1 /* crypto/ec/ectest.c */
3 * Originally written by Bodo Moeller for the OpenSSL project.
5 /* ====================================================================
6 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
34 * 6. Redistributions of any form whatsoever must retain the following
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
58 /* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
61 * Portions of the attached software ("Contribution") are developed by
62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
64 * The Contribution is licensed pursuant to the OpenSSL open source
65 * license provided above.
67 * The elliptic curve binary polynomial software is originally written by
68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
83 int main(int argc, char *argv[])
85 puts("Elliptic curves are disabled.");
90 # include <openssl/ec.h>
91 # ifndef OPENSSL_NO_ENGINE
92 # include <openssl/engine.h>
94 # include <openssl/err.h>
95 # include <openssl/obj_mac.h>
96 # include <openssl/objects.h>
97 # include <openssl/rand.h>
98 # include <openssl/bn.h>
99 # include <openssl/opensslconf.h>
101 # if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12)
102 /* suppress "too big too optimize" warning */
103 # pragma warning(disable:4959)
106 # define ABORT do { \
108 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
109 ERR_print_errors_fp(stderr); \
113 # define TIMING_BASE_PT 0
114 # define TIMING_RAND_PT 1
115 # define TIMING_SIMUL 2
117 /* test multiplication with group order, long and negative scalars */
118 static void group_order_tests(EC_GROUP *group)
120 BIGNUM *n1, *n2, *order;
121 EC_POINT *P = EC_POINT_new(group);
122 EC_POINT *Q = EC_POINT_new(group);
123 BN_CTX *ctx = BN_CTX_new();
129 fprintf(stdout, "verify group order ...");
131 if (!EC_GROUP_get_order(group, order, ctx))
133 if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
135 if (!EC_POINT_is_at_infinity(group, Q))
137 fprintf(stdout, ".");
139 if (!EC_GROUP_precompute_mult(group, ctx))
141 if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
143 if (!EC_POINT_is_at_infinity(group, Q))
145 fprintf(stdout, " ok\n");
146 fprintf(stdout, "long/negative scalar tests ");
147 for (i = 1; i <= 2; i++) {
148 const BIGNUM *scalars[6];
149 const EC_POINT *points[6];
151 fprintf(stdout, i == 1 ?
152 "allowing precomputation ... " :
153 "without precomputation ... ");
154 if (!BN_set_word(n1, i))
157 * If i == 1, P will be the predefined generator for which
158 * EC_GROUP_precompute_mult has set up precomputation.
160 if (!EC_POINT_mul(group, P, n1, NULL, NULL, ctx))
166 if (!BN_sub(n1, n1, order))
168 if (!EC_POINT_mul(group, Q, NULL, P, n1, ctx))
170 if (0 != EC_POINT_cmp(group, Q, P, ctx))
174 if (!BN_add(n2, order, BN_value_one()))
176 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx))
178 if (0 != EC_POINT_cmp(group, Q, P, ctx))
181 /* n2 = (1 - order) * (1 + order) = 1 - order^2 */
182 if (!BN_mul(n2, n1, n2, ctx))
184 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx))
186 if (0 != EC_POINT_cmp(group, Q, P, ctx))
189 /* n2 = order^2 - 1 */
190 BN_set_negative(n2, 0);
191 if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx))
193 /* Add P to verify the result. */
194 if (!EC_POINT_add(group, Q, Q, P, ctx))
196 if (!EC_POINT_is_at_infinity(group, Q))
199 /* Exercise EC_POINTs_mul, including corner cases. */
200 if (EC_POINT_is_at_infinity(group, P))
203 points[0] = Q; /* => infinity */
205 points[1] = P; /* => -P */
207 points[2] = Q; /* => infinity */
209 points[3] = Q; /* => infinity */
211 points[4] = P; /* => P */
213 points[5] = Q; /* => infinity */
214 if (!EC_POINTs_mul(group, P, NULL, 6, points, scalars, ctx))
216 if (!EC_POINT_is_at_infinity(group, P))
219 fprintf(stdout, "ok\n");
229 static void prime_field_tests(void)
234 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 =
235 NULL, *P_384 = NULL, *P_521 = NULL;
238 unsigned char buf[100];
252 if (!BN_hex2bn(&p, "17"))
254 if (!BN_hex2bn(&a, "1"))
256 if (!BN_hex2bn(&b, "1"))
259 group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use
260 * EC_GROUP_new_curve_GFp so
261 * that the library gets to
262 * choose the EC_METHOD */
266 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
271 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
274 if (!EC_GROUP_copy(tmp, group))
276 EC_GROUP_free(group);
280 if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx))
284 "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
285 BN_print_fp(stdout, p);
286 fprintf(stdout, ")\n a = 0x");
287 BN_print_fp(stdout, a);
288 fprintf(stdout, "\n b = 0x");
289 BN_print_fp(stdout, b);
290 fprintf(stdout, "\n");
292 P = EC_POINT_new(group);
293 Q = EC_POINT_new(group);
294 R = EC_POINT_new(group);
298 if (!EC_POINT_set_to_infinity(group, P))
300 if (!EC_POINT_is_at_infinity(group, P))
304 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx))
307 if (!EC_POINT_add(group, P, P, Q, ctx))
309 if (!EC_POINT_is_at_infinity(group, P))
318 if (!BN_hex2bn(&x, "D"))
320 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx))
