2 * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
10 /* ====================================================================
11 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
13 * Portions of the attached software ("Contribution") are developed by
14 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
16 * The Contribution is licensed pursuant to the OpenSSL open source
17 * license provided above.
19 * The elliptic curve binary polynomial software is originally written by
20 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
35 int main(int argc
, char *argv
[])
37 puts("Elliptic curves are disabled.");
42 # include <openssl/ec.h>
43 # ifndef OPENSSL_NO_ENGINE
44 # include <openssl/engine.h>
46 # include <openssl/err.h>
47 # include <openssl/obj_mac.h>
48 # include <openssl/objects.h>
49 # include <openssl/rand.h>
50 # include <openssl/bn.h>
51 # include <openssl/opensslconf.h>
53 # if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12)
54 /* suppress "too big too optimize" warning */
55 # pragma warning(disable:4959)
60 fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
61 ERR_print_errors_fp(stderr); \
65 # define TIMING_BASE_PT 0
66 # define TIMING_RAND_PT 1
67 # define TIMING_SIMUL 2
69 /* test multiplication with group order, long and negative scalars */
70 static void group_order_tests(EC_GROUP
*group
)
72 BIGNUM
*n1
, *n2
, *order
;
73 EC_POINT
*P
= EC_POINT_new(group
);
74 EC_POINT
*Q
= EC_POINT_new(group
);
75 EC_POINT
*R
= EC_POINT_new(group
);
76 EC_POINT
*S
= EC_POINT_new(group
);
77 BN_CTX
*ctx
= BN_CTX_new();
83 fprintf(stdout
, "verify group order ...");
85 if (!EC_GROUP_get_order(group
, order
, ctx
))
87 if (!EC_POINT_mul(group
, Q
, order
, NULL
, NULL
, ctx
))
89 if (!EC_POINT_is_at_infinity(group
, Q
))
93 if (!EC_GROUP_precompute_mult(group
, ctx
))
95 if (!EC_POINT_mul(group
, Q
, order
, NULL
, NULL
, ctx
))
97 if (!EC_POINT_is_at_infinity(group
, Q
))
99 fprintf(stdout
, " ok\n");
100 fprintf(stdout
, "long/negative scalar tests ");
101 for (i
= 1; i
<= 2; i
++) {
102 const BIGNUM
*scalars
[6];
103 const EC_POINT
*points
[6];
105 fprintf(stdout
, i
== 1 ?
106 "allowing precomputation ... " :
107 "without precomputation ... ");
108 if (!BN_set_word(n1
, i
))
111 * If i == 1, P will be the predefined generator for which
112 * EC_GROUP_precompute_mult has set up precomputation.
114 if (!EC_POINT_mul(group
, P
, n1
, NULL
, NULL
, ctx
))
120 if (!BN_sub(n1
, n1
, order
))
122 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n1
, ctx
))
124 if (0 != EC_POINT_cmp(group
, Q
, P
, ctx
))
128 if (!BN_add(n2
, order
, BN_value_one()))
130 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n2
, ctx
))
132 if (0 != EC_POINT_cmp(group
, Q
, P
, ctx
))
135 /* n2 = (1 - order) * (1 + order) = 1 - order^2 */
136 if (!BN_mul(n2
, n1
, n2
, ctx
))
138 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n2
, ctx
))
140 if (0 != EC_POINT_cmp(group
, Q
, P
, ctx
))
143 /* n2 = order^2 - 1 */
144 BN_set_negative(n2
, 0);
145 if (!EC_POINT_mul(group
, Q
, NULL
, P
, n2
, ctx
))
147 /* Add P to verify the result. */
148 if (!EC_POINT_add(group
, Q
, Q
, P
, ctx
))
150 if (!EC_POINT_is_at_infinity(group
, Q
))
153 /* Exercise EC_POINTs_mul, including corner cases. */
154 if (EC_POINT_is_at_infinity(group
, P
))
157 scalars
[0] = scalars
[1] = BN_value_one();
158 points
[0] = points
[1] = P
;
160 if (!EC_POINTs_mul(group
, R
, NULL
, 2, points
, scalars
, ctx
))
162 if (!EC_POINT_dbl(group
, S
, points
[0], ctx
))
164 if (0 != EC_POINT_cmp(group
, R
, S
, ctx
))
168 points
[0] = Q
; /* => infinity */
170 points
[1] = P
; /* => -P */
172 points
[2] = Q
; /* => infinity */
174 points
[3] = Q
; /* => infinity */
176 points
[4] = P
; /* => P */
178 points
[5] = Q
; /* => infinity */
179 if (!EC_POINTs_mul(group
, P
, NULL
, 6, points
, scalars
, ctx
))
181 if (!EC_POINT_is_at_infinity(group
, P
))
184 fprintf(stdout
, "ok\n");
196 static void prime_field_tests(void)
201 EC_GROUP
*P_160
= NULL
, *P_192
= NULL
, *P_224
= NULL
, *P_256
=
202 NULL
, *P_384
= NULL
, *P_521
= NULL
;
205 unsigned char buf
[100];
219 if (!BN_hex2bn(&p
, "17"))
221 if (!BN_hex2bn(&a
, "1"))
223 if (!BN_hex2bn(&b
, "1"))
226 group
= EC_GROUP_new(EC_GFp_mont_method()); /* applications should use
227 * EC_GROUP_new_curve_GFp so
228 * that the library gets to
229 * choose the EC_METHOD */
233 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
238 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
241 if (!EC_GROUP_copy(tmp
, group
))
243 EC_GROUP_free(group
);
247 if (!EC_GROUP_get_curve_GFp(group
, p
, a
, b
, ctx
))
251 "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
252 BN_print_fp(stdout
, p
);
253 fprintf(stdout
, ")\n a = 0x");
254 BN_print_fp(stdout
, a
);
255 fprintf(stdout
, "\n b = 0x");
256 BN_print_fp(stdout
, b
);
257 fprintf(stdout
, "\n");
