2 * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
11 #include "internal/nelem.h"
15 # include <openssl/ec.h>
16 # ifndef OPENSSL_NO_ENGINE
17 # include <openssl/engine.h>
19 # include <openssl/err.h>
20 # include <openssl/obj_mac.h>
21 # include <openssl/objects.h>
22 # include <openssl/rand.h>
23 # include <openssl/bn.h>
24 # include <openssl/opensslconf.h>
26 static size_t crv_len = 0;
27 static EC_builtin_curve *curves = NULL;
29 /* test multiplication with group order, long and negative scalars */
30 static int group_order_tests(EC_GROUP *group)
32 BIGNUM *n1 = NULL, *n2 = NULL, *order = NULL;
33 EC_POINT *P = NULL, *Q = NULL, *R = NULL, *S = NULL;
37 if (!TEST_ptr(n1 = BN_new())
38 || !TEST_ptr(n2 = BN_new())
39 || !TEST_ptr(order = BN_new())
40 || !TEST_ptr(ctx = BN_CTX_new())
41 || !TEST_ptr(P = EC_POINT_new(group))
42 || !TEST_ptr(Q = EC_POINT_new(group))
43 || !TEST_ptr(R = EC_POINT_new(group))
44 || !TEST_ptr(S = EC_POINT_new(group)))
47 if (!TEST_true(EC_GROUP_get_order(group, order, ctx))
48 || !TEST_true(EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
49 || !TEST_true(EC_POINT_is_at_infinity(group, Q))
50 || !TEST_true(EC_GROUP_precompute_mult(group, ctx))
51 || !TEST_true(EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
52 || !TEST_true(EC_POINT_is_at_infinity(group, Q)))
55 for (i = 1; i <= 2; i++) {
56 const BIGNUM *scalars[6];
57 const EC_POINT *points[6];
59 if (!TEST_true(BN_set_word(n1, i))
61 * If i == 1, P will be the predefined generator for which
62 * EC_GROUP_precompute_mult has set up precomputation.
64 || !TEST_true(EC_POINT_mul(group, P, n1, NULL, NULL, ctx))
65 || !TEST_true(BN_one(n1))
67 || !TEST_true(BN_sub(n1, n1, order))
68 || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n1, ctx))
69 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
72 || !TEST_true(BN_add(n2, order, BN_value_one()))
73 || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
74 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
76 /* n2 = (1 - order) * (1 + order) = 1 - order^2 */
77 || !TEST_true(BN_mul(n2, n1, n2, ctx))
78 || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
79 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx)))
82 /* n2 = order^2 - 1 */
83 BN_set_negative(n2, 0);
84 if (!TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
85 /* Add P to verify the result. */
86 || !TEST_true(EC_POINT_add(group, Q, Q, P, ctx))
87 || !TEST_true(EC_POINT_is_at_infinity(group, Q))
89 /* Exercise EC_POINTs_mul, including corner cases. */
90 || !TEST_false(EC_POINT_is_at_infinity(group, P)))
93 scalars[0] = scalars[1] = BN_value_one();
94 points[0] = points[1] = P;
96 if (!TEST_true(EC_POINTs_mul(group, R, NULL, 2, points, scalars, ctx))
97 || !TEST_true(EC_POINT_dbl(group, S, points[0], ctx))
98 || !TEST_int_eq(0, EC_POINT_cmp(group, R, S, ctx)))
102 points[0] = Q; /* => infinity */
104 points[1] = P; /* => -P */
106 points[2] = Q; /* => infinity */
108 points[3] = Q; /* => infinity */
110 points[4] = P; /* => P */
112 points[5] = Q; /* => infinity */
113 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 6, points, scalars, ctx))
114 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
120 if (r == 0 && i != 0)
121 TEST_info(i == 1 ? "allowing precomputation" :
122 "without precomputation");
134 static int prime_field_tests(void)
137 BIGNUM *p = NULL, *a = NULL, *b = NULL, *scalar3 = NULL;
138 EC_GROUP *group = NULL, *tmp = NULL;
139 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL,
140 *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
141 EC_POINT *P = NULL, *Q = NULL, *R = NULL;
142 BIGNUM *x = NULL, *y = NULL, *z = NULL, *yplusone = NULL;
143 const EC_POINT *points[4];
144 const BIGNUM *scalars[4];
145 unsigned char buf[100];
149 if (!TEST_ptr(ctx = BN_CTX_new())
150 || !TEST_ptr(p = BN_new())
151 || !TEST_ptr(a = BN_new())
152 || !TEST_ptr(b = BN_new())
153 || !TEST_true(BN_hex2bn(&p, "17"))
154 || !TEST_true(BN_hex2bn(&a, "1"))
155 || !TEST_true(BN_hex2bn(&b, "1"))
157 * applications should use EC_GROUP_new_curve_GFp so
158 * that the library gets to choose the EC_METHOD
