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;
204 BIGNUM *x, *y, *z, *yplusone;
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))
283 if (x == NULL || y == NULL || z == NULL || yplusone == NULL)
286 if (!BN_hex2bn(&x, "D"))
288 if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx))
290 if (EC_POINT_is_on_curve(group, Q, ctx) <= 0) {
291 if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx))
293 fprintf(stderr, "Point is not on curve: x = 0x");
294 BN_print_fp(stderr, x);
295 fprintf(stderr, ", y = 0x");
296 BN_print_fp(stderr, y);
297 fprintf(stderr, "\n");
301 fprintf(stdout, "A cyclic subgroup:\n");
307 if (EC_POINT_is_at_infinity(group, P))
308 fprintf(stdout, " point at infinity\n");
310 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
313 fprintf(stdout, " x = 0x");
314 BN_print_fp(stdout, x);
315 fprintf(stdout, ", y = 0x");
316 BN_print_fp(stdout, y);
317 fprintf(stdout, "\n");
320 if (!EC_POINT_copy(R, P))
322 if (!EC_POINT_add(group, P, P, Q, ctx))
326 while (!EC_POINT_is_at_infinity(group, P));
328 if (!EC_POINT_add(group, P, Q, R, ctx))
330 if (!EC_POINT_is_at_infinity(group, P))
334 EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf,
338 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
340 if (0 != EC_POINT_cmp(group, P, Q, ctx))
342 fprintf(stdout, "Generator as octet string, compressed form:\n ");
343 for (i = 0; i < len; i++)
344 fprintf(stdout, "%02X", buf[i]);
347 EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf,
351 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
353 if (0 != EC_POINT_cmp(group, P, Q, ctx))
355 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
356 for (i = 0; i < len; i++)
357 fprintf(stdout, "%02X", buf[i]);
360 EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf,
364 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
366 if (0 != EC_POINT_cmp(group, P, Q, ctx))
368 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
369 for (i = 0; i < len; i++)
370 fprintf(stdout, "%02X", buf[i]);
372 if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx))
375 "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
376 BN_print_fp(stdout, x);
377 fprintf(stdout, ", Y = 0x");
378 BN_print_fp(stdout, y);
379 fprintf(stdout, ", Z = 0x");
380 BN_print_fp(stdout, z);
381 fprintf(stdout, "\n");
383 if (!EC_POINT_invert(group, P, ctx))
385 if (0 != EC_POINT_cmp(group, P, R, ctx))
389 * Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2,
390 * 2000) -- not a NIST curve, but commonly used
393 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"))
395 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
397 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"))
399 if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45"))
401 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
404 if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82"))
406 if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32"))
408 if (!BN_add(yplusone, y, BN_value_one()))
411 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
412 * and therefore setting the coordinates should fail.
414 if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
416 if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx))
418 if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
420 if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257"))
422 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
425 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
427 fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
428 BN_print_fp(stdout, x);
429 fprintf(stdout, "\n y = 0x");
430 BN_print_fp(stdout, y);
431 fprintf(stdout, "\n");
432 /* G_y value taken from the standard: */
433 if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32"))
435 if (0 != BN_cmp(y, z))
438 fprintf(stdout, "verify degree ...");
439 if (EC_GROUP_get_degree(group) != 160)
441 fprintf(stdout, " ok\n");
443 group_order_tests(group);
445 if ((P_160 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
447 if (!EC_GROUP_copy(P_160, group))
450 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
452 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"))
454 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
456 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"))
458 if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"))
460 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
463 if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"))
465 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx))
467 if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
469 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"))
471 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
474 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
476 fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
477 BN_print_fp(stdout, x);
478 fprintf(stdout, "\n y = 0x");
479 BN_print_fp(stdout, y);
480 fprintf(stdout, "\n");
481 /* G_y value taken from the standard: */
482 if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"))
484 if (0 != BN_cmp(y, z))
487 if (!BN_add(yplusone, y, BN_value_one()))
490 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
491 * and therefore setting the coordinates should fail.
