2 * Originally written by Bodo Moeller for the OpenSSL project.
4 /* ====================================================================
5 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
11 * 1. Redistributions of source code must retain the above copyright
12 * notice, this list of conditions and the following disclaimer.
14 * 2. Redistributions in binary form must reproduce the above copyright
15 * notice, this list of conditions and the following disclaimer in
16 * the documentation and/or other materials provided with the
19 * 3. All advertising materials mentioning features or use of this
20 * software must display the following acknowledgment:
21 * "This product includes software developed by the OpenSSL Project
22 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
24 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
25 * endorse or promote products derived from this software without
26 * prior written permission. For written permission, please contact
27 * openssl-core@openssl.org.
29 * 5. Products derived from this software may not be called "OpenSSL"
30 * nor may "OpenSSL" appear in their names without prior written
31 * permission of the OpenSSL Project.
33 * 6. Redistributions of any form whatsoever must retain the following
35 * "This product includes software developed by the OpenSSL Project
36 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
39 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
40 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
41 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
42 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
43 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
44 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
45 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
46 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
47 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
48 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
49 * OF THE POSSIBILITY OF SUCH DAMAGE.
50 * ====================================================================
52 * This product includes cryptographic software written by Eric Young
53 * (eay@cryptsoft.com). This product includes software written by Tim
54 * Hudson (tjh@cryptsoft.com).
57 /* ====================================================================
58 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
60 * Portions of the attached software ("Contribution") are developed by
61 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
63 * The Contribution is licensed pursuant to the OpenSSL open source
64 * license provided above.
66 * The elliptic curve binary polynomial software is originally written by
67 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
82 int main(int argc
, char *argv
[])
84 puts("Elliptic curves are disabled.");
89 # include <openssl/ec.h>
90 # ifndef OPENSSL_NO_ENGINE
91 # include <openssl/engine.h>
93 # include <openssl/err.h>
94 # include <openssl/obj_mac.h>
95 # include <openssl/objects.h>
96 # include <openssl/rand.h>
97 # include <openssl/bn.h>
98 # include <openssl/opensslconf.h>
100 # if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12)
101 /* suppress "too big too optimize" warning */
102 # pragma warning(disable:4959)
105 # define ABORT do { \
107 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
108 ERR_print_errors_fp(stderr); \
112 # define TIMING_BASE_PT 0
113 # define TIMING_RAND_PT 1
114 # define TIMING_SIMUL 2
116 /* test multiplication with group order, long and negative scalars */
117 static void group_order_tests(EC_GROUP
*group
)
119 BIGNUM
*n1
, *n2
, *order
;
120 EC_POINT
*P
= EC_POINT_new(group
);
121 EC_POINT
*Q
= EC_POINT_new(group
);
122 BN_CTX
*ctx
= BN_CTX_new();
128 fprintf(stdout
, "verify group order ...");
130 if (!EC_GROUP_get_order(group
, order
, ctx
))
132 if (!EC_POINT_mul(group
, Q
, order
, NULL
, NULL
, ctx
))
134 if (!EC_POINT_is_at_infinity(group
, Q
))
136 fprintf(stdout
, ".");
138 if (!EC_GROUP_precompute_mult(group
, ctx
))
140 if (!EC_POINT_mul(group
, Q
, order
, NULL
, NULL
, ctx
))
142 if (!EC_POINT_is_at_infinity(group
, Q
))
144 fprintf(stdout
, " ok\n");
145 fprintf(stdout
, "long/negative scalar tests ");
146 for (i
= 1; i
<= 2; i
++) {
147 const BIGNUM
*scalars
[6];
148 const EC_POINT
*points
[6];
150 fprintf(stdout
, i
== 1 ?
151 "allowing precomputation ... " :
152 "without precomputation ... ");
153 if (!BN_set_word(n1
, i
))
156 * If i == 1, P will be the predefined generator for which
157 * EC_GROUP_precompute_mult has set up precomputation.