160 || !TEST_ptr(group = EC_GROUP_new(EC_GFp_mont_method()))
161 || !TEST_true(EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
162 || !TEST_ptr(tmp = EC_GROUP_new(EC_GROUP_method_of(group)))
163 || !TEST_true(EC_GROUP_copy(tmp, group)))
165 EC_GROUP_free(group);
169 if (!TEST_true(EC_GROUP_get_curve_GFp(group, p, a, b, ctx)))
172 TEST_info("Curve defined by Weierstrass equation");
173 TEST_note(" y^2 = x^3 + a*x + b (mod p)");
174 test_output_bignum("a", a);
175 test_output_bignum("b", b);
176 test_output_bignum("p", p);
179 if (!TEST_ptr(P = EC_POINT_new(group))
180 || !TEST_ptr(Q = EC_POINT_new(group))
181 || !TEST_ptr(R = EC_POINT_new(group))
182 || !TEST_true(EC_POINT_set_to_infinity(group, P))
183 || !TEST_true(EC_POINT_is_at_infinity(group, P))
184 || !TEST_true(EC_POINT_oct2point(group, Q, buf, 1, ctx))
185 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx))
186 || !TEST_true(EC_POINT_is_at_infinity(group, P))
187 || !TEST_ptr(x = BN_new())
188 || !TEST_ptr(y = BN_new())
189 || !TEST_ptr(z = BN_new())
190 || !TEST_ptr(yplusone = BN_new())
191 || !TEST_true(BN_hex2bn(&x, "D"))
192 || !TEST_true(EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1,
196 if (!TEST_int_gt(EC_POINT_is_on_curve(group, Q, ctx), 0)) {
197 if (!TEST_true(EC_POINT_get_affine_coordinates_GFp(group, Q, x, y,
200 TEST_info("Point is not on curve");
201 test_output_bignum("x", x);
202 test_output_bignum("y", y);
206 TEST_note("A cyclic subgroup:");
209 if (!TEST_int_ne(k--, 0))
212 if (EC_POINT_is_at_infinity(group, P)) {
213 TEST_note(" point at infinity");
215 if (!TEST_true(EC_POINT_get_affine_coordinates_GFp(group, P, x, y,
219 test_output_bignum("x", x);
220 test_output_bignum("y", y);
223 if (!TEST_true(EC_POINT_copy(R, P))
224 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx)))
227 } while (!EC_POINT_is_at_infinity(group, P));
229 if (!TEST_true(EC_POINT_add(group, P, Q, R, ctx))
230 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
234 EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf,
236 if (!TEST_size_t_ne(len, 0)
237 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
238 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
240 test_output_memory("Generator as octet string, compressed form:",
243 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED,
244 buf, sizeof(buf), ctx);
245 if (!TEST_size_t_ne(len, 0)
246 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
247 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
249 test_output_memory("Generator as octet string, uncompressed form:",
252 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID,
253 buf, sizeof(buf), ctx);
254 if (!TEST_size_t_ne(len, 0)
255 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
256 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
258 test_output_memory("Generator as octet string, hybrid form:",
261 if (!TEST_true(EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z,
264 TEST_info("A representation of the inverse of that generator in");
265 TEST_note("Jacobian projective coordinates");
266 test_output_bignum("x", x);
267 test_output_bignum("y", y);
268 test_output_bignum("z", z);
270 if (!TEST_true(EC_POINT_invert(group, P, ctx))
271 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
274 * Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2,
275 * 2000) -- not a NIST curve, but commonly used
278 || !TEST_true(BN_hex2bn(&p, "FFFFFFFF"
279 "FFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"))
280 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
281 || !TEST_true(BN_hex2bn(&a, "FFFFFFFF"
282 "FFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"))
283 || !TEST_true(BN_hex2bn(&b, "1C97BEFC"
284 "54BD7A8B65ACF89F81D4D4ADC565FA45"))
285 || !TEST_true(EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
286 || !TEST_true(BN_hex2bn(&x, "4A96B568"
287 "8EF573284664698968C38BB913CBFC82"))
288 || !TEST_true(BN_hex2bn(&y, "23a62855"
289 "3168947d59dcc912042351377ac5fb32"))
290 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
292 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
293 * and therefore setting the coordinates should fail.
