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
118 static void timings(EC_GROUP
*group
, int type
, BN_CTX
*ctx
)
123 BIGNUM
*r
[10], *r0
[10];
130 fprintf(stdout
, "Timings for %d-bit field, ", EC_GROUP_get_degree(group
));
131 if (!EC_GROUP_get_order(group
, s
, ctx
))
133 fprintf(stdout
, "%d-bit scalars ", (int)BN_num_bits(s
));
136 P
= EC_POINT_new(group
);
139 EC_POINT_copy(P
, EC_GROUP_get0_generator(group
));
141 for (i
= 0; i
< 10; i
++) {
142 if ((r
[i
] = BN_new()) == NULL
)
144 if (!BN_pseudo_rand(r
[i
], BN_num_bits(s
), 0, 0))
146 if (type
!= TIMING_BASE_PT
) {
147 if ((r0
[i
] = BN_new()) == NULL
)
149 if (!BN_pseudo_rand(r0
[i
], BN_num_bits(s
), 0, 0))
155 for (i
= 0; i
< 10; i
++) {
156 for (j
= 0; j
< 10; j
++) {
158 (group
, P
, (type
!= TIMING_RAND_PT
) ? r
[i
] : NULL
,
159 (type
!= TIMING_BASE_PT
) ? P
: NULL
,
160 (type
!= TIMING_BASE_PT
) ? r0
[i
] : NULL
, ctx
))
164 clck
= clock() - clck
;
166 fprintf(stdout
, "\n");
168 # ifdef CLOCKS_PER_SEC
170 * "To determine the time in seconds, the value returned by the clock
171 * function should be divided by the value of the macro CLOCKS_PER_SEC."
177 * "`CLOCKS_PER_SEC' undeclared (first use this function)" -- cc on
180 # define UNIT "units"
181 # define CLOCKS_PER_SEC 1
184 if (type
== TIMING_BASE_PT
) {
185 fprintf(stdout
, "%i %s in %.2f " UNIT
"\n", i
* j
,
186 "base point multiplications", (double)clck
/ CLOCKS_PER_SEC
);
187 } else if (type
== TIMING_RAND_PT
) {
188 fprintf(stdout
, "%i %s in %.2f " UNIT
"\n", i
* j
,
189 "random point multiplications",
190 (double)clck
/ CLOCKS_PER_SEC
);
191 } else if (type
== TIMING_SIMUL
) {
192 fprintf(stdout
, "%i %s in %.2f " UNIT
"\n", i
* j
,
193 "s*P+t*Q operations", (double)clck
/ CLOCKS_PER_SEC
);
195 fprintf(stdout
, "average: %.4f " UNIT
"\n",
196 (double)clck
/ (CLOCKS_PER_SEC
* i
* j
));
200 for (i
= 0; i
< 10; i
++) {
202 if (type
!= TIMING_BASE_PT
)
208 /* test multiplication with group order, long and negative scalars */
209 static void group_order_tests(EC_GROUP
*group
)
211 BIGNUM
*n1
, *n2
, *order
;
212 EC_POINT
*P
= EC_POINT_new(group
);
213 EC_POINT
*Q
= EC_POINT_new(group
);
214 BN_CTX
*ctx
= BN_CTX_new();
220 fprintf(stdout
, "verify group order ...");
222 if (!EC_GROUP_get_order(group
, order
, ctx
))
224 if (!EC_POINT_mul(group
, Q
, order
, NULL
, NULL
, ctx
))
226 if (!EC_POINT_is_at_infinity(group
, Q
))
228 fprintf(stdout
, ".");
230 if (!EC_GROUP_precompute_mult(group
, ctx
))
232 if (!EC_POINT_mul(group
, Q
, order
, NULL
, NULL
, ctx
))
234 if (!EC_POINT_is_at_infinity(group
, Q
))
236 fprintf(stdout
, " ok\n");
237 fprintf(stdout
, "long/negative scalar tests ");
238 for (i
= 1; i
<= 2; i
++) {
239 const BIGNUM
*scalars
[6];
240 const EC_POINT
*points
[6];
242 fprintf(stdout
, i
== 1 ?
243 "allowing precomputation ... " :
244 "without precomputation ... ");
245 if (!BN_set_word(n1
, i
))
248 * If i == 1, P will be the predefined generator for which
249 * EC_GROUP_precompute_mult has set up precomputation.