493 if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
496 fprintf(stdout, "verify degree ...");
497 if (EC_GROUP_get_degree(group) != 192)
499 fprintf(stdout, " ok\n");
501 group_order_tests(group);
503 if ((P_192 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
505 if (!EC_GROUP_copy(P_192, group))
508 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
511 (&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"))
513 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
516 (&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"))
519 (&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"))
521 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
525 (&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"))
527 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx))
529 if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
532 (&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"))
534 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
537 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
539 fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
540 BN_print_fp(stdout, x);
541 fprintf(stdout, "\n y = 0x");
542 BN_print_fp(stdout, y);
543 fprintf(stdout, "\n");
544 /* G_y value taken from the standard: */
546 (&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"))
548 if (0 != BN_cmp(y, z))
551 if (!BN_add(yplusone, y, BN_value_one()))
554 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
555 * and therefore setting the coordinates should fail.
557 if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
560 fprintf(stdout, "verify degree ...");
561 if (EC_GROUP_get_degree(group) != 224)
563 fprintf(stdout, " ok\n");
565 group_order_tests(group);
567 if ((P_224 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
569 if (!EC_GROUP_copy(P_224, group))
572 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
576 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"))
578 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
582 "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC"))
586 "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"))
588 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
593 "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"))
595 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx))
597 if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
599 if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
600 "84F3B9CAC2FC632551"))
602 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
605 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
607 fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
608 BN_print_fp(stdout, x);
609 fprintf(stdout, "\n y = 0x");
610 BN_print_fp(stdout, y);
611 fprintf(stdout, "\n");
612 /* G_y value taken from the standard: */
615 "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"))
617 if (0 != BN_cmp(y, z))
620 if (!BN_add(yplusone, y, BN_value_one()))
623 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
624 * and therefore setting the coordinates should fail.
626 if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
629 fprintf(stdout, "verify degree ...");
630 if (EC_GROUP_get_degree(group) != 256)
632 fprintf(stdout, " ok\n");
634 group_order_tests(group);
636 if ((P_256 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
638 if (!EC_GROUP_copy(P_256, group))
641 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
643 if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
644 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"))
646 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
648 if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
649 "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC"))
651 if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
652 "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"))
654 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
657 if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
658 "9859F741E082542A385502F25DBF55296C3A545E3872760AB7"))
660 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx))
662 if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
664 if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
665 "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"))
667 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
670 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
672 fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x");
673 BN_print_fp(stdout, x);
674 fprintf(stdout, "\n y = 0x");
675 BN_print_fp(stdout, y);
676 fprintf(stdout, "\n");
677 /* G_y value taken from the standard: */
678 if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
679 "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"))
681 if (0 != BN_cmp(y, z))
684 if (!BN_add(yplusone, y, BN_value_one()))
687 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
688 * and therefore setting the coordinates should fail.
690 if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
693 fprintf(stdout, "verify degree ...");
694 if (EC_GROUP_get_degree(group) != 384)
696 fprintf(stdout, " ok\n");
698 group_order_tests(group);
700 if ((P_384 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
702 if (!EC_GROUP_copy(P_384, group))
705 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
707 if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
708 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
709 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
711 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
713 if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
714 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
715 "FFFFFFFFFFFFFFFFFFFFFFFFFFFC"))
717 if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
718 "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
719 "DF883D2C34F1EF451FD46B503F00"))
721 if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
724 if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
725 "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
726 "3C1856A429BF97E7E31C2E5BD66"))
728 if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx))
730 if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
732 if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
733 "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
734 "C9B8899C47AEBB6FB71E91386409"))
736 if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
739 if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
741 fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
742 BN_print_fp(stdout, x);
743 fprintf(stdout, "\n y = 0x");
744 BN_print_fp(stdout, y);
745 fprintf(stdout, "\n");
746 /* G_y value taken from the standard: */
747 if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
748 "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
749 "7086A272C24088BE94769FD16650"))
751 if (0 != BN_cmp(y, z))
754 if (!BN_add(yplusone, y, BN_value_one()))
757 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
758 * and therefore setting the coordinates should fail.