159 if (!EC_POINT_mul(group
, P
, n1
, NULL
, NULL
, ctx
))
165 if (!BN_sub(n1
, n1
, order
))
167 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n1
, ctx
))
169 if (0 != EC_POINT_cmp(group
, Q
, P
, ctx
))
173 if (!BN_add(n2
, order
, BN_value_one()))
175 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n2
, ctx
))
177 if (0 != EC_POINT_cmp(group
, Q
, P
, ctx
))
180 /* n2 = (1 - order) * (1 + order) = 1 - order^2 */
181 if (!BN_mul(n2
, n1
, n2
, ctx
))
183 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n2
, ctx
))
185 if (0 != EC_POINT_cmp(group
, Q
, P
, ctx
))
188 /* n2 = order^2 - 1 */
189 BN_set_negative(n2
, 0);
190 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n2
, ctx
))
192 /* Add P to verify the result. */
193 if (!EC_POINT_add(group
, Q
, Q
, P
, ctx
))
195 if (!EC_POINT_is_at_infinity(group
, Q
))
198 /* Exercise EC_POINTs_mul, including corner cases. */
199 if (EC_POINT_is_at_infinity(group
, P
))
202 points
[0] = Q
; /* => infinity */
204 points
[1] = P
; /* => -P */
206 points
[2] = Q
; /* => infinity */
208 points
[3] = Q
; /* => infinity */
210 points
[4] = P
; /* => P */
212 points
[5] = Q
; /* => infinity */
213 if (!EC_POINTs_mul(group
, P
, NULL
, 6, points
, scalars
, ctx
))
215 if (!EC_POINT_is_at_infinity(group
, P
))
218 fprintf(stdout
, "ok\n");
228 static void prime_field_tests(void)
233 EC_GROUP
*P_160
= NULL
, *P_192
= NULL
, *P_224
= NULL
, *P_256
=
234 NULL
, *P_384
= NULL
, *P_521
= NULL
;
237 unsigned char buf
[100];
251 if (!BN_hex2bn(&p
, "17"))
253 if (!BN_hex2bn(&a
, "1"))
255 if (!BN_hex2bn(&b
, "1"))
258 group
= EC_GROUP_new(EC_GFp_mont_method()); /* applications should use
259 * EC_GROUP_new_curve_GFp so
260 * that the library gets to
261 * choose the EC_METHOD */
265 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
270 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
273 if (!EC_GROUP_copy(tmp
, group
))
275 EC_GROUP_free(group
);
279 if (!EC_GROUP_get_curve_GFp(group
, p
, a
, b
, ctx
))
283 "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
284 BN_print_fp(stdout
, p
);
285 fprintf(stdout
, ")\n a = 0x");
286 BN_print_fp(stdout
, a
);
287 fprintf(stdout
, "\n b = 0x");
288 BN_print_fp(stdout
, b
);
289 fprintf(stdout
, "\n");
291 P
= EC_POINT_new(group
);
292 Q
= EC_POINT_new(group
);
293 R
= EC_POINT_new(group
);
297 if (!EC_POINT_set_to_infinity(group
, P
))
299 if (!EC_POINT_is_at_infinity(group
, P
))
303 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
))
306 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
308 if (!EC_POINT_is_at_infinity(group
, P
))
317 if (!BN_hex2bn(&x
, "D"))
319 if (!EC_POINT_set_compressed_coordinates_GFp(group
, Q
, x
, 1, ctx
))
321 if (EC_POINT_is_on_curve(group
, Q
, ctx
) <= 0) {
322 if (!EC_POINT_get_affine_coordinates_GFp(group
, Q
, x
, y
, ctx
))
324 fprintf(stderr
, "Point is not on curve: x = 0x");
325 BN_print_fp(stderr
, x
);
326 fprintf(stderr
, ", y = 0x");
327 BN_print_fp(stderr
, y
);
328 fprintf(stderr
, "\n");
332 fprintf(stdout
, "A cyclic subgroup:\n");
338 if (EC_POINT_is_at_infinity(group
, P
))
339 fprintf(stdout
, " point at infinity\n");
341 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
344 fprintf(stdout
, " x = 0x");
345 BN_print_fp(stdout
, x
);
346 fprintf(stdout
, ", y = 0x");
347 BN_print_fp(stdout
, y
);
348 fprintf(stdout
, "\n");
351 if (!EC_POINT_copy(R
, P
))
353 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
357 while (!EC_POINT_is_at_infinity(group
, P
));
359 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
))
361 if (!EC_POINT_is_at_infinity(group
, P
))
365 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
,
369 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
371 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
373 fprintf(stdout
, "Generator as octet string, compressed form:\n ");
374 for (i
= 0; i
< len
; i
++)
375 fprintf(stdout
, "%02X", buf
[i
]);
378 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
,
382 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
384 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
386 fprintf(stdout
, "\nGenerator as octet string, uncompressed form:\n ");
387 for (i
= 0; i
< len
; i
++)
388 fprintf(stdout
, "%02X", buf
[i
]);
391 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
,
395 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
397 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
399 fprintf(stdout
, "\nGenerator as octet string, hybrid form:\n ");
400 for (i
= 0; i
< len
; i
++)
401 fprintf(stdout
, "%02X", buf
[i
]);
403 if (!EC_POINT_get_Jprojective_coordinates_GFp(group
, R
, x
, y
, z
, ctx
))
406 "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
407 BN_print_fp(stdout
, x
);
408 fprintf(stdout
, ", Y = 0x");
409 BN_print_fp(stdout
, y
);
410 fprintf(stdout
, ", Z = 0x");
411 BN_print_fp(stdout
, z
);
412 fprintf(stdout
, "\n");
414 if (!EC_POINT_invert(group
, P
, ctx
))
416 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
420 * Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2,
421 * 2000) -- not a NIST curve, but commonly used