251 if (!EC_POINT_mul(group
, P
, n1
, NULL
, NULL
, ctx
))
257 if (!BN_sub(n1
, n1
, order
))
259 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n1
, ctx
))
261 if (0 != EC_POINT_cmp(group
, Q
, P
, ctx
))
265 if (!BN_add(n2
, order
, BN_value_one()))
267 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n2
, ctx
))
269 if (0 != EC_POINT_cmp(group
, Q
, P
, ctx
))
272 /* n2 = (1 - order) * (1 + order) = 1 - order^2 */
273 if (!BN_mul(n2
, n1
, n2
, ctx
))
275 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n2
, ctx
))
277 if (0 != EC_POINT_cmp(group
, Q
, P
, ctx
))
280 /* n2 = order^2 - 1 */
281 BN_set_negative(n2
, 0);
282 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n2
, ctx
))
284 /* Add P to verify the result. */
285 if (!EC_POINT_add(group
, Q
, Q
, P
, ctx
))
287 if (!EC_POINT_is_at_infinity(group
, Q
))
290 /* Exercise EC_POINTs_mul, including corner cases. */
291 if (EC_POINT_is_at_infinity(group
, P
))
294 points
[0] = Q
; /* => infinity */
296 points
[1] = P
; /* => -P */
298 points
[2] = Q
; /* => infinity */
300 points
[3] = Q
; /* => infinity */
302 points
[4] = P
; /* => P */
304 points
[5] = Q
; /* => infinity */
305 if (!EC_POINTs_mul(group
, P
, NULL
, 6, points
, scalars
, ctx
))
307 if (!EC_POINT_is_at_infinity(group
, P
))
310 fprintf(stdout
, "ok\n");
320 static void prime_field_tests(void)
325 EC_GROUP
*P_160
= NULL
, *P_192
= NULL
, *P_224
= NULL
, *P_256
=
326 NULL
, *P_384
= NULL
, *P_521
= NULL
;
329 unsigned char buf
[100];
333 # if 1 /* optional */
345 if (!BN_hex2bn(&p
, "17"))
347 if (!BN_hex2bn(&a
, "1"))
349 if (!BN_hex2bn(&b
, "1"))
352 group
= EC_GROUP_new(EC_GFp_mont_method()); /* applications should use
353 * EC_GROUP_new_curve_GFp so
354 * that the library gets to
355 * choose the EC_METHOD */
359 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
364 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
367 if (!EC_GROUP_copy(tmp
, group
))
369 EC_GROUP_free(group
);
373 if (!EC_GROUP_get_curve_GFp(group
, p
, a
, b
, ctx
))
377 "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
378 BN_print_fp(stdout
, p
);
379 fprintf(stdout
, ")\n a = 0x");
380 BN_print_fp(stdout
, a
);
381 fprintf(stdout
, "\n b = 0x");
382 BN_print_fp(stdout
, b
);
383 fprintf(stdout
, "\n");
385 P
= EC_POINT_new(group
);
386 Q
= EC_POINT_new(group
);
387 R
= EC_POINT_new(group
);
391 if (!EC_POINT_set_to_infinity(group
, P
))
393 if (!EC_POINT_is_at_infinity(group
, P
))
397 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
))
400 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
402 if (!EC_POINT_is_at_infinity(group
, P
))
411 if (!BN_hex2bn(&x
, "D"))
413 if (!EC_POINT_set_compressed_coordinates_GFp(group
, Q
, x
, 1, ctx
))
415 if (EC_POINT_is_on_curve(group
, Q
, ctx
) <= 0) {
416 if (!EC_POINT_get_affine_coordinates_GFp(group
, Q
, x
, y
, ctx
))
418 fprintf(stderr
, "Point is not on curve: x = 0x");
419 BN_print_fp(stderr
, x
);
420 fprintf(stderr
, ", y = 0x");
421 BN_print_fp(stderr
, y
);
422 fprintf(stderr
, "\n");
426 fprintf(stdout
, "A cyclic subgroup:\n");
432 if (EC_POINT_is_at_infinity(group
, P
))
433 fprintf(stdout
, " point at infinity\n");
435 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
438 fprintf(stdout
, " x = 0x");
439 BN_print_fp(stdout
, x
);
440 fprintf(stdout
, ", y = 0x");
441 BN_print_fp(stdout
, y
);
442 fprintf(stdout
, "\n");
445 if (!EC_POINT_copy(R
, P
))
447 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
450 # if 0 /* optional */
457 if (!EC_POINTs_make_affine(group
, 2, points
, ctx
))
463 while (!EC_POINT_is_at_infinity(group
, P
));
465 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
))
467 if (!EC_POINT_is_at_infinity(group
, P
))
471 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
,
475 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
477 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
479 fprintf(stdout
, "Generator as octet string, compressed form:\n ");
480 for (i
= 0; i
< len
; i
++)
481 fprintf(stdout
, "%02X", buf
[i
]);
484 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
,
488 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
490 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
492 fprintf(stdout
, "\nGenerator as octet string, uncompressed form:\n ");
493 for (i
= 0; i
< len
; i
++)
494 fprintf(stdout
, "%02X", buf
[i
]);
497 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
,
501 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
503 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
505 fprintf(stdout
, "\nGenerator as octet string, hybrid form:\n ");
506 for (i
= 0; i
< len
; i
++)
507 fprintf(stdout
, "%02X", buf
[i
]);
509 if (!EC_POINT_get_Jprojective_coordinates_GFp(group
, R
, x
, y
, z
, ctx
))
512 "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
513 BN_print_fp(stdout
, x
);
514 fprintf(stdout
, ", Y = 0x");
515 BN_print_fp(stdout
, y
);
516 fprintf(stdout
, ", Z = 0x");
517 BN_print_fp(stdout
, z
);
518 fprintf(stdout
, "\n");
520 if (!EC_POINT_invert(group
, P
, ctx
))
522 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
526 * Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2,
527 * 2000) -- not a NIST curve, but commonly used
530 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"))