760 if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
763 fprintf(stdout, "verify degree ...");
764 if (EC_GROUP_get_degree(group) != 521)
766 fprintf(stdout, " ok\n");
768 group_order_tests(group);
770 if ((P_521 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
772 if (!EC_GROUP_copy(P_521, group))
775 /* more tests using the last curve */
777 /* Restore the point that got mangled in the (x, y + 1) test. */
778 if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx))
781 if (!EC_POINT_copy(Q, P))
783 if (EC_POINT_is_at_infinity(group, Q))
785 if (!EC_POINT_dbl(group, P, P, ctx))
787 if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
789 if (!EC_POINT_invert(group, Q, ctx))
792 if (!EC_POINT_add(group, R, P, Q, ctx))
794 if (!EC_POINT_add(group, R, R, Q, ctx))
796 if (!EC_POINT_is_at_infinity(group, R))
797 ABORT; /* R = P + 2Q */
800 const EC_POINT *points[4];
801 const BIGNUM *scalars[4];
804 if (EC_POINT_is_at_infinity(group, Q))
811 if (!EC_GROUP_get_order(group, z, ctx))
813 if (!BN_add(y, z, BN_value_one()))
817 if (!BN_rshift1(y, y))
819 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
822 fprintf(stdout, "combined multiplication ...");
825 /* z is still the group order */
826 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
828 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
830 if (0 != EC_POINT_cmp(group, P, R, ctx))
832 if (0 != EC_POINT_cmp(group, R, Q, ctx))
835 fprintf(stdout, ".");
838 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0))
840 if (!BN_add(z, z, y))
842 BN_set_negative(z, 1);
844 scalars[1] = z; /* z = -(order + y) */
846 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
848 if (!EC_POINT_is_at_infinity(group, P))
851 fprintf(stdout, ".");
854 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0))
856 if (!BN_add(z, x, y))
858 BN_set_negative(z, 1);
861 scalars[2] = z; /* z = -(x+y) */
867 scalars[3] = scalar3;
869 if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx))
871 if (!EC_POINT_is_at_infinity(group, P))
874 fprintf(stdout, " ok\n\n");
883 EC_GROUP_free(group);
892 EC_GROUP_free(P_160);
893 EC_GROUP_free(P_192);
894 EC_GROUP_free(P_224);
895 EC_GROUP_free(P_256);
896 EC_GROUP_free(P_384);
897 EC_GROUP_free(P_521);
901 /* Change test based on whether binary point compression is enabled or not. */
902 # ifdef OPENSSL_EC_BIN_PT_COMP
903 # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
904 if (!BN_hex2bn(&x, _x)) ABORT; \
905 if (!BN_hex2bn(&y, _y)) ABORT; \
906 if (!BN_add(yplusone, y, BN_value_one())) ABORT; \
908 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, \
909 * and therefore setting the coordinates should fail. \
911 if (EC_POINT_set_affine_coordinates_GF2m(group, P, x, yplusone, ctx)) ABORT; \
912 if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
913 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \
914 if (!BN_hex2bn(&z, _order)) ABORT; \
915 if (!BN_hex2bn(&cof, _cof)) ABORT; \
916 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
917 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
918 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
919 BN_print_fp(stdout, x); \
920 fprintf(stdout, "\n y = 0x"); \
921 BN_print_fp(stdout, y); \
922 fprintf(stdout, "\n"); \
923 /* G_y value taken from the standard: */ \
924 if (!BN_hex2bn(&z, _y)) ABORT; \
925 if (0 != BN_cmp(y, z)) ABORT;
927 # define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
928 if (!BN_hex2bn(&x, _x)) ABORT; \
929 if (!BN_hex2bn(&y, _y)) ABORT; \
930 if (!BN_add(yplusone, y, BN_value_one())) ABORT; \
932 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not, \
933 * and therefore setting the coordinates should fail. \
935 if (EC_POINT_set_affine_coordinates_GF2m(group, P, x, yplusone, ctx)) ABORT; \
936 if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
937 if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \
938 if (!BN_hex2bn(&z, _order)) ABORT; \
939 if (!BN_hex2bn(&cof, _cof)) ABORT; \
940 if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
941 fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
942 BN_print_fp(stdout, x); \
943 fprintf(stdout, "\n y = 0x"); \
944 BN_print_fp(stdout, y); \
945 fprintf(stdout, "\n");
948 # define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
949 if (!BN_hex2bn(&p, _p)) ABORT; \
950 if (!BN_hex2bn(&a, _a)) ABORT; \
951 if (!BN_hex2bn(&b, _b)) ABORT; \
952 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
953 CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
954 fprintf(stdout, "verify degree ..."); \
955 if (EC_GROUP_get_degree(group) != _degree) ABORT; \
956 fprintf(stdout, " ok\n"); \
957 group_order_tests(group); \
958 if ((_variable = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL) ABORT; \
959 if (!EC_GROUP_copy(_variable, group)) ABORT; \
961 # ifndef OPENSSL_NO_EC2M