259 P
= EC_POINT_new(group
);
260 Q
= EC_POINT_new(group
);
261 R
= EC_POINT_new(group
);
265 if (!EC_POINT_set_to_infinity(group
, P
))
267 if (!EC_POINT_is_at_infinity(group
, P
))
271 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
))
274 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
276 if (!EC_POINT_is_at_infinity(group
, P
))
285 if (!BN_hex2bn(&x
, "D"))
287 if (!EC_POINT_set_compressed_coordinates_GFp(group
, Q
, x
, 1, ctx
))
289 if (EC_POINT_is_on_curve(group
, Q
, ctx
) <= 0) {
290 if (!EC_POINT_get_affine_coordinates_GFp(group
, Q
, x
, y
, ctx
))
292 fprintf(stderr
, "Point is not on curve: x = 0x");
293 BN_print_fp(stderr
, x
);
294 fprintf(stderr
, ", y = 0x");
295 BN_print_fp(stderr
, y
);
296 fprintf(stderr
, "\n");
300 fprintf(stdout
, "A cyclic subgroup:\n");
306 if (EC_POINT_is_at_infinity(group
, P
))
307 fprintf(stdout
, " point at infinity\n");
309 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
312 fprintf(stdout
, " x = 0x");
313 BN_print_fp(stdout
, x
);
314 fprintf(stdout
, ", y = 0x");
315 BN_print_fp(stdout
, y
);
316 fprintf(stdout
, "\n");
319 if (!EC_POINT_copy(R
, P
))
321 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
325 while (!EC_POINT_is_at_infinity(group
, P
));
327 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
))
329 if (!EC_POINT_is_at_infinity(group
, P
))
333 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
,
337 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
339 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
341 fprintf(stdout
, "Generator as octet string, compressed form:\n ");
342 for (i
= 0; i
< len
; i
++)
343 fprintf(stdout
, "%02X", buf
[i
]);
346 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
,
350 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
352 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
354 fprintf(stdout
, "\nGenerator as octet string, uncompressed form:\n ");
355 for (i
= 0; i
< len
; i
++)
356 fprintf(stdout
, "%02X", buf
[i
]);
359 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
,
363 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
365 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
367 fprintf(stdout
, "\nGenerator as octet string, hybrid form:\n ");
368 for (i
= 0; i
< len
; i
++)
369 fprintf(stdout
, "%02X", buf
[i
]);
371 if (!EC_POINT_get_Jprojective_coordinates_GFp(group
, R
, x
, y
, z
, ctx
))
374 "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
375 BN_print_fp(stdout
, x
);
376 fprintf(stdout
, ", Y = 0x");
377 BN_print_fp(stdout
, y
);
378 fprintf(stdout
, ", Z = 0x");
379 BN_print_fp(stdout
, z
);
380 fprintf(stdout
, "\n");
382 if (!EC_POINT_invert(group
, P
, ctx
))
384 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
388 * Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2,
389 * 2000) -- not a NIST curve, but commonly used
392 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"))
394 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
396 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"))
398 if (!BN_hex2bn(&b
, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45"))
400 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
403 if (!BN_hex2bn(&x
, "4A96B5688EF573284664698968C38BB913CBFC82"))
405 if (!BN_hex2bn(&y
, "23a628553168947d59dcc912042351377ac5fb32"))
407 if (!EC_POINT_set_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
409 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
411 if (!BN_hex2bn(&z
, "0100000000000000000001F4C8F927AED3CA752257"))
413 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
416 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
418 fprintf(stdout
, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
419 BN_print_fp(stdout
, x
);
420 fprintf(stdout
, "\n y = 0x");
421 BN_print_fp(stdout
, y
);
422 fprintf(stdout
, "\n");
423 /* G_y value taken from the standard: */
424 if (!BN_hex2bn(&z
, "23a628553168947d59dcc912042351377ac5fb32"))
426 if (0 != BN_cmp(y
, z
))
429 fprintf(stdout
, "verify degree ...");
430 if (EC_GROUP_get_degree(group
) != 160)
432 fprintf(stdout
, " ok\n");
434 group_order_tests(group
);
436 if ((P_160
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
438 if (!EC_GROUP_copy(P_160
, group
))
441 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
443 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"))
445 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
447 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"))
449 if (!BN_hex2bn(&b
, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"))
451 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
454 if (!BN_hex2bn(&x
, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"))
456 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
))
458 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
460 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"))