532 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
534 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"))
536 if (!BN_hex2bn(&b
, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45"))
538 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
541 if (!BN_hex2bn(&x
, "4A96B5688EF573284664698968C38BB913CBFC82"))
543 if (!BN_hex2bn(&y
, "23a628553168947d59dcc912042351377ac5fb32"))
545 if (!EC_POINT_set_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
547 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
549 if (!BN_hex2bn(&z
, "0100000000000000000001F4C8F927AED3CA752257"))
551 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
554 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
556 fprintf(stdout
, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
557 BN_print_fp(stdout
, x
);
558 fprintf(stdout
, "\n y = 0x");
559 BN_print_fp(stdout
, y
);
560 fprintf(stdout
, "\n");
561 /* G_y value taken from the standard: */
562 if (!BN_hex2bn(&z
, "23a628553168947d59dcc912042351377ac5fb32"))
564 if (0 != BN_cmp(y
, z
))
567 fprintf(stdout
, "verify degree ...");
568 if (EC_GROUP_get_degree(group
) != 160)
570 fprintf(stdout
, " ok\n");
572 group_order_tests(group
);
574 if (!(P_160
= EC_GROUP_new(EC_GROUP_method_of(group
))))
576 if (!EC_GROUP_copy(P_160
, group
))
579 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
581 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"))
583 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
585 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"))
587 if (!BN_hex2bn(&b
, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"))
589 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
592 if (!BN_hex2bn(&x
, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"))
594 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
))
596 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
598 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"))
600 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
603 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
605 fprintf(stdout
, "\nNIST curve P-192 -- Generator:\n x = 0x");
606 BN_print_fp(stdout
, x
);
607 fprintf(stdout
, "\n y = 0x");
608 BN_print_fp(stdout
, y
);
609 fprintf(stdout
, "\n");
610 /* G_y value taken from the standard: */
611 if (!BN_hex2bn(&z
, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"))
613 if (0 != BN_cmp(y
, z
))
616 fprintf(stdout
, "verify degree ...");
617 if (EC_GROUP_get_degree(group
) != 192)
619 fprintf(stdout
, " ok\n");
621 group_order_tests(group
);
623 if (!(P_192
= EC_GROUP_new(EC_GROUP_method_of(group
))))
625 if (!EC_GROUP_copy(P_192
, group
))
628 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
631 (&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"))
633 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
636 (&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"))
639 (&b
, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"))
641 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
645 (&x
, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"))
647 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
))
649 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
652 (&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"))
654 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
657 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
659 fprintf(stdout
, "\nNIST curve P-224 -- Generator:\n x = 0x");
660 BN_print_fp(stdout
, x
);
661 fprintf(stdout
, "\n y = 0x");
662 BN_print_fp(stdout
, y
);
663 fprintf(stdout
, "\n");
664 /* G_y value taken from the standard: */
666 (&z
, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"))
668 if (0 != BN_cmp(y
, z
))
671 fprintf(stdout
, "verify degree ...");
672 if (EC_GROUP_get_degree(group
) != 224)
674 fprintf(stdout
, " ok\n");
676 group_order_tests(group
);
678 if (!(P_224
= EC_GROUP_new(EC_GROUP_method_of(group
))))
680 if (!EC_GROUP_copy(P_224
, group
))
683 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
687 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"))
689 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
693 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC"))
697 "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"))
699 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
704 "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"))
706 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
))
708 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
710 if (!BN_hex2bn(&z
, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
711 "84F3B9CAC2FC632551"))
713 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
716 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
718 fprintf(stdout
, "\nNIST curve P-256 -- Generator:\n x = 0x");
719 BN_print_fp(stdout
, x
);
720 fprintf(stdout
, "\n y = 0x");
721 BN_print_fp(stdout
, y
);
722 fprintf(stdout
, "\n");
723 /* G_y value taken from the standard: */
726 "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"))
728 if (0 != BN_cmp(y
, z
))
731 fprintf(stdout
, "verify degree ...");
732 if (EC_GROUP_get_degree(group
) != 256)
734 fprintf(stdout
, " ok\n");
736 group_order_tests(group
);
738 if (!(P_256
= EC_GROUP_new(EC_GROUP_method_of(group
))))
740 if (!EC_GROUP_copy(P_256
, group
))