963 static void char2_field_tests(void)
968 EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 =
969 NULL, *C2_K571 = NULL;
970 EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 =
971 NULL, *C2_B571 = NULL;
973 BIGNUM *x, *y, *z, *cof, *yplusone;
974 unsigned char buf[100];
985 if (p == NULL || a == NULL || b == NULL)
988 if (!BN_hex2bn(&p, "13"))
990 if (!BN_hex2bn(&a, "3"))
992 if (!BN_hex2bn(&b, "1"))
995 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use
996 * EC_GROUP_new_curve_GF2m
997 * so that the library gets
998 * to choose the EC_METHOD */
1001 if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx))
1006 tmp = EC_GROUP_new(EC_GROUP_method_of(group));
1009 if (!EC_GROUP_copy(tmp, group))
1011 EC_GROUP_free(group);
1015 if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx))
1019 "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
1020 BN_print_fp(stdout, p);
1021 fprintf(stdout, ")\n a = 0x");
1022 BN_print_fp(stdout, a);
1023 fprintf(stdout, "\n b = 0x");
1024 BN_print_fp(stdout, b);
1025 fprintf(stdout, "\n(0x... means binary polynomial)\n");
1027 P = EC_POINT_new(group);
1028 Q = EC_POINT_new(group);
1029 R = EC_POINT_new(group);
1033 if (!EC_POINT_set_to_infinity(group, P))
1035 if (!EC_POINT_is_at_infinity(group, P))
1039 if (!EC_POINT_oct2point(group, Q, buf, 1, ctx))
1042 if (!EC_POINT_add(group, P, P, Q, ctx))
1044 if (!EC_POINT_is_at_infinity(group, P))
1051 yplusone = BN_new();
1052 if (x == NULL || y == NULL || z == NULL || cof == NULL || yplusone == NULL)
1055 if (!BN_hex2bn(&x, "6"))
1057 /* Change test based on whether binary point compression is enabled or not. */
1058 # ifdef OPENSSL_EC_BIN_PT_COMP
1059 if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx))
1062 if (!BN_hex2bn(&y, "8"))
1064 if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx))
1067 if (EC_POINT_is_on_curve(group, Q, ctx) <= 0) {
1068 /* Change test based on whether binary point compression is enabled or not. */
1069 # ifdef OPENSSL_EC_BIN_PT_COMP
1070 if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx))
1073 fprintf(stderr, "Point is not on curve: x = 0x");
1074 BN_print_fp(stderr, x);
1075 fprintf(stderr, ", y = 0x");
1076 BN_print_fp(stderr, y);
1077 fprintf(stderr, "\n");
1081 fprintf(stdout, "A cyclic subgroup:\n");
1087 if (EC_POINT_is_at_infinity(group, P))
1088 fprintf(stdout, " point at infinity\n");
1090 if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx))
1093 fprintf(stdout, " x = 0x");
1094 BN_print_fp(stdout, x);
1095 fprintf(stdout, ", y = 0x");
1096 BN_print_fp(stdout, y);
1097 fprintf(stdout, "\n");
1100 if (!EC_POINT_copy(R, P))
1102 if (!EC_POINT_add(group, P, P, Q, ctx))
1105 while (!EC_POINT_is_at_infinity(group, P));
1107 if (!EC_POINT_add(group, P, Q, R, ctx))
1109 if (!EC_POINT_is_at_infinity(group, P))
1112 /* Change test based on whether binary point compression is enabled or not. */
1113 # ifdef OPENSSL_EC_BIN_PT_COMP
1115 EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf,
1119 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
1121 if (0 != EC_POINT_cmp(group, P, Q, ctx))
1123 fprintf(stdout, "Generator as octet string, compressed form:\n ");
1124 for (i = 0; i < len; i++)
1125 fprintf(stdout, "%02X", buf[i]);
1129 EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf,
1133 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
1135 if (0 != EC_POINT_cmp(group, P, Q, ctx))
1137 fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
1138 for (i = 0; i < len; i++)
1139 fprintf(stdout, "%02X", buf[i]);
1141 /* Change test based on whether binary point compression is enabled or not. */
1142 # ifdef OPENSSL_EC_BIN_PT_COMP
1144 EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf,
1148 if (!EC_POINT_oct2point(group, P, buf, len, ctx))
1150 if (0 != EC_POINT_cmp(group, P, Q, ctx))
1152 fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
1153 for (i = 0; i < len; i++)
1154 fprintf(stdout, "%02X", buf[i]);
1157 fprintf(stdout, "\n");
1159 if (!EC_POINT_invert(group, P, ctx))
1161 if (0 != EC_POINT_cmp(group, P, R, ctx))
1164 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
1166 ("NIST curve K-163",
1167 "0800000000000000000000000000000000000000C9",
1170 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
1171 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
1172 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163, C2_K163);
1174 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
1176 ("NIST curve B-163",
1177 "0800000000000000000000000000000000000000C9",
1179 "020A601907B8C953CA1481EB10512F78744A3205FD",
1180 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
1181 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
1182 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163, C2_B163);
1184 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
