = x;
1093                 scalars[1] = y;
1094                 scalars[2] = z; /* z = -(x+y) */
1095
1096                 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
1097                 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
1098
1099                 fprintf(stdout, " ok\n\n");
1100         }
1101
1102
1103 #if 0
1104         timings(C2_K163, 0, ctx);
1105         timings(C2_K163, 1, ctx);
1106         timings(C2_B163, 0, ctx);
1107         timings(C2_B163, 1, ctx);
1108         timings(C2_K233, 0, ctx);
1109         timings(C2_K233, 1, ctx);
1110         timings(C2_B233, 0, ctx);
1111         timings(C2_B233, 1, ctx);
1112         timings(C2_K283, 0, ctx);
1113         timings(C2_K283, 1, ctx);
1114         timings(C2_B283, 0, ctx);
1115         timings(C2_B283, 1, ctx);
1116         timings(C2_K409, 0, ctx);
1117         timings(C2_K409, 1, ctx);
1118         timings(C2_B409, 0, ctx);
1119         timings(C2_B409, 1, ctx);
1120         timings(C2_K571, 0, ctx);
1121         timings(C2_K571, 1, ctx);
1122         timings(C2_B571, 0, ctx);
1123         timings(C2_B571, 1, ctx);
1124 #endif
1125
1126
1127         if (ctx)
1128                 BN_CTX_free(ctx);
1129         BN_free(p); BN_free(a); BN_free(b);
1130         EC_GROUP_free(group);
1131         EC_POINT_free(P);
1132         EC_POINT_free(Q);
1133         EC_POINT_free(R);
1134         BN_free(x); BN_free(y); BN_free(z); BN_free(cof);
1135
1136         if (C2_K163) EC_GROUP_free(C2_K163);
1137         if (C2_B163) EC_GROUP_free(C2_B163);
1138         if (C2_K233) EC_GROUP_free(C2_K233);
1139         if (C2_B233) EC_GROUP_free(C2_B233);
1140         if (C2_K283) EC_GROUP_free(C2_K283);
1141         if (C2_B283) EC_GROUP_free(C2_B283);
1142         if (C2_K409) EC_GROUP_free(C2_K409);
1143         if (C2_B409) EC_GROUP_free(C2_B409);
1144         if (C2_K571) EC_GROUP_free(C2_K571);
1145         if (C2_B571) EC_GROUP_free(C2_B571);
1146
1147         }
1148
1149 static const char rnd_seed[] = "string to make the random number generator think it has entropy";
1150
1151 int main(int argc, char *argv[])
1152         {
1153
1154         /* enable memory leak checking unless explicitly disabled */
1155         if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
1156                 {
1157                 CRYPTO_malloc_debug_init();
1158                 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
1159                 }
1160         else
1161                 {
1162                 /* OPENSSL_DEBUG_MEMORY=off */
1163                 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1164                 }
1165         CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
1166         ERR_load_crypto_strings();
1167
1168         RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
1169
1170         prime_field_tests();
1171         char2_field_tests();
1172
1173         ENGINE_cleanup();
1174         CRYPTO_cleanup_all_ex_data();
1175         ERR_free_strings();
1176         ERR_remove_state(0);
1177         CRYPTO_mem_leaks_fp(stderr);
1178
1179         return 0;
1180         }
1181 #endif