743 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
745 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
746 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"))
748 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
750 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
751 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC"))
753 if (!BN_hex2bn(&b
, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
754 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"))
756 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
759 if (!BN_hex2bn(&x
, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
760 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7"))
762 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
))
764 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
766 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
767 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"))
769 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
772 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
774 fprintf(stdout
, "\nNIST curve P-384 -- Generator:\n x = 0x");
775 BN_print_fp(stdout
, x
);
776 fprintf(stdout
, "\n y = 0x");
777 BN_print_fp(stdout
, y
);
778 fprintf(stdout
, "\n");
779 /* G_y value taken from the standard: */
780 if (!BN_hex2bn(&z
, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
781 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"))
783 if (0 != BN_cmp(y
, z
))
786 fprintf(stdout
, "verify degree ...");
787 if (EC_GROUP_get_degree(group
) != 384)
789 fprintf(stdout
, " ok\n");
791 group_order_tests(group
);
793 if (!(P_384
= EC_GROUP_new(EC_GROUP_method_of(group
))))
795 if (!EC_GROUP_copy(P_384
, group
))
798 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
800 if (!BN_hex2bn(&p
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
801 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
802 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
804 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
806 if (!BN_hex2bn(&a
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
807 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
808 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC"))
810 if (!BN_hex2bn(&b
, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
811 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
812 "DF883D2C34F1EF451FD46B503F00"))
814 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
817 if (!BN_hex2bn(&x
, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
818 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
819 "3C1856A429BF97E7E31C2E5BD66"))
821 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
))
823 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
825 if (!BN_hex2bn(&z
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
826 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
827 "C9B8899C47AEBB6FB71E91386409"))
829 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
832 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
834 fprintf(stdout
, "\nNIST curve P-521 -- Generator:\n x = 0x");
835 BN_print_fp(stdout
, x
);
836 fprintf(stdout
, "\n y = 0x");
837 BN_print_fp(stdout
, y
);
838 fprintf(stdout
, "\n");
839 /* G_y value taken from the standard: */
840 if (!BN_hex2bn(&z
, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
841 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
842 "7086A272C24088BE94769FD16650"))
844 if (0 != BN_cmp(y
, z
))
847 fprintf(stdout
, "verify degree ...");
848 if (EC_GROUP_get_degree(group
) != 521)
850 fprintf(stdout
, " ok\n");
852 group_order_tests(group
);
854 if (!(P_521
= EC_GROUP_new(EC_GROUP_method_of(group
))))
856 if (!EC_GROUP_copy(P_521
, group
))
859 /* more tests using the last curve */
861 if (!EC_POINT_copy(Q
, P
))
863 if (EC_POINT_is_at_infinity(group
, Q
))
865 if (!EC_POINT_dbl(group
, P
, P
, ctx
))
867 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
869 if (!EC_POINT_invert(group
, Q
, ctx
))
872 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
))
874 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
))
876 if (!EC_POINT_is_at_infinity(group
, R
))
877 ABORT
; /* R = P + 2Q */
880 const EC_POINT
*points
[4];
881 const BIGNUM
*scalars
[4];
884 if (EC_POINT_is_at_infinity(group
, Q
))
891 if (!EC_GROUP_get_order(group
, z
, ctx
))
893 if (!BN_add(y
, z
, BN_value_one()))
897 if (!BN_rshift1(y
, y
))
899 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
902 fprintf(stdout
, "combined multiplication ...");
905 /* z is still the group order */
906 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
908 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
))
910 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
912 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
))
915 fprintf(stdout
, ".");
918 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0))
920 if (!BN_add(z
, z
, y
))
922 BN_set_negative(z
, 1);
924 scalars
[1] = z
; /* z = -(order + y) */
926 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
928 if (!EC_POINT_is_at_infinity(group
, P
))
931 fprintf(stdout
, ".");
934 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0))
936 if (!BN_add(z
, x
, y
))
938 BN_set_negative(z
, 1);
941 scalars
[2] = z
; /* z = -(x+y) */
945 scalars
[3] = &scalar3
;
947 if (!EC_POINTs_mul(group