1186 ("NIST curve K-233",
1187 "020000000000000000000000000000000000000004000000000000000001",
1190 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
1191 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
1193 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
1196 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
1198 ("NIST curve B-233",
1199 "020000000000000000000000000000000000000004000000000000000001",
1200 "000000000000000000000000000000000000000000000000000000000001",
1201 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
1202 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
1203 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1205 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
1208 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
1210 ("NIST curve K-283",
1211 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1214 "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
1215 "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
1217 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
1220 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
1222 ("NIST curve B-283",
1223 "0800000000000000000000000000000000000000000000000000000000000000000010A1",
1224 "000000000000000000000000000000000000000000000000000000000000000000000001",
1225 "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
1226 "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
1227 "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1229 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
1232 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
1234 ("NIST curve K-409",
1235 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1238 "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
1239 "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1241 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
1244 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
1246 ("NIST curve B-409",
1247 "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
1248 "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1249 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
1250 "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
1251 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1253 "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
1256 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
1258 ("NIST curve K-571",
1259 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1262 "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
1263 "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
1265 "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
1268 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
1270 ("NIST curve B-571",
1271 "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
1272 "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
1273 "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
1274 "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
1275 "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1277 "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
1280 /* more tests using the last curve */
1282 if (!EC_POINT_copy(Q, P))
1284 if (EC_POINT_is_at_infinity(group, Q))
1286 if (!EC_POINT_dbl(group, P, P, ctx))
1288 if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
1290 if (!EC_POINT_invert(group, Q, ctx))
1291 ABORT; /* P = -2Q */
1293 if (!EC_POINT_add(group, R, P, Q, ctx))
1295 if (!EC_POINT_add(group, R, R, Q, ctx))
1297 if (!EC_POINT_is_at_infinity(group, R))
1298 ABORT; /* R = P + 2Q */
1301 const EC_POINT *points[3];
1302 const BIGNUM *scalars[3];
1304 if (EC_POINT_is_at_infinity(group, Q))
1310 if (!BN_add(y, z, BN_value_one()))
1314 if (!BN_rshift1(y, y))
1316 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
1319 fprintf(stdout, "combined multiplication ...");
1322 /* z is still the group order */
1323 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
1325 if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
1327 if (0 != EC_POINT_cmp(group, P, R, ctx))
1329 if (0 != EC_POINT_cmp(group, R, Q, ctx))
1332 fprintf(stdout, ".");
1335 if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0))
1337 if (!BN_add(z, z, y))
1339 BN_set_negative(z, 1);
1341 scalars[1] = z; /* z = -(order + y) */
1343 if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
1345 if (!EC_POINT_is_at_infinity(group, P))
1348 fprintf(stdout, ".");
1351 if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0))
1353 if (!BN_add(z, x, y))
1355 BN_set_negative(z, 1);
1358 scalars[2] = z; /* z = -(x+y) */
1360 if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx))
1362 if (!EC_POINT_is_at_infinity(group, P))
1365 fprintf(stdout, " ok\n\n");
1372 EC_GROUP_free(group);
1382 EC_GROUP_free(C2_K163);
1383 EC_GROUP_free(C2_B163);
1384 EC_GROUP_free(C2_K233);
1385 EC_GROUP_free(C2_B233);
