1 /* crypto/ec/ectest.c */
2 /* ====================================================================
3 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
31 * 6. Redistributions of any form whatsoever must retain the following
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
62 int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
66 #include <openssl/ec.h>
67 #include <openssl/err.h>
71 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
72 ERR_print_errors_fp(stderr); \
77 void timings(EC_GROUP *group, int simult, BN_CTX *ctx)
86 if (s == NULL || s0 == NULL) ABORT;
88 if (!EC_GROUP_get_curve_GFp(group, s, NULL, NULL, ctx)) ABORT;
89 fprintf(stdout, "Timings for %d bit prime, ", (int)BN_num_bits(s));
90 if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
91 fprintf(stdout, "%d bit scalars ", (int)BN_num_bits(s));
94 P = EC_POINT_new(group);
96 EC_POINT_copy(P, EC_GROUP_get0_generator(group));
99 for (i = 0; i < 10; i++)
101 if (!BN_pseudo_rand(s, BN_num_bits(s), 0, 0)) ABORT;
104 if (!BN_pseudo_rand(s0, BN_num_bits(s), 0, 0)) ABORT;
106 for (j = 0; j < 10; j++)
108 if (!EC_POINT_mul(group, P, s, simult ? P : NULL, simult ? s0 : NULL, ctx)) ABORT;
110 fprintf(stdout, ".");
113 fprintf(stdout, "\n");
115 clck = clock() - clck;
117 #ifdef CLOCKS_PER_SEC
118 /* "To determine the time in seconds, the value returned
119 * by the clock function should be divided by the value
120 * of the macro CLOCKS_PER_SEC."
124 /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
125 * -- cc on NeXTstep/OpenStep */
126 # define UNIT "units"
127 # define CLOCKS_PER_SEC 1
130 fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
131 simult ? "s*P+t*Q operations" : "point multiplications",
132 (double)clck/CLOCKS_PER_SEC);
133 fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
141 int main(int argc, char *argv[])
146 EC_GROUP *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
149 unsigned char buf[100];
153 /* enable memory leak checking unless explicitly disabled */
154 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
156 CRYPTO_malloc_debug_init();
157 CRYPTO_dbg_set_options(V_CRYPTO_MDEBUG_ALL);
159 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
160 ERR_load_crypto_strings();
170 if (!p || !a || !b) ABORT;
172 if (!BN_hex2bn(&p, "17")) ABORT;
173 if (!BN_hex2bn(&a, "1")) ABORT;
174 if (!BN_hex2bn(&b, "1")) ABORT;
176 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
177 * so that the library gets to choose the EC_METHOD */
180 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
184 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
186 if (!EC_GROUP_copy(tmp, group));
187 EC_GROUP_free(group);
191 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
193 fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
194 BN_print_fp(stdout, p);
195 fprintf(stdout, ")\n a = 0x");
196 BN_print_fp(stdout, a);
197 fprintf(stdout, "\n b = 0x");
198 BN_print_fp(stdout, b);
199 fprintf(stdout, "\n");
201 P = EC_POINT_new(group);
202 Q = EC_POINT_new(group);
203 R = EC_POINT_new(group);
204 if (!P || !Q || !R) ABORT;
206 if (!EC_POINT_set_to_infinity(group, P)) ABORT;
207 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
210 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
212 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
213 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
218 if (!x || !y || !z) ABORT;
220 if (!BN_hex2bn(&x, "D")) ABORT;
221 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
222 if (!EC_POINT_is_on_curve(group, Q, ctx))
224 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
225 fprintf(stderr, "Point is not on curve: x = 0x");
226 BN_print_fp(stderr, x);
227 fprintf(stderr, ", y = 0x");
228 BN_print_fp(stderr, y);
229 fprintf(stderr, "\n");
233 fprintf(stdout, "A cyclic subgroup:\n");
239 if (EC_POINT_is_at_infinity(group, P))
240 fprintf(stdout, " point at infinity\n");
243 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
245 fprintf(stdout, " x = 0x");
246 BN_print_fp(stdout, x);
247 fprintf(stdout, ", y = 0x");
248 BN_print_fp(stdout, y);
249 fprintf(stdout, "\n");
252 if (!EC_POINT_copy(R, P)) ABORT;
253 if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
262 if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
267 while (!EC_POINT_is_at_infinity(group, P));
269 if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
270 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
272 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
274 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
275 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
276 fprintf(stdout, "Generator as octect string, compressed form:\n ");
277 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
279 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
281 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
282 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
283 fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n ");
284 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
286 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
288 if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
289 if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
290 fprintf(stdout, "\nGenerator as octect string, hybrid form:\n ");
291 for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
293 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
294 fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
295 BN_print_fp(stdout, x);
296 fprintf(stdout, ", Y = 0x");
297 BN_print_fp(stdout, y);
298 fprintf(stdout, ", Z = 0x");
299 BN_print_fp(stdout, z);
300 fprintf(stdout, "\n");
302 if (!EC_POINT_invert(group, P, ctx)) ABORT;
303 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
306 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
308 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
309 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
310 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
311 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
312 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
314 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
315 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
316 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
317 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
318 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
320 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
321 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
322 BN_print_fp(stdout, x);
323 fprintf(stdout, "\n y = 0x");
324 BN_print_fp(stdout, y);
325 fprintf(stdout, "\n");
326 /* G_y value taken from the standard: */
327 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
328 if (0 != BN_cmp(y, z)) ABORT;
330 fprintf(stdout, "verify group order ...");
332 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
333 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
334 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
335 fprintf(stdout, ".");
337 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
338 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
339 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
340 fprintf(stdout, " ok\n");
342 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
343 if (!EC_GROUP_copy(P_192, group)) ABORT;
346 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
348 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
349 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
350 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
351 if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
352 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
354 if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
355 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
356 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
357 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
358 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
360 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
361 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
362 BN_print_fp(stdout, x);
363 fprintf(stdout, "\n y = 0x");
364 BN_print_fp(stdout, y);
365 fprintf(stdout, "\n");
366 /* G_y value taken from the standard: */
367 if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
368 if (0 != BN_cmp(y, z)) ABORT;
370 fprintf(stdout, "verify group order ...");
372 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