, P
, NULL
, 4, points
, scalars
, ctx
))
949 if (!EC_POINT_is_at_infinity(group
, P
))
952 fprintf(stdout
, " ok\n\n");
958 timings(P_160
, TIMING_BASE_PT
, ctx
);
959 timings(P_160
, TIMING_RAND_PT
, ctx
);
960 timings(P_160
, TIMING_SIMUL
, ctx
);
961 timings(P_192
, TIMING_BASE_PT
, ctx
);
962 timings(P_192
, TIMING_RAND_PT
, ctx
);
963 timings(P_192
, TIMING_SIMUL
, ctx
);
964 timings(P_224
, TIMING_BASE_PT
, ctx
);
965 timings(P_224
, TIMING_RAND_PT
, ctx
);
966 timings(P_224
, TIMING_SIMUL
, ctx
);
967 timings(P_256
, TIMING_BASE_PT
, ctx
);
968 timings(P_256
, TIMING_RAND_PT
, ctx
);
969 timings(P_256
, TIMING_SIMUL
, ctx
);
970 timings(P_384
, TIMING_BASE_PT
, ctx
);
971 timings(P_384
, TIMING_RAND_PT
, ctx
);
972 timings(P_384
, TIMING_SIMUL
, ctx
);
973 timings(P_521
, TIMING_BASE_PT
, ctx
);
974 timings(P_521
, TIMING_RAND_PT
, ctx
);
975 timings(P_521
, TIMING_SIMUL
, ctx
);
983 EC_GROUP_free(group
);
992 EC_GROUP_free(P_160
);
994 EC_GROUP_free(P_192
);
996 EC_GROUP_free(P_224
);
998 EC_GROUP_free(P_256
);
1000 EC_GROUP_free(P_384
);
1002 EC_GROUP_free(P_521
);
1006 /* Change test based on whether binary point compression is enabled or not. */
1007 # ifdef OPENSSL_EC_BIN_PT_COMP
1008 # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
1009 if (!BN_hex2bn(&x, _x)) ABORT; \
1010 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
1011 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \
1012 if (!BN_hex2bn(&z, _order)) ABORT; \
1013 if (!BN_hex2bn(&cof, _cof)) ABORT; \
1014 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
1015 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
1016 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
1017 BN_print_fp(stdout, x); \
1018 fprintf(stdout, "\n y = 0x"); \
1019 BN_print_fp(stdout, y); \
1020 fprintf(stdout, "\n"); \
1021 /* G_y value taken from the standard: */ \
1022 if (!BN_hex2bn(&z, _y)) ABORT; \
1023 if (0 != BN_cmp(y, z)) ABORT;
1025 # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
1026 if (!BN_hex2bn(&x, _x)) ABORT; \
1027 if (!BN_hex2bn(&y, _y)) ABORT; \
1028 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
1029 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \
1030 if (!BN_hex2bn(&z, _order)) ABORT; \
1031 if (!BN_hex2bn(&cof, _cof)) ABORT; \
1032 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
1033 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
1034 BN_print_fp(stdout, x); \
1035 fprintf(stdout, "\n y = 0x"); \
1036 BN_print_fp(stdout, y); \
1037 fprintf(stdout, "\n");
1040 # define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
1041 if (!BN_hex2bn(&p, _p)) ABORT; \
1042 if (!BN_hex2bn(&a, _a)) ABORT; \
1043 if (!BN_hex2bn(&b, _b)) ABORT; \
1044 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
1045 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
1046 fprintf(stdout, "verify degree ..."); \
1047 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
1048 fprintf(stdout, " ok\n"); \
1049 group_order_tests(group); \
1050 if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
1051 if (!EC_GROUP_copy(_variable, group)) ABORT; \
1053 # ifndef OPENSSL_NO_EC2M
1055 static void char2_field_tests(void)
1060 EC_GROUP
*C2_K163
= NULL
, *C2_K233
= NULL
, *C2_K283
= NULL
, *C2_K409
=
1061 NULL
, *C2_K571
= NULL
;
1062 EC_GROUP
*C2_B163
= NULL
, *C2_B233
= NULL
, *C2_B283
= NULL
, *C2_B409
=
1063 NULL
, *C2_B571
= NULL
;
1064 EC_POINT
*P
, *Q
, *R
;
1065 BIGNUM
*x
, *y
, *z
, *cof
;
1066 unsigned char buf
[100];
1070 # if 1 /* optional */
1082 if (!BN_hex2bn(&p
, "13"))
1084 if (!BN_hex2bn(&a
, "3"))
1086 if (!BN_hex2bn(&b
, "1"))
1089 group
= EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use
1090 * EC_GROUP_new_curve_GF2m
1091 * so that the library gets
1092 * to choose the EC_METHOD */
1095 if (!EC_GROUP_set_curve_GF2m(group
, p
, a
, b
, ctx
))
1100 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
1103 if (!EC_GROUP_copy(tmp
, group
))
1105 EC_GROUP_free(group
);
1109 if (!EC_GROUP_get_curve_GF2m(group
, p
, a
, b
, ctx
))
1113 "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
1114 BN_print_fp(stdout
, p
);
1115 fprintf(stdout
, ")\n a = 0x");
1116 BN_print_fp(stdout
, a
);
1117 fprintf(stdout
, "\n b = 0x");
1118 BN_print_fp(stdout
, b
);
1119 fprintf(stdout
, "\n(0x... means binary polynomial)\n");
1121 P
= EC_POINT_new(group
);
1122 Q
= EC_POINT_new(group
);
1123 R
= EC_POINT_new(group
);
1127 if (!EC_POINT_set_to_infinity(group
, P
))
1129 if (!EC_POINT_is_at_infinity(group
, P
))
1133 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
))
1136 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
1138 if (!EC_POINT_is_at_infinity(group
, P
))
1145 if (!x
|| !y
|| !z
|| !cof
)
1148 if (!BN_hex2bn(&x
, "6"))
1150 /* Change test based on whether binary point compression is enabled or not. */
1151 # ifdef OPENSSL_EC_BIN_PT_COMP
1152 if (!EC_POINT_set_compressed_coordinates_GF2m(group
, Q
, x
, 1, ctx
))
1155 if (!BN_hex2bn(&y
, "8"))
1157 if (!EC_POINT_set_affine_coordinates_GF2m(group
, Q
, x
, y
, ctx
))
1160 if (EC_POINT_is_on_curve(group
, Q
, ctx
) <= 0) {
1161 /* Change test based on whether binary point compression is enabled or not. */
1162 # ifdef OPENSSL_EC_BIN_PT_COMP
1163 if (!EC_POINT_get_affine_coordinates_GF2m(group
, Q
, x
, y