462 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
465 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
467 fprintf(stdout
, "\nNIST curve P-192 -- Generator:\n x = 0x");
468 BN_print_fp(stdout
, x
);
469 fprintf(stdout
, "\n y = 0x");
470 BN_print_fp(stdout
, y
);
471 fprintf(stdout
, "\n");
472 /* G_y value taken from the standard: */
473 if (!BN_hex2bn(&z
, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"))
475 if (0 != BN_cmp(y
, z
))
478 fprintf(stdout
, "verify degree ...");
479 if (EC_GROUP_get_degree(group
) != 192)
481 fprintf(stdout
, " ok\n");
483 group_order_tests(group
);
485 if ((P_192
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
487 if (!EC_GROUP_copy(P_192
, group
))
490 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
493 (&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"))
495 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
498 (&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"))
501 (&b
, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"))
503 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
507 (&x
, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"))
509 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
))
511 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
514 (&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"))
516 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
519 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
521 fprintf(stdout
, "\nNIST curve P-224 -- Generator:\n x = 0x");
522 BN_print_fp(stdout
, x
);
523 fprintf(stdout
, "\n y = 0x");
524 BN_print_fp(stdout
, y
);
525 fprintf(stdout
, "\n");
526 /* G_y value taken from the standard: */
528 (&z
, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"))
530 if (0 != BN_cmp(y
, z
))
533 fprintf(stdout
, "verify degree ...");
534 if (EC_GROUP_get_degree(group
) != 224)
536 fprintf(stdout
, " ok\n");
538 group_order_tests(group
);
540 if ((P_224
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
542 if (!EC_GROUP_copy(P_224
, group
))
545 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
549 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"))
551 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
555 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC"))
559 "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"))
561 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
566 "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"))
568 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
))
570 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
572 if (!BN_hex2bn(&z
, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
573 "84F3B9CAC2FC632551"))
575 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
578 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
580 fprintf(stdout
, "\nNIST curve P-256 -- Generator:\n x = 0x");
581 BN_print_fp(stdout
, x
);
582 fprintf(stdout
, "\n y = 0x");
583 BN_print_fp(stdout
, y
);
584 fprintf(stdout
, "\n");
585 /* G_y value taken from the standard: */
588 "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"))
590 if (0 != BN_cmp(y
, z
))
593 fprintf(stdout
, "verify degree ...");
594 if (EC_GROUP_get_degree(group
) != 256)
596 fprintf(stdout
, " ok\n");
598 group_order_tests(group
);
600 if ((P_256
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
602 if (!EC_GROUP_copy(P_256
, group
))
605 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
607 if (!BN_hex2bn(&p
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
608 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"))
610 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
612 if (!BN_hex2bn(&a
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
613 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC"))
615 if (!BN_hex2bn(&b
, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
616 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"))
618 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
621 if (!BN_hex2bn(&x
, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
622 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7"))
624 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 1, ctx
))
626 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
628 if (!BN_hex2bn(&z
, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
629 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"))
631 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
634 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
636 fprintf(stdout
, "\nNIST curve P-384 -- Generator:\n x = 0x");
637 BN_print_fp(stdout
, x
);
638 fprintf(stdout
, "\n y = 0x");
639 BN_print_fp(stdout
, y
);
640 fprintf(stdout
, "\n");
641 /* G_y value taken from the standard: */
642 if (!BN_hex2bn(&z
, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
643 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"))