424 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"))
426 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
428 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"))
430 if (!BN_hex2bn(&b
, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45"))
432 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
435 if (!BN_hex2bn(&x
, "4A96B5688EF573284664698968C38BB913CBFC82"))
437 if (!BN_hex2bn(&y
, "23a628553168947d59dcc912042351377ac5fb32"))
439 if (!EC_POINT_set_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
441 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
443 if (!BN_hex2bn(&z
, "0100000000000000000001F4C8F927AED3CA752257"))
445 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
448 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
450 fprintf(stdout
, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
451 BN_print_fp(stdout
, x
);
452 fprintf(stdout
, "\n y = 0x");
453 BN_print_fp(stdout
, y
);
454 fprintf(stdout
, "\n");
455 /* G_y value taken from the standard: */
456 if (!BN_hex2bn(&z
, "23a628553168947d59dcc912042351377ac5fb32"))
458 if (0 != BN_cmp(y
, z
))
461 fprintf(stdout
, "verify degree ...");
462 if (EC_GROUP_get_degree(group
) != 160)
464 fprintf(stdout
, " ok\n");
466 group_order_tests(group
);
468 if ((P_160
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
470 if (!EC_GROUP_copy(P_160
, group
))
473 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
475 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"))
477 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
479 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"))
481 if (!BN_hex2bn(&b
, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"))
483 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
486 if (!BN_hex2bn(&x
, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"))
488 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
))
490 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
492 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"))
494 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
497 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
499 fprintf(stdout
, "\nNIST curve P-192 -- Generator:\n x = 0x");
500 BN_print_fp(stdout
, x
);
501 fprintf(stdout
, "\n y = 0x");
502 BN_print_fp(stdout
, y
);
503 fprintf(stdout
, "\n");
504 /* G_y value taken from the standard: */
505 if (!BN_hex2bn(&z
, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"))
507 if (0 != BN_cmp(y
, z
))
510 fprintf(stdout
, "verify degree ...");
511 if (EC_GROUP_get_degree(group
) != 192)
513 fprintf(stdout
, " ok\n");
515 group_order_tests(group
);
517 if ((P_192
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
519 if (!EC_GROUP_copy(P_192
, group
))
522 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
525 (&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"))
527 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
530 (&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"))
533 (&b
, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"))
535 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
539 (&x
, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"))
541 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
))
543 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
546 (&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"))
548 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
551 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
553 fprintf(stdout
, "\nNIST curve P-224 -- Generator:\n x = 0x");
554 BN_print_fp(stdout
, x
);
555 fprintf(stdout
, "\n y = 0x");
556 BN_print_fp(stdout
, y
);
557 fprintf(stdout
, "\n");
558 /* G_y value taken from the standard: */
560 (&z
, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"))
562 if (0 != BN_cmp(y
, z
))
565 fprintf(stdout
, "verify degree ...");
566 if (EC_GROUP_get_degree(group
) != 224)
568 fprintf(stdout
, " ok\n");
570 group_order_tests(group
);
572 if ((P_224
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
574 if (!EC_GROUP_copy(P_224
, group
))
577 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
581 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"))
583 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
587 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC"))
591 "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"))
593 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
598 "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"))
600 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
))
602 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
604 if (!BN_hex2bn(&z
, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
605 "84F3B9CAC2FC632551"))
607 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
610 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
612 fprintf(stdout
, "\nNIST curve P-256 -- Generator:\n x = 0x");
613 BN_print_fp(stdout
, x
);
614 fprintf(stdout
, "\n y = 0x");
615 BN_print_fp(stdout
, y
);
616 fprintf(stdout
, "\n");
617 /* G_y value taken from the standard: */