, ctx
))
1166 fprintf(stderr
, "Point is not on curve: x = 0x");
1167 BN_print_fp(stderr
, x
);
1168 fprintf(stderr
, ", y = 0x");
1169 BN_print_fp(stderr
, y
);
1170 fprintf(stderr
, "\n");
1174 fprintf(stdout
, "A cyclic subgroup:\n");
1180 if (EC_POINT_is_at_infinity(group
, P
))
1181 fprintf(stdout
, " point at infinity\n");
1183 if (!EC_POINT_get_affine_coordinates_GF2m(group
, P
, x
, y
, ctx
))
1186 fprintf(stdout
, " x = 0x");
1187 BN_print_fp(stdout
, x
);
1188 fprintf(stdout
, ", y = 0x");
1189 BN_print_fp(stdout
, y
);
1190 fprintf(stdout
, "\n");
1193 if (!EC_POINT_copy(R
, P
))
1195 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
1198 while (!EC_POINT_is_at_infinity(group
, P
));
1200 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
))
1202 if (!EC_POINT_is_at_infinity(group
, P
))
1205 /* Change test based on whether binary point compression is enabled or not. */
1206 # ifdef OPENSSL_EC_BIN_PT_COMP
1208 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
,
1212 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
1214 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
1216 fprintf(stdout
, "Generator as octet string, compressed form:\n ");
1217 for (i
= 0; i
< len
; i
++)
1218 fprintf(stdout
, "%02X", buf
[i
]);
1222 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
,
1226 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
1228 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
1230 fprintf(stdout
, "\nGenerator as octet string, uncompressed form:\n ");
1231 for (i
= 0; i
< len
; i
++)
1232 fprintf(stdout
, "%02X", buf
[i
]);
1234 /* Change test based on whether binary point compression is enabled or not. */
1235 # ifdef OPENSSL_EC_BIN_PT_COMP
1237 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
,
1241 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
1243 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
1245 fprintf(stdout
, "\nGenerator as octet string, hybrid form:\n ");
1246 for (i
= 0; i
< len
; i
++)
1247 fprintf(stdout
, "%02X", buf
[i
]);
1250 fprintf(stdout
, "\n");
1252 if (!EC_POINT_invert(group
, P
, ctx
))
1254 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
1257 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
1259 ("NIST curve K-163",
1260 "0800000000000000000000000000000000000000C9",
1263 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
1264 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
1265 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163, C2_K163
);
1267 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
1269 ("NIST curve B-163",
1270 "0800000000000000000000000000000000000000C9",
1272 "020A601907B8C953CA1481EB10512F78744A3205FD",
1273 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
1274 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
1275 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163, C2_B163
);
1277 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
1279 ("NIST curve K-233",
1280 "020000000000000000000000000000000000000004000000000000000001",
1283 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
1284 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
1286 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
1289 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
1291 ("NIST curve B-233",
1292 "020000000000000000000000000000000000000004000000000000000001",
1293 "000000000000000000000000000000000000000000000000000000000001",
1294 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1295 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1296 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1298 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1301 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1303 ("NIST curve K-283",
1304 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1307 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1308 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1310 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1313 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1315 ("NIST curve B-283",
1316 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1317 "000000000000000000000000000000000000000000000000000000000000000000000001",
1318 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1319 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1320 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1322 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1325 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1327 ("NIST curve K-409",
1328 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1331 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1332 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1334 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1337 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1339 ("NIST curve B-409",
1340 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1341 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1342 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1343 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1344 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1346 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1349 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1351 ("NIST curve K-571",