1386 EC_GROUP_free(C2_K283);
1387 EC_GROUP_free(C2_B283);
1388 EC_GROUP_free(C2_K409);
1389 EC_GROUP_free(C2_B409);
1390 EC_GROUP_free(C2_K571);
1391 EC_GROUP_free(C2_B571);
1396 static void internal_curve_test(void)
1398 EC_builtin_curve *curves = NULL;
1399 size_t crv_len = 0, n = 0;
1402 crv_len = EC_get_builtin_curves(NULL, 0);
1403 curves = OPENSSL_malloc(sizeof(*curves) * crv_len);
1407 if (!EC_get_builtin_curves(curves, crv_len)) {
1408 OPENSSL_free(curves);
1412 fprintf(stdout, "testing internal curves: ");
1414 for (n = 0; n < crv_len; n++) {
1415 EC_GROUP *group = NULL;
1416 int nid = curves[n].nid;
1417 if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL) {
1419 fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with"
1420 " curve %s\n", OBJ_nid2sn(nid));
1421 /* try next curve */
1424 if (!EC_GROUP_check(group, NULL)) {
1426 fprintf(stdout, "\nEC_GROUP_check() failed with"
1427 " curve %s\n", OBJ_nid2sn(nid));
1428 EC_GROUP_free(group);
1429 /* try the next curve */
1432 fprintf(stdout, ".");
1434 EC_GROUP_free(group);
1437 fprintf(stdout, " ok\n\n");
1439 fprintf(stdout, " failed\n\n");
1443 /* Test all built-in curves and let the library choose the EC_METHOD */
1444 for (n = 0; n < crv_len; n++) {
1445 EC_GROUP *group = NULL;
1446 int nid = curves[n].nid;
1448 * Skip for X25519 because low level operations such as EC_POINT_mul()
1449 * are not supported for this curve
1451 if (nid == NID_X25519)
1453 fprintf(stdout, "%s:\n", OBJ_nid2sn(nid));
1455 if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL) {
1458 group_order_tests(group);
1459 EC_GROUP_free(group);
1462 OPENSSL_free(curves);
1466 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1468 * nistp_test_params contains magic numbers for testing our optimized
1469 * implementations of several NIST curves with characteristic > 3.
1471 struct nistp_test_params {
1472 const EC_METHOD *(*meth) ();
1475 * Qx, Qy and D are taken from
1476 * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
1477 * Otherwise, values are standard curve parameters from FIPS 180-3
1479 const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d;
1482 static const struct nistp_test_params nistp_tests_params[] = {
1485 EC_GFp_nistp224_method,
1488 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
1490 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
1492 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
1494 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E",
1496 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555",
1498 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
1500 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
1502 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
1504 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8",
1508 EC_GFp_nistp256_method,
1511 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
1513 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc",
1515 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
1517 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19",
1519 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09",
1521 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
1523 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5",
1525 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
1527 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96",
1531 EC_GFp_nistp521_method,
1534 "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
1536 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc",
1538 "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00",
1540 "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4",
1542 "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e",
1544 "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66",
1546 "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650",
1548 "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409",
1550 "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722",
1554 static void nistp_single_test(const struct nistp_test_params *test)
1557 BIGNUM *p, *a, *b, *x, *y, *n, *m, *order, *yplusone;
1559 EC_POINT *G, *P, *Q, *Q_CHECK;
1561 fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n",
1572 yplusone = BN_new();
1574 NISTP = EC_GROUP_new(test->meth());
1577 if (!BN_hex2bn(&p, test->p))
1579 if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
1581 if (!BN_hex2bn(&a, test->a))
1583 if (!BN_hex2bn(&b, test->b))
1585 if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx))
1587 G = EC_POINT_new(NISTP);
1588 P = EC_POINT_new(NISTP);
1589 Q = EC_POINT_new(NISTP);
1590 Q_CHECK = EC_POINT_new(NISTP);
1591 if (!BN_hex2bn(&x, test->Qx))
1593 if (!BN_hex2bn(&y, test->Qy))
1595 if (!BN_add(yplusone, y, BN_value_one()))
1598 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
1599 * and therefore setting the coordinates should fail.