620 "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"))
622 if (0 != BN_cmp(y
, z
))
625 fprintf(stdout
, "verify degree ...");
626 if (EC_GROUP_get_degree(group
) != 256)
628 fprintf(stdout
, " ok\n");
630 group_order_tests(group
);
632 if ((P_256
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
634 if (!EC_GROUP_copy(P_256
, group
))
637 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
639 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
640 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"))
642 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
644 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
645 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC"))
647 if (!BN_hex2bn(&b
, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
648 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"))
650 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
653 if (!BN_hex2bn(&x
, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
654 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7"))
656 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
))
658 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
660 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
661 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"))
663 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
666 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
668 fprintf(stdout
, "\nNIST curve P-384 -- Generator:\n x = 0x");
669 BN_print_fp(stdout
, x
);
670 fprintf(stdout
, "\n y = 0x");
671 BN_print_fp(stdout
, y
);
672 fprintf(stdout
, "\n");
673 /* G_y value taken from the standard: */
674 if (!BN_hex2bn(&z
, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
675 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"))
677 if (0 != BN_cmp(y
, z
))
680 fprintf(stdout
, "verify degree ...");
681 if (EC_GROUP_get_degree(group
) != 384)
683 fprintf(stdout
, " ok\n");
685 group_order_tests(group
);
687 if ((P_384
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
689 if (!EC_GROUP_copy(P_384
, group
))
692 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
694 if (!BN_hex2bn(&p
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
695 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
696 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
698 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
700 if (!BN_hex2bn(&a
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
701 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
702 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC"))
704 if (!BN_hex2bn(&b
, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
705 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
706 "DF883D2C34F1EF451FD46B503F00"))
708 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
711 if (!BN_hex2bn(&x
, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
712 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
713 "3C1856A429BF97E7E31C2E5BD66"))
715 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
))
717 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
719 if (!BN_hex2bn(&z
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
720 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
721 "C9B8899C47AEBB6FB71E91386409"))
723 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
726 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
728 fprintf(stdout
, "\nNIST curve P-521 -- Generator:\n x = 0x");
729 BN_print_fp(stdout
, x
);
730 fprintf(stdout
, "\n y = 0x");
731 BN_print_fp(stdout
, y
);
732 fprintf(stdout
, "\n");
733 /* G_y value taken from the standard: */
734 if (!BN_hex2bn(&z
, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
735 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
736 "7086A272C24088BE94769FD16650"))
738 if (0 != BN_cmp(y
, z
))
741 fprintf(stdout
, "verify degree ...");
742 if (EC_GROUP_get_degree(group
) != 521)
744 fprintf(stdout
, " ok\n");
746 group_order_tests(group
);
748 if ((P_521
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
750 if (!EC_GROUP_copy(P_521
, group
))
753 /* more tests using the last curve */
755 if (!EC_POINT_copy(Q
, P
))
757 if (EC_POINT_is_at_infinity(group
, Q
))
759 if (!EC_POINT_dbl(group
, P
, P
, ctx
))
761 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
763 if (!EC_POINT_invert(group
, Q
, ctx
))
766 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
))
768 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
))
770 if (!EC_POINT_is_at_infinity(group
, R
))
771 ABORT
; /* R = P + 2Q */
774 const EC_POINT
*points
[4];
775 const BIGNUM
*scalars
[4];
778 if (EC_POINT_is_at_infinity(group
, Q
))
785 if (!EC_GROUP_get_order(group
, z
, ctx
))
787 if (!BN_add(y
, z
, BN_value_one()))
791 if (!BN_rshift1(y
, y
))
793 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
796 fprintf(stdout
, "combined multiplication ...");
799 /* z is still the group order */
800 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
802 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
))
804 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
806 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