1352 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1355 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1356 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1358 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1361 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1363 ("NIST curve B-571",
1364 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1365 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1366 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1367 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1368 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1370 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1373 /* more tests using the last curve */
1375 if (!EC_POINT_copy(Q
, P
))
1377 if (EC_POINT_is_at_infinity(group
, Q
))
1379 if (!EC_POINT_dbl(group
, P
, P
, ctx
))
1381 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
1383 if (!EC_POINT_invert(group
, Q
, ctx
))
1384 ABORT
; /* P = -2Q */
1386 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
))
1388 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
))
1390 if (!EC_POINT_is_at_infinity(group
, R
))
1391 ABORT
; /* R = P + 2Q */
1394 const EC_POINT
*points
[3];
1395 const BIGNUM
*scalars
[3];
1397 if (EC_POINT_is_at_infinity(group
, Q
))
1403 if (!BN_add(y
, z
, BN_value_one()))
1407 if (!BN_rshift1(y
, y
))
1409 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
1412 fprintf(stdout
, "combined multiplication ...");
1415 /* z is still the group order */
1416 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
1418 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
))
1420 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
1422 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
))
1425 fprintf(stdout
, ".");
1428 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0))
1430 if (!BN_add(z
, z
, y
))
1432 BN_set_negative(z
, 1);
1434 scalars
[1] = z
; /* z = -(order + y) */
1436 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
1438 if (!EC_POINT_is_at_infinity(group
, P
))
1441 fprintf(stdout
, ".");
1444 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0))
1446 if (!BN_add(z
, x
, y
))
1448 BN_set_negative(z
, 1);
1451 scalars
[2] = z
; /* z = -(x+y) */
1453 if (!EC_POINTs_mul(group
, P
, NULL
, 3, points
, scalars
, ctx
))
1455 if (!EC_POINT_is_at_infinity(group
, P
))
1458 fprintf(stdout
, " ok\n\n");
1462 timings(C2_K163
, TIMING_BASE_PT
, ctx
);
1463 timings(C2_K163
, TIMING_RAND_PT
, ctx
);
1464 timings(C2_K163
, TIMING_SIMUL
, ctx
);
1465 timings(C2_B163
, TIMING_BASE_PT
, ctx
);
1466 timings(C2_B163
, TIMING_RAND_PT
, ctx
);
1467 timings(C2_B163
, TIMING_SIMUL
, ctx
);
1468 timings(C2_K233
, TIMING_BASE_PT
, ctx
);
1469 timings(C2_K233
, TIMING_RAND_PT
, ctx
);
1470 timings(C2_K233
, TIMING_SIMUL
, ctx
);
1471 timings(C2_B233
, TIMING_BASE_PT
, ctx
);
1472 timings(C2_B233
, TIMING_RAND_PT
, ctx
);
1473 timings(C2_B233
, TIMING_SIMUL
, ctx
);
1474 timings(C2_K283
, TIMING_BASE_PT
, ctx
);
1475 timings(C2_K283
, TIMING_RAND_PT
, ctx
);
1476 timings(C2_K283
, TIMING_SIMUL
, ctx
);
1477 timings(C2_B283
, TIMING_BASE_PT
, ctx
);
1478 timings(C2_B283
, TIMING_RAND_PT
, ctx
);
1479 timings(C2_B283
, TIMING_SIMUL
, ctx
);
1480 timings(C2_K409
, TIMING_BASE_PT
, ctx
);
1481 timings(C2_K409
, TIMING_RAND_PT
, ctx
);
1482 timings(C2_K409
, TIMING_SIMUL
, ctx
);
1483 timings(C2_B409
, TIMING_BASE_PT
, ctx
);
1484 timings(C2_B409
, TIMING_RAND_PT
, ctx
);
1485 timings(C2_B409
, TIMING_SIMUL
, ctx
);
1486 timings(C2_K571
, TIMING_BASE_PT
, ctx
);
1487 timings(C2_K571
, TIMING_RAND_PT
, ctx
);
1488 timings(C2_K571
, TIMING_SIMUL
, ctx
);
1489 timings(C2_B571
, TIMING_BASE_PT
, ctx
);
1490 timings(C2_B571
, TIMING_RAND_PT
, ctx
);
1491 timings(C2_B571
, TIMING_SIMUL
, ctx
);
1499 EC_GROUP_free(group
);
1509 EC_GROUP_free(C2_K163
);
1511 EC_GROUP_free(C2_B163
);
1513 EC_GROUP_free(C2_K233
);
1515 EC_GROUP_free(C2_B233
);
1517 EC_GROUP_free(C2_K283
);
1519 EC_GROUP_free(C2_B283
);
1521 EC_GROUP_free(C2_K409
);
1523 EC_GROUP_free(C2_B409
);
1525 EC_GROUP_free(C2_K571
);
1527 EC_GROUP_free(C2_B571
);
1532 static void internal_curve_test(void)
1534 EC_builtin_curve
*curves
= NULL
;
1535 size_t crv_len
= 0, n
= 0;
1538 crv_len
= EC_get_builtin_curves(NULL
, 0);
1540 curves
= OPENSSL_malloc(sizeof(EC_builtin_curve
) * crv_len
);
1545 if (!EC_get_builtin_curves(curves
, crv_len
)) {
1546 OPENSSL_free(curves
);
1550 fprintf(stdout
, "testing internal curves: ");
1552 for (n
= 0; n
< crv_len
; n
++) {
1553 EC_GROUP
*group
= NULL
;
1554 int nid
= curves
[n
].nid
;
1555 if ((group
= EC_GROUP_new_by_curve_name(nid
)) == NULL
) {
1557 fprintf(stdout
, "\nEC_GROUP_new_curve_name() failed with"
1558 " curve %s\n", OBJ_nid2sn(nid
));
1559 /* try next curve */
1562 if (!EC_GROUP_check(group
, NULL
)) {
1564 fprintf(stdout
, "\nEC_GROUP_check() failed with"
1565 " curve %s\n", OBJ_nid2sn(nid
));
1566 EC_GROUP_free(group
);
1567 /* try the next curve */
1570 fprintf(stdout
, ".");
1572 EC_GROUP_free(group
);
1575 fprintf(stdout
, " ok\n\n");
1577 fprintf(stdout
, " failed\n\n");
1580 OPENSSL_free(curves
);
1584 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1586 * nistp_test_params contains magic numbers for testing our optimized
1587 * implementations of several NIST curves with characteristic > 3.