322 if (!EC_POINT_is_on_curve(group, Q, ctx)) {
323 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx))
325 fprintf(stderr, "Point is not on curve: x = 0x");
326 BN_print_fp(stderr, x);
327 fprintf(stderr, ", y = 0x");
328 BN_print_fp(stderr, y);
329 fprintf(stderr, "\n");
333 fprintf(stdout, "A cyclic subgroup:\n");
339 if (EC_POINT_is_at_infinity(group, P))
340 fprintf(stdout, " point at infinity\n");
342 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
345 fprintf(stdout, " x = 0x");
346 BN_print_fp(stdout, x);
347 fprintf(stdout, ", y = 0x");
348 BN_print_fp(stdout, y);
349 fprintf(stdout, "\n");
352 if (!EC_POINT_copy(R, P))
354 if (!EC_POINT_add(group, P, P, Q, ctx))
358 while (!EC_POINT_is_at_infinity(group, P));
360 if (!EC_POINT_add(group, P, Q, R, ctx))
362 if (!EC_POINT_is_at_infinity(group, P))
366 EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf,
370 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
372 if (0 != EC_POINT_cmp(group, P, Q, ctx))
374 fprintf(stdout, "Generator as octet string, compressed form:\n ");
375 for (i = 0; i < len; i++)
376 fprintf(stdout, "%02X", buf[i]);
379 EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf,
383 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
385 if (0 != EC_POINT_cmp(group, P, Q, ctx))
387 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
388 for (i = 0; i < len; i++)
389 fprintf(stdout, "%02X", buf[i]);
392 EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf,
396 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
398 if (0 != EC_POINT_cmp(group, P, Q, ctx))
400 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
401 for (i = 0; i < len; i++)
402 fprintf(stdout, "%02X", buf[i]);
404 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx))
407 "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
408 BN_print_fp(stdout, x);
409 fprintf(stdout, ", Y = 0x");
410 BN_print_fp(stdout, y);
411 fprintf(stdout, ", Z = 0x");
412 BN_print_fp(stdout, z);
413 fprintf(stdout, "\n");
415 if (!EC_POINT_invert(group, P, ctx))
417 if (0 != EC_POINT_cmp(group, P, R, ctx))
421 * Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2,
422 * 2000) -- not a NIST curve, but commonly used
425 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"))
427 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
429 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"))
431 if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45"))
433 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
436 if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82"))
438 if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32"))
440 if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx))
442 if (!EC_POINT_is_on_curve(group, P, ctx))
444 if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257"))
446 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
449 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
451 fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
452 BN_print_fp(stdout, x);
453 fprintf(stdout, "\n y = 0x");
454 BN_print_fp(stdout, y);
455 fprintf(stdout, "\n");
456 /* G_y value taken from the standard: */
457 if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32"))
459 if (0 != BN_cmp(y, z))
462 fprintf(stdout, "verify degree ...");
463 if (EC_GROUP_get_degree(group) != 160)
465 fprintf(stdout, " ok\n");
467 group_order_tests(group);
469 if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group))))
471 if (!EC_GROUP_copy(P_160, group))
474 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
476 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"))
478 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
480 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"))
482 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"))
484 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
487 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"))
489 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx))
491 if (!EC_POINT_is_on_curve(group, P, ctx))
493 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"))
495 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
498 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
500 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
501 BN_print_fp(stdout, x);
502 fprintf(stdout, "\n y = 0x");
503 BN_print_fp(stdout, y);
504 fprintf(stdout, "\n");
505 /* G_y value taken from the standard: */
506 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"))
508 if (0 != BN_cmp(y, z))
511 fprintf(stdout, "verify degree ...");
512 if (EC_GROUP_get_degree(group) != 192)
514 fprintf(stdout, " ok\n");
516 group_order_tests(group);
518 if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group))))
520 if (!EC_GROUP_copy(P_192, group))
523 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
526 (&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"))
528 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
531 (&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"))
534 (&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"))