))
809 fprintf(stdout
, ".");
812 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0))
814 if (!BN_add(z
, z
, y
))
816 BN_set_negative(z
, 1);
818 scalars
[1] = z
; /* z = -(order + y) */
820 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
822 if (!EC_POINT_is_at_infinity(group
, P
))
825 fprintf(stdout
, ".");
828 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0))
830 if (!BN_add(z
, x
, y
))
832 BN_set_negative(z
, 1);
835 scalars
[2] = z
; /* z = -(x+y) */
841 scalars
[3] = scalar3
;
843 if (!EC_POINTs_mul(group
, P
, NULL
, 4, points
, scalars
, ctx
))
845 if (!EC_POINT_is_at_infinity(group
, P
))
848 fprintf(stdout
, " ok\n\n");
857 EC_GROUP_free(group
);
865 EC_GROUP_free(P_160
);
866 EC_GROUP_free(P_192
);
867 EC_GROUP_free(P_224
);
868 EC_GROUP_free(P_256
);
869 EC_GROUP_free(P_384
);
870 EC_GROUP_free(P_521
);
874 /* Change test based on whether binary point compression is enabled or not. */
875 # ifdef OPENSSL_EC_BIN_PT_COMP
876 # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
877 if (!BN_hex2bn(&x, _x)) ABORT; \
878 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
879 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \
880 if (!BN_hex2bn(&z, _order)) ABORT; \
881 if (!BN_hex2bn(&cof, _cof)) ABORT; \
882 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
883 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
884 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
885 BN_print_fp(stdout, x); \
886 fprintf(stdout, "\n y = 0x"); \
887 BN_print_fp(stdout, y); \
888 fprintf(stdout, "\n"); \
889 /* G_y value taken from the standard: */ \
890 if (!BN_hex2bn(&z, _y)) ABORT; \
891 if (0 != BN_cmp(y, z)) ABORT;
893 # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
894 if (!BN_hex2bn(&x, _x)) ABORT; \
895 if (!BN_hex2bn(&y, _y)) ABORT; \
896 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
897 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \
898 if (!BN_hex2bn(&z, _order)) ABORT; \
899 if (!BN_hex2bn(&cof, _cof)) ABORT; \
900 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
901 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
902 BN_print_fp(stdout, x); \
903 fprintf(stdout, "\n y = 0x"); \
904 BN_print_fp(stdout, y); \
905 fprintf(stdout, "\n");
908 # define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
909 if (!BN_hex2bn(&p, _p)) ABORT; \
910 if (!BN_hex2bn(&a, _a)) ABORT; \
911 if (!BN_hex2bn(&b, _b)) ABORT; \
912 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
913 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
914 fprintf(stdout, "verify degree ..."); \
915 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
916 fprintf(stdout, " ok\n"); \
917 group_order_tests(group); \
918 if ((_variable = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL) ABORT; \
919 if (!EC_GROUP_copy(_variable, group)) ABORT; \
921 # ifndef OPENSSL_NO_EC2M
923 static void char2_field_tests(void)
928 EC_GROUP
*C2_K163
= NULL
, *C2_K233
= NULL
, *C2_K283
= NULL
, *C2_K409
=
929 NULL
, *C2_K571
= NULL
;
930 EC_GROUP
*C2_B163
= NULL
, *C2_B233
= NULL
, *C2_B283
= NULL
, *C2_B409
=
931 NULL
, *C2_B571
= NULL
;
933 BIGNUM
*x
, *y
, *z
, *cof
;
934 unsigned char buf
[100];
948 if (!BN_hex2bn(&p
, "13"))
950 if (!BN_hex2bn(&a
, "3"))
952 if (!BN_hex2bn(&b
, "1"))
955 group
= EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use
956 * EC_GROUP_new_curve_GF2m
957 * so that the library gets
958 * to choose the EC_METHOD */
961 if (!EC_GROUP_set_curve_GF2m(group
, p
, a
, b
, ctx
))
966 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
969 if (!EC_GROUP_copy(tmp
, group
))
971 EC_GROUP_free(group
);
975 if (!EC_GROUP_get_curve_GF2m(group
, p
, a
, b
, ctx
))
979 "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
980 BN_print_fp(stdout
, p
);
981 fprintf(stdout
, ")\n a = 0x");
982 BN_print_fp(stdout
, a
);
983 fprintf(stdout
, "\n b = 0x");
984 BN_print_fp(stdout
, b
);
985 fprintf(stdout
, "\n(0x... means binary polynomial)\n");
987 P
= EC_POINT_new(group
);
988 Q
= EC_POINT_new(group
);
989 R
= EC_POINT_new(group
);
993 if (!EC_POINT_set_to_infinity(group
, P
))
995 if (!EC_POINT_is_at_infinity(group
, P
))
999 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
))
1002 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
1004 if (!EC_POINT_is_at_infinity(group
, P
))
1011 if (!x
|| !y
|| !z
|| !cof
)
1014 if (!BN_hex2bn(&x
, "6"))
1016 /* Change test based on whether binary point compression is enabled or not. */
1017 # ifdef OPENSSL_EC_BIN_PT_COMP
1018 if (!EC_POINT_set_compressed_coordinates_GF2m(group
, Q
, x
, 1, ctx
))
1021 if (!BN_hex2bn(&y
, "8"))
1023 if (!EC_POINT_set_affine_coordinates_GF2m(group
, Q
, x
, y
, ctx
))
1026 if (EC_POINT_is_on_curve(group
, Q
, ctx
) <= 0) {
1027 /* Change test based on whether binary point compression is enabled or not. */
1028 # ifdef OPENSSL_EC_BIN_PT_COMP
1029 if (!EC_POINT_get_affine_coordinates_GF2m(group
, Q
, x
, y
, ctx
))
1032 fprintf(stderr
, "Point is not on curve: x = 0x");
1033 BN_print_fp(stderr
, x
);
1034 fprintf(stderr
, ", y = 0x");