645 if (0 != BN_cmp(y
, z
))
648 fprintf(stdout
, "verify degree ...");
649 if (EC_GROUP_get_degree(group
) != 384)
651 fprintf(stdout
, " ok\n");
653 group_order_tests(group
);
655 if ((P_384
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
657 if (!EC_GROUP_copy(P_384
, group
))
660 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
662 if (!BN_hex2bn(&p
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
663 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
664 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
666 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
668 if (!BN_hex2bn(&a
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
669 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
670 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC"))
672 if (!BN_hex2bn(&b
, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
673 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
674 "DF883D2C34F1EF451FD46B503F00"))
676 if (!EC_GROUP_set_curve_GFp(group
, p
, a
, b
, ctx
))
679 if (!BN_hex2bn(&x
, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
680 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
681 "3C1856A429BF97E7E31C2E5BD66"))
683 if (!EC_POINT_set_compressed_coordinates_GFp(group
, P
, x
, 0, ctx
))
685 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
687 if (!BN_hex2bn(&z
, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
688 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
689 "C9B8899C47AEBB6FB71E91386409"))
691 if (!EC_GROUP_set_generator(group
, P
, z
, BN_value_one()))
694 if (!EC_POINT_get_affine_coordinates_GFp(group
, P
, x
, y
, ctx
))
696 fprintf(stdout
, "\nNIST curve P-521 -- Generator:\n x = 0x");
697 BN_print_fp(stdout
, x
);
698 fprintf(stdout
, "\n y = 0x");
699 BN_print_fp(stdout
, y
);
700 fprintf(stdout
, "\n");
701 /* G_y value taken from the standard: */
702 if (!BN_hex2bn(&z
, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
703 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
704 "7086A272C24088BE94769FD16650"))
706 if (0 != BN_cmp(y
, z
))
709 fprintf(stdout
, "verify degree ...");
710 if (EC_GROUP_get_degree(group
) != 521)
712 fprintf(stdout
, " ok\n");
714 group_order_tests(group
);
716 if ((P_521
= EC_GROUP_new(EC_GROUP_method_of(group
))) == NULL
)
718 if (!EC_GROUP_copy(P_521
, group
))
721 /* more tests using the last curve */
723 if (!EC_POINT_copy(Q
, P
))
725 if (EC_POINT_is_at_infinity(group
, Q
))
727 if (!EC_POINT_dbl(group
, P
, P
, ctx
))
729 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
731 if (!EC_POINT_invert(group
, Q
, ctx
))
734 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
))
736 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
))
738 if (!EC_POINT_is_at_infinity(group
, R
))
739 ABORT
; /* R = P + 2Q */
742 const EC_POINT
*points
[4];
743 const BIGNUM
*scalars
[4];
746 if (EC_POINT_is_at_infinity(group
, Q
))
753 if (!EC_GROUP_get_order(group
, z
, ctx
))
755 if (!BN_add(y
, z
, BN_value_one()))
759 if (!BN_rshift1(y
, y
))
761 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
764 fprintf(stdout
, "combined multiplication ...");
767 /* z is still the group order */
768 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
770 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
))
772 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
774 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
))
777 fprintf(stdout
, ".");
780 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0))
782 if (!BN_add(z
, z
, y
))
784 BN_set_negative(z
, 1);
786 scalars
[1] = z
; /* z = -(order + y) */
788 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
790 if (!EC_POINT_is_at_infinity(group
, P
))
793 fprintf(stdout
, ".");
796 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0))
798 if (!BN_add(z
, x
, y
))
800 BN_set_negative(z
, 1);
803 scalars
[2] = z
; /* z = -(x+y) */
809 scalars
[3] = scalar3
;
811 if (!EC_POINTs_mul(group
, P
, NULL
, 4, points
, scalars
, ctx
))
813 if (!EC_POINT_is_at_infinity(group
, P
))
816 fprintf(stdout
, " ok\n\n");
825 EC_GROUP_free(group
);
833 EC_GROUP_free(P_160
);
834 EC_GROUP_free(P_192
);
835 EC_GROUP_free(P_224
);
836 EC_GROUP_free(P_256
);
837 EC_GROUP_free(P_384
);
838 EC_GROUP_free(P_521
);
842 /* Change test based on whether binary point compression is enabled or not. */
843 # ifdef OPENSSL_EC_BIN_PT_COMP
844 # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
845 if (!BN_hex2bn(&x, _x)) ABORT; \
846 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
847 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \
848 if (!BN_hex2bn(&z, _order)) ABORT; \
849 if (!BN_hex2bn(&cof, _cof)) ABORT; \
850 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
851 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
852 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