536 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
540 (&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"))
542 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx))
544 if (!EC_POINT_is_on_curve(group, P, ctx))
547 (&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"))
549 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
552 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
554 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
555 BN_print_fp(stdout, x);
556 fprintf(stdout, "\n y = 0x");
557 BN_print_fp(stdout, y);
558 fprintf(stdout, "\n");
559 /* G_y value taken from the standard: */
561 (&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"))
563 if (0 != BN_cmp(y, z))
566 fprintf(stdout, "verify degree ...");
567 if (EC_GROUP_get_degree(group) != 224)
569 fprintf(stdout, " ok\n");
571 group_order_tests(group);
573 if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group))))
575 if (!EC_GROUP_copy(P_224, group))
578 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
582 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"))
584 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
588 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC"))
592 "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"))
594 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
599 "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"))
601 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx))
603 if (!EC_POINT_is_on_curve(group, P, ctx))
605 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
606 "84F3B9CAC2FC632551"))
608 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
611 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
613 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
614 BN_print_fp(stdout, x);
615 fprintf(stdout, "\n y = 0x");
616 BN_print_fp(stdout, y);
617 fprintf(stdout, "\n");
618 /* G_y value taken from the standard: */
621 "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"))
623 if (0 != BN_cmp(y, z))
626 fprintf(stdout, "verify degree ...");
627 if (EC_GROUP_get_degree(group) != 256)
629 fprintf(stdout, " ok\n");
631 group_order_tests(group);
633 if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group))))
635 if (!EC_GROUP_copy(P_256, group))
638 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
640 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
641 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"))
643 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
645 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
646 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC"))
648 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
649 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"))
651 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
654 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
655 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7"))
657 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx))
659 if (!EC_POINT_is_on_curve(group, P, ctx))
661 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
662 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"))
664 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
667 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
669 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x");
670 BN_print_fp(stdout, x);
671 fprintf(stdout, "\n y = 0x");
672 BN_print_fp(stdout, y);
673 fprintf(stdout, "\n");
674 /* G_y value taken from the standard: */
675 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
676 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"))
678 if (0 != BN_cmp(y, z))
681 fprintf(stdout, "verify degree ...");
682 if (EC_GROUP_get_degree(group) != 384)
684 fprintf(stdout, " ok\n");
686 group_order_tests(group);
688 if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group))))
690 if (!EC_GROUP_copy(P_384, group))
693 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
695 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
696 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
697 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
699 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
701 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
702 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
703 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC"))
705 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
706 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
707 "DF883D2C34F1EF451FD46B503F00"))
709 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
712 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
713 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
714 "3C1856A429BF97E7E31C2E5BD66"))
716 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx))
718 if (!EC_POINT_is_on_curve(group, P, ctx))
720 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
721 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
722 "C9B8899C47AEBB6FB71E91386409"))
724 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
727 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