1035 BN_print_fp(stderr
, y
);
1036 fprintf(stderr
, "\n");
1040 fprintf(stdout
, "A cyclic subgroup:\n");
1046 if (EC_POINT_is_at_infinity(group
, P
))
1047 fprintf(stdout
, " point at infinity\n");
1049 if (!EC_POINT_get_affine_coordinates_GF2m(group
, P
, x
, y
, ctx
))
1052 fprintf(stdout
, " x = 0x");
1053 BN_print_fp(stdout
, x
);
1054 fprintf(stdout
, ", y = 0x");
1055 BN_print_fp(stdout
, y
);
1056 fprintf(stdout
, "\n");
1059 if (!EC_POINT_copy(R
, P
))
1061 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
1064 while (!EC_POINT_is_at_infinity(group
, P
));
1066 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
))
1068 if (!EC_POINT_is_at_infinity(group
, P
))
1071 /* Change test based on whether binary point compression is enabled or not. */
1072 # ifdef OPENSSL_EC_BIN_PT_COMP
1074 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
,
1078 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
1080 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
1082 fprintf(stdout
, "Generator as octet string, compressed form:\n ");
1083 for (i
= 0; i
< len
; i
++)
1084 fprintf(stdout
, "%02X", buf
[i
]);
1088 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
,
1092 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
1094 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
1096 fprintf(stdout
, "\nGenerator as octet string, uncompressed form:\n ");
1097 for (i
= 0; i
< len
; i
++)
1098 fprintf(stdout
, "%02X", buf
[i
]);
1100 /* Change test based on whether binary point compression is enabled or not. */
1101 # ifdef OPENSSL_EC_BIN_PT_COMP
1103 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
,
1107 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
1109 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
1111 fprintf(stdout
, "\nGenerator as octet string, hybrid form:\n ");
1112 for (i
= 0; i
< len
; i
++)
1113 fprintf(stdout
, "%02X", buf
[i
]);
1116 fprintf(stdout
, "\n");
1118 if (!EC_POINT_invert(group
, P
, ctx
))
1120 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
1123 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
1125 ("NIST curve K-163",
1126 "0800000000000000000000000000000000000000C9",
1129 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
1130 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
1131 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163, C2_K163
);
1133 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
1135 ("NIST curve B-163",
1136 "0800000000000000000000000000000000000000C9",
1138 "020A601907B8C953CA1481EB10512F78744A3205FD",
1139 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
1140 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
1141 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163, C2_B163
);
1143 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
1145 ("NIST curve K-233",
1146 "020000000000000000000000000000000000000004000000000000000001",
1149 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
1150 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
1152 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
1155 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
1157 ("NIST curve B-233",
1158 "020000000000000000000000000000000000000004000000000000000001",
1159 "000000000000000000000000000000000000000000000000000000000001",
1160 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1161 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1162 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1164 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1167 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1169 ("NIST curve K-283",
1170 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1173 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1174 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1176 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1179 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1181 ("NIST curve B-283",
1182 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1183 "000000000000000000000000000000000000000000000000000000000000000000000001",
1184 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1185 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1186 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1188 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1191 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1193 ("NIST curve K-409",
1194 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1197 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1198 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1200 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1203 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1205 ("NIST curve B-409",
1206 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1207 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1208 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1209 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1210 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1212 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1215 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1217 ("NIST curve K-571",