853 BN_print_fp(stdout, x); \
854 fprintf(stdout, "\n y = 0x"); \
855 BN_print_fp(stdout, y); \
856 fprintf(stdout, "\n"); \
857 /* G_y value taken from the standard: */ \
858 if (!BN_hex2bn(&z, _y)) ABORT; \
859 if (0 != BN_cmp(y, z)) ABORT;
861 # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
862 if (!BN_hex2bn(&x, _x)) ABORT; \
863 if (!BN_hex2bn(&y, _y)) ABORT; \
864 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
865 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \
866 if (!BN_hex2bn(&z, _order)) ABORT; \
867 if (!BN_hex2bn(&cof, _cof)) ABORT; \
868 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
869 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
870 BN_print_fp(stdout, x); \
871 fprintf(stdout, "\n y = 0x"); \
872 BN_print_fp(stdout, y); \
873 fprintf(stdout, "\n");
876 # define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
877 if (!BN_hex2bn(&p, _p)) ABORT; \
878 if (!BN_hex2bn(&a, _a)) ABORT; \
879 if (!BN_hex2bn(&b, _b)) ABORT; \
880 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
881 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
882 fprintf(stdout, "verify degree ..."); \
883 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
884 fprintf(stdout, " ok\n"); \
885 group_order_tests(group); \
886 if ((_variable = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL) ABORT; \
887 if (!EC_GROUP_copy(_variable, group)) ABORT; \
889 # ifndef OPENSSL_NO_EC2M
891 static void char2_field_tests(void)
896 EC_GROUP
*C2_K163
= NULL
, *C2_K233
= NULL
, *C2_K283
= NULL
, *C2_K409
=
897 NULL
, *C2_K571
= NULL
;
898 EC_GROUP
*C2_B163
= NULL
, *C2_B233
= NULL
, *C2_B283
= NULL
, *C2_B409
=
899 NULL
, *C2_B571
= NULL
;
901 BIGNUM
*x
, *y
, *z
, *cof
;
902 unsigned char buf
[100];
916 if (!BN_hex2bn(&p
, "13"))
918 if (!BN_hex2bn(&a
, "3"))
920 if (!BN_hex2bn(&b
, "1"))
923 group
= EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use
924 * EC_GROUP_new_curve_GF2m
925 * so that the library gets
926 * to choose the EC_METHOD */
929 if (!EC_GROUP_set_curve_GF2m(group
, p
, a
, b
, ctx
))
934 tmp
= EC_GROUP_new(EC_GROUP_method_of(group
));
937 if (!EC_GROUP_copy(tmp
, group
))
939 EC_GROUP_free(group
);
943 if (!EC_GROUP_get_curve_GF2m(group
, p
, a
, b
, ctx
))
947 "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
948 BN_print_fp(stdout
, p
);
949 fprintf(stdout
, ")\n a = 0x");
950 BN_print_fp(stdout
, a
);
951 fprintf(stdout
, "\n b = 0x");
952 BN_print_fp(stdout
, b
);
953 fprintf(stdout
, "\n(0x... means binary polynomial)\n");
955 P
= EC_POINT_new(group
);
956 Q
= EC_POINT_new(group
);
957 R
= EC_POINT_new(group
);
961 if (!EC_POINT_set_to_infinity(group
, P
))
963 if (!EC_POINT_is_at_infinity(group
, P
))
967 if (!EC_POINT_oct2point(group
, Q
, buf
, 1, ctx
))
970 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
972 if (!EC_POINT_is_at_infinity(group
, P
))
979 if (!x
|| !y
|| !z
|| !cof
)
982 if (!BN_hex2bn(&x
, "6"))
984 /* Change test based on whether binary point compression is enabled or not. */
985 # ifdef OPENSSL_EC_BIN_PT_COMP
986 if (!EC_POINT_set_compressed_coordinates_GF2m(group
, Q
, x
, 1, ctx
))
989 if (!BN_hex2bn(&y
, "8"))
991 if (!EC_POINT_set_affine_coordinates_GF2m(group
, Q
, x
, y
, ctx
))
994 if (EC_POINT_is_on_curve(group
, Q
, ctx
) <= 0) {
995 /* Change test based on whether binary point compression is enabled or not. */
996 # ifdef OPENSSL_EC_BIN_PT_COMP
997 if (!EC_POINT_get_affine_coordinates_GF2m(group
, Q
, x
, y
, ctx
))
1000 fprintf(stderr
, "Point is not on curve: x = 0x");
1001 BN_print_fp(stderr
, x
);
1002 fprintf(stderr
, ", y = 0x");
1003 BN_print_fp(stderr
, y
);
1004 fprintf(stderr
, "\n");
1008 fprintf(stdout
, "A cyclic subgroup:\n");
1014 if (EC_POINT_is_at_infinity(group
, P
))
1015 fprintf(stdout
, " point at infinity\n");
1017 if (!EC_POINT_get_affine_coordinates_GF2m(group
, P
, x
, y
, ctx
))
1020 fprintf(stdout
, " x = 0x");
1021 BN_print_fp(stdout
, x
);
1022 fprintf(stdout
, ", y = 0x");
1023 BN_print_fp(stdout
, y
);
1024 fprintf(stdout
, "\n");
1027 if (!EC_POINT_copy(R
, P
))
1029 if (!EC_POINT_add(group
, P
, P
, Q
, ctx
))
1032 while (!EC_POINT_is_at_infinity(group
, P
));
1034 if (!EC_POINT_add(group
, P
, Q
, R
, ctx
))
1036 if (!EC_POINT_is_at_infinity(group
, P
))
1039 /* Change test based on whether binary point compression is enabled or not. */
1040 # ifdef OPENSSL_EC_BIN_PT_COMP
1042 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_COMPRESSED
, buf
,
1046 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
1048 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
1050 fprintf(stdout
, "Generator as octet string, compressed form:\n ");
1051 for (i
= 0; i
< len
; i
++)
1052 fprintf(stdout
, "%02X", buf
[i
]);
1056 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_UNCOMPRESSED
, buf
,
1060 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