729 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
730 BN_print_fp(stdout, x);
731 fprintf(stdout, "\n y = 0x");
732 BN_print_fp(stdout, y);
733 fprintf(stdout, "\n");
734 /* G_y value taken from the standard: */
735 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
736 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
737 "7086A272C24088BE94769FD16650"))
739 if (0 != BN_cmp(y, z))
742 fprintf(stdout, "verify degree ...");
743 if (EC_GROUP_get_degree(group) != 521)
745 fprintf(stdout, " ok\n");
747 group_order_tests(group);
749 if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group))))
751 if (!EC_GROUP_copy(P_521, group))
754 /* more tests using the last curve */
756 if (!EC_POINT_copy(Q, P))
758 if (EC_POINT_is_at_infinity(group, Q))
760 if (!EC_POINT_dbl(group, P, P, ctx))
762 if (!EC_POINT_is_on_curve(group, P, ctx))
764 if (!EC_POINT_invert(group, Q, ctx))
767 if (!EC_POINT_add(group, R, P, Q, ctx))
769 if (!EC_POINT_add(group, R, R, Q, ctx))
771 if (!EC_POINT_is_at_infinity(group, R))
772 ABORT; /* R = P + 2Q */
775 const EC_POINT *points[4];
776 const BIGNUM *scalars[4];
779 if (EC_POINT_is_at_infinity(group, Q))
786 if (!EC_GROUP_get_order(group, z, ctx))
788 if (!BN_add(y, z, BN_value_one()))
792 if (!BN_rshift1(y, y))
794 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
797 fprintf(stdout, "combined multiplication ...");
800 /* z is still the group order */
801 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
803 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
805 if (0 != EC_POINT_cmp(group, P, R, ctx))
807 if (0 != EC_POINT_cmp(group, R, Q, ctx))
810 fprintf(stdout, ".");
813 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0))
815 if (!BN_add(z, z, y))
817 BN_set_negative(z, 1);
819 scalars[1] = z; /* z = -(order + y) */
821 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
823 if (!EC_POINT_is_at_infinity(group, P))
826 fprintf(stdout, ".");
829 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0))
831 if (!BN_add(z, x, y))
833 BN_set_negative(z, 1);
836 scalars[2] = z; /* z = -(x+y) */
842 scalars[3] = scalar3;
844 if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx))
846 if (!EC_POINT_is_at_infinity(group, P))
849 fprintf(stdout, " ok\n\n");
859 EC_GROUP_free(group);
867 EC_GROUP_free(P_160);
868 EC_GROUP_free(P_192);
869 EC_GROUP_free(P_224);
870 EC_GROUP_free(P_256);
871 EC_GROUP_free(P_384);
872 EC_GROUP_free(P_521);
876 /* Change test based on whether binary point compression is enabled or not. */
877 # ifdef OPENSSL_EC_BIN_PT_COMP
878 # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
879 if (!BN_hex2bn(&x, _x)) ABORT; \
880 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
881 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
882 if (!BN_hex2bn(&z, _order)) ABORT; \
883 if (!BN_hex2bn(&cof, _cof)) ABORT; \
884 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
885 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
886 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
887 BN_print_fp(stdout, x); \
888 fprintf(stdout, "\n y = 0x"); \
889 BN_print_fp(stdout, y); \
890 fprintf(stdout, "\n"); \
891 /* G_y value taken from the standard: */ \
892 if (!BN_hex2bn(&z, _y)) ABORT; \
893 if (0 != BN_cmp(y, z)) ABORT;
895 # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
896 if (!BN_hex2bn(&x, _x)) ABORT; \
897 if (!BN_hex2bn(&y, _y)) ABORT; \
898 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
899 if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
900 if (!BN_hex2bn(&z, _order)) ABORT; \
901 if (!BN_hex2bn(&cof, _cof)) ABORT; \
902 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
903 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
904 BN_print_fp(stdout, x); \
905 fprintf(stdout, "\n y = 0x"); \
906 BN_print_fp(stdout, y); \
907 fprintf(stdout, "\n");
910 # define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
911 if (!BN_hex2bn(&p, _p)) ABORT; \
912 if (!BN_hex2bn(&a, _a)) ABORT; \
913 if (!BN_hex2bn(&b, _b)) ABORT; \
914 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
915 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
916 fprintf(stdout, "verify degree ..."); \
917 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
918 fprintf(stdout, " ok\n"); \
919 group_order_tests(group); \
920 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
921 if (!EC_GROUP_copy(_variable, group)) ABORT; \
923 # ifndef OPENSSL_NO_EC2M
925 static void char2_field_tests(void)
930 EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 =
931 NULL, *C2_K571 = NULL;
932 EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 =
933 NULL, *C2_B571 = NULL;
935 BIGNUM *x, *y, *z, *cof;
936 unsigned char buf[100];
950 if (!BN_hex2bn(&p, "13"))
952 if (!BN_hex2bn(&a, "3"))
954 if (!BN_hex2bn(&b, "1"))
957 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use
958 * EC_GROUP_new_curve_GF2m
959 * so that the library gets
960 * to choose the EC_METHOD */
963 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx))
968 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