1218 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1221 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1222 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1224 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1227 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1229 ("NIST curve B-571",
1230 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1231 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1232 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1233 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1234 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1236 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1239 /* more tests using the last curve */
1241 if (!EC_POINT_copy(Q
, P
))
1243 if (EC_POINT_is_at_infinity(group
, Q
))
1245 if (!EC_POINT_dbl(group
, P
, P
, ctx
))
1247 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
1249 if (!EC_POINT_invert(group
, Q
, ctx
))
1250 ABORT
; /* P = -2Q */
1252 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
))
1254 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
))
1256 if (!EC_POINT_is_at_infinity(group
, R
))
1257 ABORT
; /* R = P + 2Q */
1260 const EC_POINT
*points
[3];
1261 const BIGNUM
*scalars
[3];
1263 if (EC_POINT_is_at_infinity(group
, Q
))
1269 if (!BN_add(y
, z
, BN_value_one()))
1273 if (!BN_rshift1(y
, y
))
1275 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
1278 fprintf(stdout
, "combined multiplication ...");
1281 /* z is still the group order */
1282 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
1284 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
))
1286 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
1288 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
))
1291 fprintf(stdout
, ".");
1294 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0))
1296 if (!BN_add(z
, z
, y
))
1298 BN_set_negative(z
, 1);
1300 scalars
[1] = z
; /* z = -(order + y) */
1302 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
1304 if (!EC_POINT_is_at_infinity(group
, P
))
1307 fprintf(stdout
, ".");
1310 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0))
1312 if (!BN_add(z
, x
, y
))
1314 BN_set_negative(z
, 1);
1317 scalars
[2] = z
; /* z = -(x+y) */
1319 if (!EC_POINTs_mul(group
, P
, NULL
, 3, points
, scalars
, ctx
))
1321 if (!EC_POINT_is_at_infinity(group
, P
))
1324 fprintf(stdout
, " ok\n\n");
1331 EC_GROUP_free(group
);
1340 EC_GROUP_free(C2_K163
);
1341 EC_GROUP_free(C2_B163
);
1342 EC_GROUP_free(C2_K233
);
1343 EC_GROUP_free(C2_B233
);
1344 EC_GROUP_free(C2_K283
);
1345 EC_GROUP_free(C2_B283
);
1346 EC_GROUP_free(C2_K409
);
1347 EC_GROUP_free(C2_B409
);
1348 EC_GROUP_free(C2_K571
);
1349 EC_GROUP_free(C2_B571
);
1354 static void internal_curve_test(void)
1356 EC_builtin_curve
*curves
= NULL
;
1357 size_t crv_len
= 0, n
= 0;
1360 crv_len
= EC_get_builtin_curves(NULL
, 0);
1361 curves
= OPENSSL_malloc(sizeof(*curves
) * crv_len
);
1365 if (!EC_get_builtin_curves(curves
, crv_len
)) {
1366 OPENSSL_free(curves
);
1370 fprintf(stdout
, "testing internal curves: ");
1372 for (n
= 0; n
< crv_len
; n
++) {
1373 EC_GROUP
*group
= NULL
;
1374 int nid
= curves
[n
].nid
;
1375 if ((group
= EC_GROUP_new_by_curve_name(nid
)) == NULL
) {
1377 fprintf(stdout
, "\nEC_GROUP_new_curve_name() failed with"
1378 " curve %s\n", OBJ_nid2sn(nid
));
1379 /* try next curve */
1382 if (!EC_GROUP_check(group
, NULL
)) {
1384 fprintf(stdout
, "\nEC_GROUP_check() failed with"
1385 " curve %s\n", OBJ_nid2sn(nid
));
1386 EC_GROUP_free(group
);
1387 /* try the next curve */
1390 fprintf(stdout
, ".");
1392 EC_GROUP_free(group
);
1395 fprintf(stdout
, " ok\n\n");
1397 fprintf(stdout
, " failed\n\n");
1400 OPENSSL_free(curves
);
1404 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1406 * nistp_test_params contains magic numbers for testing our optimized
1407 * implementations of several NIST curves with characteristic > 3.
1409 struct nistp_test_params
{
1410 const EC_METHOD
*(*meth
) ();
1413 * Qx, Qy and D are taken from
1414 * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
1415 * Otherwise, values are standard curve parameters from FIPS 180-3
1417 const char *p
, *a
, *b
, *Qx
, *Qy
, *Gx
, *Gy
, *order
, *d
;
1420 static const struct nistp_test_params nistp_tests_params
[] = {
1423 EC_GFp_nistp224_method
,
1426 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
1428 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
1430 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
1432 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E",
1434 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555",
1436 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
1438 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
1440 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
1442 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8",
1446 EC_GFp_nistp256_method
,
1449 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
1451 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc",
1453 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