1062 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
1064 fprintf(stdout
, "\nGenerator as octet string, uncompressed form:\n ");
1065 for (i
= 0; i
< len
; i
++)
1066 fprintf(stdout
, "%02X", buf
[i
]);
1068 /* Change test based on whether binary point compression is enabled or not. */
1069 # ifdef OPENSSL_EC_BIN_PT_COMP
1071 EC_POINT_point2oct(group
, Q
, POINT_CONVERSION_HYBRID
, buf
, sizeof buf
,
1075 if (!EC_POINT_oct2point(group
, P
, buf
, len
, ctx
))
1077 if (0 != EC_POINT_cmp(group
, P
, Q
, ctx
))
1079 fprintf(stdout
, "\nGenerator as octet string, hybrid form:\n ");
1080 for (i
= 0; i
< len
; i
++)
1081 fprintf(stdout
, "%02X", buf
[i
]);
1084 fprintf(stdout
, "\n");
1086 if (!EC_POINT_invert(group
, P
, ctx
))
1088 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
1091 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
1093 ("NIST curve K-163",
1094 "0800000000000000000000000000000000000000C9",
1097 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
1098 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
1099 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163, C2_K163
);
1101 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
1103 ("NIST curve B-163",
1104 "0800000000000000000000000000000000000000C9",
1106 "020A601907B8C953CA1481EB10512F78744A3205FD",
1107 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
1108 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
1109 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163, C2_B163
);
1111 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
1113 ("NIST curve K-233",
1114 "020000000000000000000000000000000000000004000000000000000001",
1117 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
1118 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
1120 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
1123 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
1125 ("NIST curve B-233",
1126 "020000000000000000000000000000000000000004000000000000000001",
1127 "000000000000000000000000000000000000000000000000000000000001",
1128 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1129 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1130 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1132 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1135 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1137 ("NIST curve K-283",
1138 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1141 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1142 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1144 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1147 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1149 ("NIST curve B-283",
1150 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1151 "000000000000000000000000000000000000000000000000000000000000000000000001",
1152 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1153 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1154 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1156 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1159 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1161 ("NIST curve K-409",
1162 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1165 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1166 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1168 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1171 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1173 ("NIST curve B-409",
1174 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1175 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1176 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1177 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1178 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1180 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1183 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1185 ("NIST curve K-571",
1186 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1189 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1190 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1192 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1195 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1197 ("NIST curve B-571",
1198 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1199 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1200 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1201 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1202 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1204 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1207 /* more tests using the last curve */
1209 if (!EC_POINT_copy(Q
, P
))
1211 if (EC_POINT_is_at_infinity(group
, Q
))
1213 if (!EC_POINT_dbl(group
, P
, P
, ctx
))
1215 if (EC_POINT_is_on_curve(group
, P
, ctx
) <= 0)
1217 if (!EC_POINT_invert(group
, Q
, ctx
))
1218 ABORT