1601 if (EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, yplusone, ctx))
1603 if (!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx))
1605 if (!BN_hex2bn(&x, test->Gx))
1607 if (!BN_hex2bn(&y, test->Gy))
1609 if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx))
1611 if (!BN_hex2bn(&order, test->order))
1613 if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one()))
1616 fprintf(stdout, "verify degree ... ");
1617 if (EC_GROUP_get_degree(NISTP) != test->degree)
1619 fprintf(stdout, "ok\n");
1621 fprintf(stdout, "NIST test vectors ... ");
1622 if (!BN_hex2bn(&n, test->d))
1624 /* fixed point multiplication */
1625 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1626 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1628 /* random point multiplication */
1629 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1630 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1633 /* set generator to P = 2*G, where G is the standard generator */
1634 if (!EC_POINT_dbl(NISTP, P, G, ctx))
1636 if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one()))
1638 /* set the scalar to m=n/2, where n is the NIST test scalar */
1639 if (!BN_rshift(m, n, 1))
1642 /* test the non-standard generator */
1643 /* fixed point multiplication */
1644 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1645 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1647 /* random point multiplication */
1648 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1649 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1653 * We have not performed precomputation so have_precompute mult should be
1656 if (EC_GROUP_have_precompute_mult(NISTP))
1659 /* now repeat all tests with precomputation */
1660 if (!EC_GROUP_precompute_mult(NISTP, ctx))
1662 if (!EC_GROUP_have_precompute_mult(NISTP))
1665 /* fixed point multiplication */
1666 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1667 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1669 /* random point multiplication */
1670 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1671 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1674 /* reset generator */
1675 if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one()))
1677 /* fixed point multiplication */
1678 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1679 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1681 /* random point multiplication */
1682 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1683 if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1686 fprintf(stdout, "ok\n");
1687 group_order_tests(NISTP);
1688 EC_GROUP_free(NISTP);
1692 EC_POINT_free(Q_CHECK);
1705 static void nistp_tests()
1709 for (i = 0; i < OSSL_NELEM(nistp_tests_params); i++) {
1710 nistp_single_test(&nistp_tests_params[i]);
1715 static void parameter_test(void)
1717 EC_GROUP *group, *group2;
1718 ECPARAMETERS *ecparameters;
1720 fprintf(stderr, "\ntesting ecparameters conversion ...");
1722 group = EC_GROUP_new_by_curve_name(NID_secp112r1);
1726 ecparameters = EC_GROUP_get_ecparameters(group, NULL);
1729 group2 = EC_GROUP_new_from_ecparameters(ecparameters);
1732 if (EC_GROUP_cmp(group, group2, NULL))
1735 fprintf(stderr, " ok\n");
1737 EC_GROUP_free(group);
1738 EC_GROUP_free(group2);
1739 ECPARAMETERS_free(ecparameters);
1742 static const char rnd_seed[] =
1743 "string to make the random number generator think it has entropy";
1745 int main(int argc, char *argv[])
1749 p = getenv("OPENSSL_DEBUG_MEMORY");
1750 if (p != NULL && strcmp(p, "on") == 0)
1751 CRYPTO_set_mem_debug(1);
1752 CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
1754 RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
1756 prime_field_tests();
1758 # ifndef OPENSSL_NO_EC2M
1759 char2_field_tests();
1761 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1764 /* test the internal curves */
1765 internal_curve_test();
1769 #ifndef OPENSSL_NO_CRYPTO_MDEBUG
1770 if (CRYPTO_mem_leaks_fp(stderr) <= 0)