1455 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19",
1457 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09",
1459 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
1461 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5",
1463 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
1465 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96",
1469 EC_GFp_nistp521_method
,
1472 "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
1474 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc",
1476 "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00",
1478 "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4",
1480 "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e",
1482 "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66",
1484 "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650",
1486 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409",
1488 "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722",
1492 static void nistp_single_test(const struct nistp_test_params
*test
)
1495 BIGNUM
*p
, *a
, *b
, *x
, *y
, *n
, *m
, *order
;
1497 EC_POINT
*G
, *P
, *Q
, *Q_CHECK
;
1499 fprintf(stdout
, "\nNIST curve P-%d (optimised implementation):\n",
1511 NISTP
= EC_GROUP_new(test
->meth());
1514 if (!BN_hex2bn(&p
, test
->p
))
1516 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
1518 if (!BN_hex2bn(&a
, test
->a
))
1520 if (!BN_hex2bn(&b
, test
->b
))
1522 if (!EC_GROUP_set_curve_GFp(NISTP
, p
, a
, b
, ctx
))
1524 G
= EC_POINT_new(NISTP
);
1525 P
= EC_POINT_new(NISTP
);
1526 Q
= EC_POINT_new(NISTP
);
1527 Q_CHECK
= EC_POINT_new(NISTP
);
1528 if (!BN_hex2bn(&x
, test
->Qx
))
1530 if (!BN_hex2bn(&y
, test
->Qy
))
1532 if (!EC_POINT_set_affine_coordinates_GFp(NISTP
, Q_CHECK
, x
, y
, ctx
))
1534 if (!BN_hex2bn(&x
, test
->Gx
))
1536 if (!BN_hex2bn(&y
, test
->Gy
))
1538 if (!EC_POINT_set_affine_coordinates_GFp(NISTP
, G
, x
, y
, ctx
))
1540 if (!BN_hex2bn(&order
, test
->order
))
1542 if (!EC_GROUP_set_generator(NISTP
, G
, order
, BN_value_one()))
1545 fprintf(stdout
, "verify degree ... ");
1546 if (EC_GROUP_get_degree(NISTP
) != test
->degree
)
1548 fprintf(stdout
, "ok\n");
1550 fprintf(stdout
, "NIST test vectors ... ");
1551 if (!BN_hex2bn(&n
, test
->d
))
1553 /* fixed point multiplication */
1554 EC_POINT_mul(NISTP
, Q
, n
, NULL
, NULL
, ctx
);
1555 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1557 /* random point multiplication */
1558 EC_POINT_mul(NISTP
, Q
, NULL
, G
, n
, ctx
);
1559 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1562 /* set generator to P = 2*G, where G is the standard generator */
1563 if (!EC_POINT_dbl(NISTP
, P
, G
, ctx
))
1565 if (!EC_GROUP_set_generator(NISTP
, P
, order
, BN_value_one()))
1567 /* set the scalar to m=n/2, where n is the NIST test scalar */
1568 if (!BN_rshift(m
, n
, 1))
1571 /* test the non-standard generator */
1572 /* fixed point multiplication */
1573 EC_POINT_mul(NISTP
, Q
, m
, NULL
, NULL
, ctx
);
1574 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1576 /* random point multiplication */
1577 EC_POINT_mul(NISTP
, Q
, NULL
, P
, m
, ctx
);
1578 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1581 /* now repeat all tests with precomputation */
1582 if (!EC_GROUP_precompute_mult(NISTP
, ctx
))
1585 /* fixed point multiplication */
1586 EC_POINT_mul(NISTP
, Q
, m
, NULL
, NULL
, ctx
);
1587 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1589 /* random point multiplication */
1590 EC_POINT_mul(NISTP
, Q
, NULL
, P
, m
, ctx
);
1591 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1594 /* reset generator */
1595 if (!EC_GROUP_set_generator(NISTP
, G
, order
, BN_value_one()))
1597 /* fixed point multiplication */
1598 EC_POINT_mul(NISTP
, Q
, n
, NULL
, NULL
, ctx
);
1599 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1601 /* random point multiplication */
1602 EC_POINT_mul(NISTP
, Q
, NULL
, G
, n
, ctx
);
1603 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1606 fprintf(stdout
, "ok\n");
1607 group_order_tests(NISTP
);
1608 EC_GROUP_free(NISTP
);
1612 EC_POINT_free(Q_CHECK
);
1624 static void nistp_tests()
1628 for (i
= 0; i
< OSSL_NELEM(nistp_tests_params
); i
++) {
1629 nistp_single_test(&nistp_tests_params
[i
]);
1634 static const char rnd_seed
[] =
1635 "string to make the random number generator think it has entropy";
1637 int main(int argc
, char *argv
[])
1641 p
= getenv("OPENSSL_DEBUG_MEMORY");
1642 if (p
!= NULL
&& strcmp(p
, "on") == 0)
1643 CRYPTO_set_mem_debug(1);
1644 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON
);
1645 ERR_load_crypto_strings();
1647 RAND_seed(rnd_seed
, sizeof rnd_seed
); /* or BN_generate_prime may fail */
1649 prime_field_tests();
1651 # ifndef OPENSSL_NO_EC2M
1652 char2_field_tests();
1654 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1657 /* test the internal curves */
1658 internal_curve_test();
1660 # ifndef OPENSSL_NO_ENGINE
1663 CRYPTO_cleanup_all_ex_data();
1665 ERR_remove_thread_state(NULL
);
1666 #ifndef OPENSSL_NO_CRYPTO_MDEBUG
1667 CRYPTO_mem_leaks_fp(stderr
);