; /* P = -2Q */
1220 if (!EC_POINT_add(group
, R
, P
, Q
, ctx
))
1222 if (!EC_POINT_add(group
, R
, R
, Q
, ctx
))
1224 if (!EC_POINT_is_at_infinity(group
, R
))
1225 ABORT
; /* R = P + 2Q */
1228 const EC_POINT
*points
[3];
1229 const BIGNUM
*scalars
[3];
1231 if (EC_POINT_is_at_infinity(group
, Q
))
1237 if (!BN_add(y
, z
, BN_value_one()))
1241 if (!BN_rshift1(y
, y
))
1243 scalars
[0] = y
; /* (group order + 1)/2, so y*Q + y*Q = Q */
1246 fprintf(stdout
, "combined multiplication ...");
1249 /* z is still the group order */
1250 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
1252 if (!EC_POINTs_mul(group
, R
, z
, 2, points
, scalars
, ctx
))
1254 if (0 != EC_POINT_cmp(group
, P
, R
, ctx
))
1256 if (0 != EC_POINT_cmp(group
, R
, Q
, ctx
))
1259 fprintf(stdout
, ".");
1262 if (!BN_pseudo_rand(y
, BN_num_bits(y
), 0, 0))
1264 if (!BN_add(z
, z
, y
))
1266 BN_set_negative(z
, 1);
1268 scalars
[1] = z
; /* z = -(order + y) */
1270 if (!EC_POINTs_mul(group
, P
, NULL
, 2, points
, scalars
, ctx
))
1272 if (!EC_POINT_is_at_infinity(group
, P
))
1275 fprintf(stdout
, ".");
1278 if (!BN_pseudo_rand(x
, BN_num_bits(y
) - 1, 0, 0))
1280 if (!BN_add(z
, x
, y
))
1282 BN_set_negative(z
, 1);
1285 scalars
[2] = z
; /* z = -(x+y) */
1287 if (!EC_POINTs_mul(group
, P
, NULL
, 3, points
, scalars
, ctx
))
1289 if (!EC_POINT_is_at_infinity(group
, P
))
1292 fprintf(stdout
, " ok\n\n");
1299 EC_GROUP_free(group
);
1308 EC_GROUP_free(C2_K163
);
1309 EC_GROUP_free(C2_B163
);
1310 EC_GROUP_free(C2_K233
);
1311 EC_GROUP_free(C2_B233
);
1312 EC_GROUP_free(C2_K283
);
1313 EC_GROUP_free(C2_B283
);
1314 EC_GROUP_free(C2_K409
);
1315 EC_GROUP_free(C2_B409
);
1316 EC_GROUP_free(C2_K571
);
1317 EC_GROUP_free(C2_B571
);
1322 static void internal_curve_test(void)
1324 EC_builtin_curve
*curves
= NULL
;
1325 size_t crv_len
= 0, n
= 0;
1328 crv_len
= EC_get_builtin_curves(NULL
, 0);
1329 curves
= OPENSSL_malloc(sizeof(*curves
) * crv_len
);
1333 if (!EC_get_builtin_curves(curves
, crv_len
)) {
1334 OPENSSL_free(curves
);
1338 fprintf(stdout
, "testing internal curves: ");
1340 for (n
= 0; n
< crv_len
; n
++) {
1341 EC_GROUP
*group
= NULL
;
1342 int nid
= curves
[n
].nid
;
1343 if ((group
= EC_GROUP_new_by_curve_name(nid
)) == NULL
) {
1345 fprintf(stdout
, "\nEC_GROUP_new_curve_name() failed with"
1346 " curve %s\n", OBJ_nid2sn(nid
));
1347 /* try next curve */
1350 if (!EC_GROUP_check(group
, NULL
)) {
1352 fprintf(stdout
, "\nEC_GROUP_check() failed with"
1353 " curve %s\n", OBJ_nid2sn(nid
));
1354 EC_GROUP_free(group
);
1355 /* try the next curve */
1358 fprintf(stdout
, ".");
1360 EC_GROUP_free(group
);
1363 fprintf(stdout
, " ok\n\n");
1365 fprintf(stdout
, " failed\n\n");
1369 /* Test all built-in curves and let the library choose the EC_METHOD */
1370 for (n
= 0; n
< crv_len
; n
++) {
1371 EC_GROUP
*group
= NULL
;
1372 int nid
= curves
[n
].nid
;
1374 * Skip for X25519 because low level operations such as EC_POINT_mul()
1375 * are not supported for this curve
1377 if (nid
== NID_X25519
)
1379 fprintf(stdout
, "%s:\n", OBJ_nid2sn(nid
));
1381 if ((group
= EC_GROUP_new_by_curve_name(nid
)) == NULL
) {
1384 group_order_tests(group
);
1385 EC_GROUP_free(group
);
1388 OPENSSL_free(curves
);
1392 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1394 * nistp_test_params contains magic numbers for testing our optimized
1395 * implementations of several NIST curves with characteristic > 3.
1397 struct nistp_test_params
{
1398 const EC_METHOD
*(*meth
) ();
1401 * Qx, Qy and D are taken from
1402 * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
1403 * Otherwise, values are standard curve parameters from FIPS 180-3
1405 const char *p
, *a
, *b
, *Qx
, *Qy
, *Gx
, *Gy
, *order
, *d
;
1408 static const struct nistp_test_params nistp_tests_params
[] = {
1411 EC_GFp_nistp224_method
,
1414 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
1416 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
1418 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
1420 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E",
1422 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555",
1424 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
1426 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
1428 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
1430 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8",
1434 EC_GFp_nistp256_method
,
1437 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
1439 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc",
1441 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
1443 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19",
1445 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09",
1447 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
1449 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5",