971 if (!EC_GROUP_copy(tmp, group))
973 EC_GROUP_free(group);
977 if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx))
981 "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
982 BN_print_fp(stdout, p);
983 fprintf(stdout, ")\n a = 0x");
984 BN_print_fp(stdout, a);
985 fprintf(stdout, "\n b = 0x");
986 BN_print_fp(stdout, b);
987 fprintf(stdout, "\n(0x... means binary polynomial)\n");
989 P = EC_POINT_new(group);
990 Q = EC_POINT_new(group);
991 R = EC_POINT_new(group);
995 if (!EC_POINT_set_to_infinity(group, P))
997 if (!EC_POINT_is_at_infinity(group, P))
1001 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx))
1004 if (!EC_POINT_add(group, P, P, Q, ctx))
1006 if (!EC_POINT_is_at_infinity(group, P))
1013 if (!x || !y || !z || !cof)
1016 if (!BN_hex2bn(&x, "6"))
1018 /* Change test based on whether binary point compression is enabled or not. */
1019 # ifdef OPENSSL_EC_BIN_PT_COMP
1020 if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx))
1023 if (!BN_hex2bn(&y, "8"))
1025 if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx))
1028 if (!EC_POINT_is_on_curve(group, Q, ctx)) {
1029 /* Change test based on whether binary point compression is enabled or not. */
1030 # ifdef OPENSSL_EC_BIN_PT_COMP
1031 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx))
1034 fprintf(stderr, "Point is not on curve: x = 0x");
1035 BN_print_fp(stderr, x);
1036 fprintf(stderr, ", y = 0x");
1037 BN_print_fp(stderr, y);
1038 fprintf(stderr, "\n");
1042 fprintf(stdout, "A cyclic subgroup:\n");
1048 if (EC_POINT_is_at_infinity(group, P))
1049 fprintf(stdout, " point at infinity\n");
1051 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx))
1054 fprintf(stdout, " x = 0x");
1055 BN_print_fp(stdout, x);
1056 fprintf(stdout, ", y = 0x");
1057 BN_print_fp(stdout, y);
1058 fprintf(stdout, "\n");
1061 if (!EC_POINT_copy(R, P))
1063 if (!EC_POINT_add(group, P, P, Q, ctx))
1066 while (!EC_POINT_is_at_infinity(group, P));
1068 if (!EC_POINT_add(group, P, Q, R, ctx))
1070 if (!EC_POINT_is_at_infinity(group, P))
1073 /* Change test based on whether binary point compression is enabled or not. */
1074 # ifdef OPENSSL_EC_BIN_PT_COMP
1076 EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf,
1080 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
1082 if (0 != EC_POINT_cmp(group, P, Q, ctx))
1084 fprintf(stdout, "Generator as octet string, compressed form:\n ");
1085 for (i = 0; i < len; i++)
1086 fprintf(stdout, "%02X", buf[i]);
1090 EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf,
1094 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
1096 if (0 != EC_POINT_cmp(group, P, Q, ctx))
1098 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
1099 for (i = 0; i < len; i++)
1100 fprintf(stdout, "%02X", buf[i]);
1102 /* Change test based on whether binary point compression is enabled or not. */
1103 # ifdef OPENSSL_EC_BIN_PT_COMP
1105 EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf,
1109 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
1111 if (0 != EC_POINT_cmp(group, P, Q, ctx))
1113 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
1114 for (i = 0; i < len; i++)
1115 fprintf(stdout, "%02X", buf[i]);
1118 fprintf(stdout, "\n");
1120 if (!EC_POINT_invert(group, P, ctx))
1122 if (0 != EC_POINT_cmp(group, P, R, ctx))
1125 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
1127 ("NIST curve K-163",
1128 "0800000000000000000000000000000000000000C9",
1131 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
1132 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
1133 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163, C2_K163);
1135 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
1137 ("NIST curve B-163",
1138 "0800000000000000000000000000000000000000C9",
1140 "020A601907B8C953CA1481EB10512F78744A3205FD",
1141 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
1142 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
1143 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163, C2_B163);
1145 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
1147 ("NIST curve K-233",
1148 "020000000000000000000000000000000000000004000000000000000001",
1151 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
1152 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
1154 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
1157 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
1159 ("NIST curve B-233",
1160 "020000000000000000000000000000000000000004000000000000000001",
1161 "000000000000000000000000000000000000000000000000000000000001",
1162 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1163 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1164 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1166 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1169 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1171 ("NIST curve K-283",
1172 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1175 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1176 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1178 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1181 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1183 ("NIST curve B-283",