373 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
374 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
375 fprintf(stdout, ".");
377 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
378 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
379 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
380 fprintf(stdout, " ok\n");
382 if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
383 if (!EC_GROUP_copy(P_224, group)) ABORT;
386 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
388 if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
389 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
390 if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
391 if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
392 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
394 if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
395 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
396 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
397 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
398 "84F3B9CAC2FC632551")) ABORT;
399 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
401 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
402 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
403 BN_print_fp(stdout, x);
404 fprintf(stdout, "\n y = 0x");
405 BN_print_fp(stdout, y);
406 fprintf(stdout, "\n");
407 /* G_y value taken from the standard: */
408 if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
409 if (0 != BN_cmp(y, z)) ABORT;
411 fprintf(stdout, "verify group order ...");
413 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
414 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
415 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
416 fprintf(stdout, ".");
418 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
419 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
420 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
421 fprintf(stdout, " ok\n");
423 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
424 if (!EC_GROUP_copy(P_256, group)) ABORT;
427 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
429 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
430 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
431 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
432 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
433 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
434 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
435 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
436 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
438 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
439 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
440 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
441 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
442 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
443 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
444 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
446 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
447 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x");
448 BN_print_fp(stdout, x);
449 fprintf(stdout, "\n y = 0x");
450 BN_print_fp(stdout, y);
451 fprintf(stdout, "\n");
452 /* G_y value taken from the standard: */
453 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
454 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
455 if (0 != BN_cmp(y, z)) ABORT;
457 fprintf(stdout, "verify group order ...");
459 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
460 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
461 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
462 fprintf(stdout, ".");
464 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
465 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
466 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
467 fprintf(stdout, " ok\n");
469 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
470 if (!EC_GROUP_copy(P_384, group)) ABORT;
473 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
475 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
476 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
477 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
478 if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
479 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
480 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
481 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
482 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
483 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
484 "DF883D2C34F1EF451FD46B503F00")) ABORT;
485 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
487 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
488 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
489 "3C1856A429BF97E7E31C2E5BD66")) ABORT;
490 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
491 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
492 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
493 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
494 "C9B8899C47AEBB6FB71E91386409")) ABORT;
495 if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
497 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
498 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
499 BN_print_fp(stdout, x);
500 fprintf(stdout, "\n y = 0x");
501 BN_print_fp(stdout, y);
502 fprintf(stdout, "\n");
503 /* G_y value taken from the standard: */
504 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
505 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
506 "7086A272C24088BE94769FD16650")) ABORT;
507 if (0 != BN_cmp(y, z)) ABORT;
509 fprintf(stdout, "verify group order ...");
511 if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
512 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
513 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
514 fprintf(stdout, ".");
516 if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
517 if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
518 if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
519 fprintf(stdout, " ok\n");
521 if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
522 if (!EC_GROUP_copy(P_521, group)) ABORT;
525 /* more tests using the last curve */
527 if (!EC_POINT_copy(Q, P)) ABORT;
528 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
529 if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
530 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
531 if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
533 if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
534 if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
535 if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
538 const EC_POINT *points[3];
539 const BIGNUM *scalars[3];
541 if (EC_POINT_is_at_infinity(group, Q)) ABORT;
546 if (!BN_add(y, z, BN_value_one())) ABORT;
547 if (BN_is_odd(y)) ABORT;
548 if (!BN_rshift1(y, y)) ABORT;
549 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
552 fprintf(stdout, "simultaneous multiplication ...");
555 /* z is still the group order */
556 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
557 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
558 if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
559 if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
561 fprintf(stdout, ".");
564 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
565 if (!BN_copy(z, y)) ABORT;
568 scalars[1] = z; /* z = -y */
570 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
571 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
573 fprintf(stdout, ".");
576 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
577 if (!BN_add(z, x, y)) ABORT;
581 scalars[2] = z; /* z = -(x+y) */
583 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
584 if (!EC_POINT_is_at_infinity(group, P)) ABORT;
586 fprintf(stdout, " ok\n\n");
591 timings(P_192, 0, ctx);
592 timings(P_192, 1, ctx);
593 timings(P_224, 0, ctx);
594 timings(P_224, 1, ctx);
595 timings(P_256, 0, ctx);
596 timings(P_256, 1, ctx);
597 timings(P_384, 0, ctx);
598 timings(P_384, 1, ctx);
599 timings(P_521, 0, ctx);
600 timings(P_521, 1, ctx);
606 BN_free(p); BN_free(a); BN_free(b);
607 EC_GROUP_free(group);
611 BN_free(x); BN_free(y); BN_free(z);
613 if (P_192) EC_GROUP_free(P_192);
614 if (P_224) EC_GROUP_free(P_224);
615 if (P_256) EC_GROUP_free(P_256);
616 if (P_384) EC_GROUP_free(P_384);
617 if (P_521) EC_GROUP_free(P_521);
621 CRYPTO_mem_leaks_fp(stderr);