1589 struct nistp_test_params
{
1590 const EC_METHOD
*(*meth
) ();
1593 * Qx, Qy and D are taken from
1594 * http://csrcdocut.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
1595 * Otherwise, values are standard curve parameters from FIPS 180-3
1597 const char *p
, *a
, *b
, *Qx
, *Qy
, *Gx
, *Gy
, *order
, *d
;
1600 static const struct nistp_test_params nistp_tests_params
[] = {
1603 EC_GFp_nistp224_method
,
1606 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
1608 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
1610 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
1612 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E",
1614 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555",
1616 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
1618 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
1620 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
1622 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8",
1626 EC_GFp_nistp256_method
,
1629 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
1631 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc",
1633 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
1635 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19",
1637 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09",
1639 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
1641 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5",
1643 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
1645 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96",
1649 EC_GFp_nistp521_method
,
1652 "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
1654 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc",
1656 "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00",
1658 "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4",
1660 "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e",
1662 "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66",
1664 "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650",
1666 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409",
1668 "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722",
1672 static void nistp_single_test(const struct nistp_test_params
*test
)
1675 BIGNUM
*p
, *a
, *b
, *x
, *y
, *n
, *m
, *order
;
1677 EC_POINT
*G
, *P
, *Q
, *Q_CHECK
;
1679 fprintf(stdout
, "\nNIST curve P-%d (optimised implementation):\n",
1691 NISTP
= EC_GROUP_new(test
->meth());
1694 if (!BN_hex2bn(&p
, test
->p
))
1696 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
1698 if (!BN_hex2bn(&a
, test
->a
))
1700 if (!BN_hex2bn(&b
, test
->b
))
1702 if (!EC_GROUP_set_curve_GFp(NISTP
, p
, a
, b
, ctx
))
1704 G
= EC_POINT_new(NISTP
);
1705 P
= EC_POINT_new(NISTP
);
1706 Q
= EC_POINT_new(NISTP
);
1707 Q_CHECK
= EC_POINT_new(NISTP
);
1708 if (!BN_hex2bn(&x
, test
->Qx
))
1710 if (!BN_hex2bn(&y
, test
->Qy
))
1712 if (!EC_POINT_set_affine_coordinates_GFp(NISTP
, Q_CHECK
, x
, y
, ctx
))
1714 if (!BN_hex2bn(&x
, test
->Gx
))
1716 if (!BN_hex2bn(&y
, test
->Gy
))
1718 if (!EC_POINT_set_affine_coordinates_GFp(NISTP
, G
, x
, y
, ctx
))
1720 if (!BN_hex2bn(&order
, test
->order
))
1722 if (!EC_GROUP_set_generator(NISTP
, G
, order
, BN_value_one()))
1725 fprintf(stdout
, "verify degree ... ");
1726 if (EC_GROUP_get_degree(NISTP
) != test
->degree
)
1728 fprintf(stdout
, "ok\n");
1730 fprintf(stdout
, "NIST test vectors ... ");
1731 if (!BN_hex2bn(&n
, test
->d
))
1733 /* fixed point multiplication */
1734 EC_POINT_mul(NISTP
, Q
, n
, NULL
, NULL
, ctx
);
1735 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1737 /* random point multiplication */
1738 EC_POINT_mul(NISTP
, Q
, NULL
, G
, n
, ctx
);
1739 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1742 /* set generator to P = 2*G, where G is the standard generator */
1743 if (!EC_POINT_dbl(NISTP
, P
, G
, ctx
))
1745 if (!EC_GROUP_set_generator(NISTP
, P
, order
, BN_value_one()))
1747 /* set the scalar to m=n/2, where n is the NIST test scalar */
1748 if (!BN_rshift(m
, n
, 1))
1751 /* test the non-standard generator */
1752 /* fixed point multiplication */
1753 EC_POINT_mul(NISTP
, Q
, m
, NULL
, NULL
, ctx
);
1754 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1756 /* random point multiplication */
1757 EC_POINT_mul(NISTP
, Q
, NULL
, P
, m
, ctx
);
1758 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1761 /* now repeat all tests with precomputation */
1762 if (!EC_GROUP_precompute_mult(NISTP
, ctx
))
1765 /* fixed point multiplication */
1766 EC_POINT_mul(NISTP
, Q
, m
, NULL
, NULL
, ctx
);
1767 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1769 /* random point multiplication */
1770 EC_POINT_mul(NISTP
, Q
, NULL
, P
, m
, ctx
);
1771 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1774 /* reset generator */
1775 if (!EC_GROUP_set_generator(NISTP
, G
, order
, BN_value_one()))
1777 /* fixed point multiplication */
1778 EC_POINT_mul(NISTP
, Q
, n
, NULL
, NULL
, ctx
);
1779 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1781 /* random point multiplication */
1782 EC_POINT_mul(NISTP
, Q
, NULL
, G
, n
, ctx
);
1783 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1786 fprintf(stdout
, "ok\n");
1787 group_order_tests(NISTP
);
1789 timings(NISTP
, TIMING_BASE_PT
, ctx
);
1790 timings(NISTP
, TIMING_RAND_PT
, ctx
);
1792 EC_GROUP_free(NISTP
);
1796 EC_POINT_free(Q_CHECK
);
1808 static void nistp_tests()
1813 i
< sizeof(nistp_tests_params
) / sizeof(struct nistp_test_params
);
1815 nistp_single_test(&nistp_tests_params
[i
]);
1820 static const char rnd_seed
[] =
1821 "string to make the random number generator think it has entropy";
1823 int main(int argc
, char *argv
[])
1826 /* enable memory leak checking unless explicitly disabled */
1827 if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL
)
1828 && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off")))) {
1829 CRYPTO_malloc_debug_init();
1830 CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL
);
1832 /* OPENSSL_DEBUG_MEMORY=off */
1833 CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
1835 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON
);
1836 ERR_load_crypto_strings();
1838 RAND_seed(rnd_seed
, sizeof rnd_seed
); /* or BN_generate_prime may fail */
1840 prime_field_tests();
1842 # ifndef OPENSSL_NO_EC2M
1843 char2_field_tests();
1845 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1848 /* test the internal curves */
1849 internal_curve_test();
1851 # ifndef OPENSSL_NO_ENGINE
1854 CRYPTO_cleanup_all_ex_data();
1856 ERR_remove_thread_state(NULL
);
1857 CRYPTO_mem_leaks_fp(stderr
);