1184 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1185 "000000000000000000000000000000000000000000000000000000000000000000000001",
1186 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1187 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1188 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1190 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1193 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1195 ("NIST curve K-409",
1196 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1199 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1200 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1202 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1205 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1207 ("NIST curve B-409",
1208 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1209 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1210 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1211 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1212 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1214 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1217 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1219 ("NIST curve K-571",
1220 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1223 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1224 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1226 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1229 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1231 ("NIST curve B-571",
1232 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1233 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1234 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1235 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1236 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1238 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1241 /* more tests using the last curve */
1243 if (!EC_POINT_copy(Q, P))
1245 if (EC_POINT_is_at_infinity(group, Q))
1247 if (!EC_POINT_dbl(group, P, P, ctx))
1249 if (!EC_POINT_is_on_curve(group, P, ctx))
1251 if (!EC_POINT_invert(group, Q, ctx))
1252 ABORT; /* P = -2Q */
1254 if (!EC_POINT_add(group, R, P, Q, ctx))
1256 if (!EC_POINT_add(group, R, R, Q, ctx))
1258 if (!EC_POINT_is_at_infinity(group, R))
1259 ABORT; /* R = P + 2Q */
1262 const EC_POINT *points[3];
1263 const BIGNUM *scalars[3];
1265 if (EC_POINT_is_at_infinity(group, Q))
1271 if (!BN_add(y, z, BN_value_one()))
1275 if (!BN_rshift1(y, y))
1277 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
1280 fprintf(stdout, "combined multiplication ...");
1283 /* z is still the group order */
1284 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
1286 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
1288 if (0 != EC_POINT_cmp(group, P, R, ctx))
1290 if (0 != EC_POINT_cmp(group, R, Q, ctx))
1293 fprintf(stdout, ".");
1296 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0))
1298 if (!BN_add(z, z, y))
1300 BN_set_negative(z, 1);
1302 scalars[1] = z; /* z = -(order + y) */
1304 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
1306 if (!EC_POINT_is_at_infinity(group, P))
1309 fprintf(stdout, ".");
1312 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0))
1314 if (!BN_add(z, x, y))
1316 BN_set_negative(z, 1);
1319 scalars[2] = z; /* z = -(x+y) */
1321 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx))
1323 if (!EC_POINT_is_at_infinity(group, P))
1326 fprintf(stdout, " ok\n\n");
1334 EC_GROUP_free(group);
1343 EC_GROUP_free(C2_K163);
1344 EC_GROUP_free(C2_B163);
1345 EC_GROUP_free(C2_K233);
1346 EC_GROUP_free(C2_B233);
1347 EC_GROUP_free(C2_K283);
1348 EC_GROUP_free(C2_B283);
1349 EC_GROUP_free(C2_K409);
1350 EC_GROUP_free(C2_B409);
1351 EC_GROUP_free(C2_K571);
1352 EC_GROUP_free(C2_B571);
1357 static void internal_curve_test(void)
1359 EC_builtin_curve *curves = NULL;
1360 size_t crv_len = 0, n = 0;
1363 crv_len = EC_get_builtin_curves(NULL, 0);
1365 curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len);
1370 if (!EC_get_builtin_curves(curves, crv_len)) {
1371 OPENSSL_free(curves);
1375 fprintf(stdout, "testing internal curves: ");
1377 for (n = 0; n < crv_len; n++) {
1378 EC_GROUP *group = NULL;
1379 int nid = curves[n].nid;
1380 if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL) {
1382 fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with"
1383 " curve %s\n", OBJ_nid2sn(nid));
1384 /* try next curve */
1387 if (!EC_GROUP_check(group, NULL)) {
1389 fprintf(stdout, "\nEC_GROUP_check() failed with"
1390 " curve %s\n", OBJ_nid2sn(nid));
1391 EC_GROUP_free(group);
1392 /* try the next curve */
1395 fprintf(stdout, ".");
1397 EC_GROUP_free(group);
1400 fprintf(stdout, " ok\n\n");
1402 fprintf(stdout, " failed\n\n");
1405 OPENSSL_free(curves);
1409 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1411 * nistp_test_params contains magic numbers for testing our optimized
1412 * implementations of several NIST curves with characteristic > 3.