1451 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
1453 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96",
1457 EC_GFp_nistp521_method
,
1460 "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
1462 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc",
1464 "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00",
1466 "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4",
1468 "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e",
1470 "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66",
1472 "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650",
1474 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409",
1476 "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722",
1480 static void nistp_single_test(const struct nistp_test_params
*test
)
1483 BIGNUM
*p
, *a
, *b
, *x
, *y
, *n
, *m
, *order
;
1485 EC_POINT
*G
, *P
, *Q
, *Q_CHECK
;
1487 fprintf(stdout
, "\nNIST curve P-%d (optimised implementation):\n",
1499 NISTP
= EC_GROUP_new(test
->meth());
1502 if (!BN_hex2bn(&p
, test
->p
))
1504 if (1 != BN_is_prime_ex(p
, BN_prime_checks
, ctx
, NULL
))
1506 if (!BN_hex2bn(&a
, test
->a
))
1508 if (!BN_hex2bn(&b
, test
->b
))
1510 if (!EC_GROUP_set_curve_GFp(NISTP
, p
, a
, b
, ctx
))
1512 G
= EC_POINT_new(NISTP
);
1513 P
= EC_POINT_new(NISTP
);
1514 Q
= EC_POINT_new(NISTP
);
1515 Q_CHECK
= EC_POINT_new(NISTP
);
1516 if (!BN_hex2bn(&x
, test
->Qx
))
1518 if (!BN_hex2bn(&y
, test
->Qy
))
1520 if (!EC_POINT_set_affine_coordinates_GFp(NISTP
, Q_CHECK
, x
, y
, ctx
))
1522 if (!BN_hex2bn(&x
, test
->Gx
))
1524 if (!BN_hex2bn(&y
, test
->Gy
))
1526 if (!EC_POINT_set_affine_coordinates_GFp(NISTP
, G
, x
, y
, ctx
))
1528 if (!BN_hex2bn(&order
, test
->order
))
1530 if (!EC_GROUP_set_generator(NISTP
, G
, order
, BN_value_one()))
1533 fprintf(stdout
, "verify degree ... ");
1534 if (EC_GROUP_get_degree(NISTP
) != test
->degree
)
1536 fprintf(stdout
, "ok\n");
1538 fprintf(stdout
, "NIST test vectors ... ");
1539 if (!BN_hex2bn(&n
, test
->d
))
1541 /* fixed point multiplication */
1542 EC_POINT_mul(NISTP
, Q
, n
, NULL
, NULL
, ctx
);
1543 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1545 /* random point multiplication */
1546 EC_POINT_mul(NISTP
, Q
, NULL
, G
, n
, ctx
);
1547 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1550 /* set generator to P = 2*G, where G is the standard generator */
1551 if (!EC_POINT_dbl(NISTP
, P
, G
, ctx
))
1553 if (!EC_GROUP_set_generator(NISTP
, P
, order
, BN_value_one()))
1555 /* set the scalar to m=n/2, where n is the NIST test scalar */
1556 if (!BN_rshift(m
, n
, 1))
1559 /* test the non-standard generator */
1560 /* fixed point multiplication */
1561 EC_POINT_mul(NISTP
, Q
, m
, NULL
, NULL
, ctx
);
1562 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1564 /* random point multiplication */
1565 EC_POINT_mul(NISTP
, Q
, NULL
, P
, m
, ctx
);
1566 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1570 * We have not performed precomputation so have_precompute mult should be
1573 if (EC_GROUP_have_precompute_mult(NISTP
))
1576 /* now repeat all tests with precomputation */
1577 if (!EC_GROUP_precompute_mult(NISTP
, ctx
))
1579 if (!EC_GROUP_have_precompute_mult(NISTP
))
1582 /* fixed point multiplication */
1583 EC_POINT_mul(NISTP
, Q
, m
, NULL
, NULL
, ctx
);
1584 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1586 /* random point multiplication */
1587 EC_POINT_mul(NISTP
, Q
, NULL
, P
, m
, ctx
);
1588 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1591 /* reset generator */
1592 if (!EC_GROUP_set_generator(NISTP
, G
, order
, BN_value_one()))
1594 /* fixed point multiplication */
1595 EC_POINT_mul(NISTP
, Q
, n
, NULL
, NULL
, ctx
);
1596 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1598 /* random point multiplication */
1599 EC_POINT_mul(NISTP
, Q
, NULL
, G
, n
, ctx
);
1600 if (0 != EC_POINT_cmp(NISTP
, Q
, Q_CHECK
, ctx
))
1603 fprintf(stdout
, "ok\n");
1604 group_order_tests(NISTP
);
1605 EC_GROUP_free(NISTP
);
1609 EC_POINT_free(Q_CHECK
);
1621 static void nistp_tests()
1625 for (i
= 0; i
< OSSL_NELEM(nistp_tests_params
); i
++) {
1626 nistp_single_test(&nistp_tests_params
[i
]);
1631 static const char rnd_seed
[] =
1632 "string to make the random number generator think it has entropy";
1634 int main(int argc
, char *argv
[])
1638 p
= getenv("OPENSSL_DEBUG_MEMORY");
1639 if (p
!= NULL
&& strcmp(p
, "on") == 0)
1640 CRYPTO_set_mem_debug(1);
1641 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON
);
1643 RAND_seed(rnd_seed
, sizeof rnd_seed
); /* or BN_generate_prime may fail */
1645 prime_field_tests();
1647 # ifndef OPENSSL_NO_EC2M
1648 char2_field_tests();
1650 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1653 /* test the internal curves */
1654 internal_curve_test();
1656 #ifndef OPENSSL_NO_CRYPTO_MDEBUG
1657 if (CRYPTO_mem_leaks_fp(stderr
) <= 0)