1414 struct nistp_test_params {
1415 const EC_METHOD *(*meth) ();
1418 * Qx, Qy and D are taken from
1419 * http://csrcdocut.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
1420 * Otherwise, values are standard curve parameters from FIPS 180-3
1422 const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d;
1425 static const struct nistp_test_params nistp_tests_params[] = {
1428 EC_GFp_nistp224_method,
1431 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
1433 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
1435 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
1437 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E",
1439 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555",
1441 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
1443 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
1445 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
1447 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8",
1451 EC_GFp_nistp256_method,
1454 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
1456 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc",
1458 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
1460 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19",
1462 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09",
1464 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
1466 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5",
1468 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
1470 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96",
1474 EC_GFp_nistp521_method,
1477 "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
1479 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc",
1481 "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00",
1483 "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4",
1485 "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e",
1487 "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66",
1489 "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650",
1491 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409",
1493 "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722",
1497 static void nistp_single_test(const struct nistp_test_params *test)
1500 BIGNUM *p, *a, *b, *x, *y, *n, *m, *order;
1502 EC_POINT *G, *P, *Q, *Q_CHECK;
1504 fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n",
1516 NISTP = EC_GROUP_new(test->meth());
1519 if (!BN_hex2bn(&p, test->p))
1521 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
1523 if (!BN_hex2bn(&a, test->a))
1525 if (!BN_hex2bn(&b, test->b))
1527 if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx))
1529 G = EC_POINT_new(NISTP);
1530 P = EC_POINT_new(NISTP);
1531 Q = EC_POINT_new(NISTP);
1532 Q_CHECK = EC_POINT_new(NISTP);
1533 if (!BN_hex2bn(&x, test->Qx))
1535 if (!BN_hex2bn(&y, test->Qy))
1537 if (!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx))
1539 if (!BN_hex2bn(&x, test->Gx))
1541 if (!BN_hex2bn(&y, test->Gy))
1543 if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx))
1545 if (!BN_hex2bn(&order, test->order))
1547 if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one()))
1550 fprintf(stdout, "verify degree ... ");
1551 if (EC_GROUP_get_degree(NISTP) != test->degree)
1553 fprintf(stdout, "ok\n");
1555 fprintf(stdout, "NIST test vectors ... ");
1556 if (!BN_hex2bn(&n, test->d))
1558 /* fixed point multiplication */
1559 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1560 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1562 /* random point multiplication */
1563 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1564 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1567 /* set generator to P = 2*G, where G is the standard generator */
1568 if (!EC_POINT_dbl(NISTP, P, G, ctx))
1570 if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one()))
1572 /* set the scalar to m=n/2, where n is the NIST test scalar */
1573 if (!BN_rshift(m, n, 1))
1576 /* test the non-standard generator */
1577 /* fixed point multiplication */
1578 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1579 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1581 /* random point multiplication */
1582 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1583 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1586 /* now repeat all tests with precomputation */
1587 if (!EC_GROUP_precompute_mult(NISTP, ctx))
1590 /* fixed point multiplication */
1591 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1592 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1594 /* random point multiplication */
1595 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1596 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1599 /* reset generator */
1600 if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one()))
1602 /* fixed point multiplication */
1603 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1604 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1606 /* random point multiplication */
1607 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1608 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1611 fprintf(stdout, "ok\n");
1612 group_order_tests(NISTP);
1613 EC_GROUP_free(NISTP);
1617 EC_POINT_free(Q_CHECK);
1629 static void nistp_tests()
1634 i < sizeof(nistp_tests_params) / sizeof(struct nistp_test_params);
1636 nistp_single_test(&nistp_tests_params[i]);
1641 static const char rnd_seed[] =
1642 "string to make the random number generator think it has entropy";
1644 int main(int argc, char *argv[])
1647 /* enable memory leak checking unless explicitly disabled */
1648 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL)
1649 && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off")))) {
1650 CRYPTO_malloc_debug_init();
1651 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
1653 /* OPENSSL_DEBUG_MEMORY=off */
1654 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1656 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
1657 ERR_load_crypto_strings();
1659 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
1661 prime_field_tests();
1663 # ifndef OPENSSL_NO_EC2M
1664 char2_field_tests();
1666 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1669 /* test the internal curves */
1670 internal_curve_test();
1672 # ifndef OPENSSL_NO_ENGINE
1675 CRYPTO_cleanup_all_ex_data();
1677 ERR_remove_thread_state(NULL);
1678 CRYPTO_mem_leaks_fp(stderr);