295 || !TEST_false(EC_POINT_set_affine_coordinates_GFp(group, P, x,
297 || !TEST_true(EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx))
298 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
299 || !TEST_true(BN_hex2bn(&z, "0100000000"
300 "000000000001F4C8F927AED3CA752257"))
301 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
302 || !TEST_true(EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)))
304 TEST_info("SEC2 curve secp160r1 -- Generator");
305 test_output_bignum("x", x);
306 test_output_bignum("y", y);
307 /* G_y value taken from the standard: */
308 if (!TEST_true(BN_hex2bn(&z, "23a62855"
309 "3168947d59dcc912042351377ac5fb32"))
311 || !TEST_int_eq(EC_GROUP_get_degree(group), 160)
312 || !group_order_tests(group)
313 || !TEST_ptr(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))
314 || !TEST_true(EC_GROUP_copy(P_160, group))
316 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
318 || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFF"
319 "FFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"))
320 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
321 || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFF"
322 "FFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"))
323 || !TEST_true(BN_hex2bn(&b, "64210519E59C80E7"
324 "0FA7E9AB72243049FEB8DEECC146B9B1"))
325 || !TEST_true(EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
326 || !TEST_true(BN_hex2bn(&x, "188DA80EB03090F6"
327 "7CBF20EB43A18800F4FF0AFD82FF1012"))
328 || !TEST_true(EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1,
330 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
331 || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFF"
332 "FFFFFFFF99DEF836146BC9B1B4D22831"))
333 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
334 || !TEST_true(EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)))
337 TEST_info("NIST curve P-192 -- Generator");
338 test_output_bignum("x", x);
339 test_output_bignum("y", y);
340 /* G_y value taken from the standard: */
341 if (!TEST_true(BN_hex2bn(&z, "07192B95FFC8DA78"
342 "631011ED6B24CDD573F977A11E794811"))
344 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
346 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
347 * and therefore setting the coordinates should fail.
349 || !TEST_false(EC_POINT_set_affine_coordinates_GFp(group, P, x,
351 || !TEST_int_eq(EC_GROUP_get_degree(group), 192)
352 || !group_order_tests(group)
353 || !TEST_ptr(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))
354 || !TEST_true(EC_GROUP_copy(P_192, group))
356 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
358 || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFF"
359 "FFFFFFFF000000000000000000000001"))
360 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
361 || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFF"
362 "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"))
363 || !TEST_true(BN_hex2bn(&b, "B4050A850C04B3ABF5413256"
364 "5044B0B7D7BFD8BA270B39432355FFB4"))
365 || !TEST_true(EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
366 || !TEST_true(BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B9"
367 "4A03C1D356C21122343280D6115C1D21"))
368 || !TEST_true(EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0,
370 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
371 || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF"
372 "FFFF16A2E0B8F03E13DD29455C5C2A3D"))
373 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
374 || !TEST_true(EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)))
377 TEST_info("NIST curve P-224 -- Generator");
378 test_output_bignum("x", x);
379 test_output_bignum("y", y);
380 /* G_y value taken from the standard: */
381 if (!TEST_true(BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6"
382 "CD4375A05A07476444D5819985007E34"))
384 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
386 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
387 * and therefore setting the coordinates should fail.
389 || !TEST_false(EC_POINT_set_affine_coordinates_GFp(group, P, x,
391 || !TEST_int_eq(EC_GROUP_get_degree(group), 224)
392 || !group_order_tests(group)
393 || !TEST_ptr(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))
394 || !TEST_true(EC_GROUP_copy(P_224, group))
396 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
398 || !TEST_true(BN_hex2bn(&p, "FFFFFFFF000000010000000000000000"
399 "00000000FFFFFFFFFFFFFFFFFFFFFFFF"))
400 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
401 || !TEST_true(BN_hex2bn(&a, "FFFFFFFF000000010000000000000000"
402 "00000000FFFFFFFFFFFFFFFFFFFFFFFC"))
403 || !TEST_true(BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC"
404 "651D06B0CC53B0F63BCE3C3E27D2604B"))
405 || !TEST_true(EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
407 || !TEST_true(BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F2"
408 "77037D812DEB33A0F4A13945D898C296"))
409 || !TEST_true(EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1,
411 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
412 || !TEST_true(BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFF"
413 "BCE6FAADA7179E84F3B9CAC2FC632551"))
414 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
415 || !TEST_true(EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)))
418 TEST_info("NIST curve P-256 -- Generator");
419 test_output_bignum("x", x);
420 test_output_bignum("y", y);
421 /* G_y value taken from the standard: */
422 if (!TEST_true(BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E16"
423 "2BCE33576B315ECECBB6406837BF51F5"))
425 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
427 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
428 * and therefore setting the coordinates should fail.
430 || !TEST_false(EC_POINT_set_affine_coordinates_GFp(group, P, x,
432 || !TEST_int_eq(EC_GROUP_get_degree(group), 256)
433 || !group_order_tests(group)
434 || !TEST_ptr(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))
435 || !TEST_true(EC_GROUP_copy(P_256, group))
437 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
439 || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
440 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
441 "FFFFFFFF0000000000000000FFFFFFFF"))
442 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
443 || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
444 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
445 "FFFFFFFF0000000000000000FFFFFFFC"))
446 || !TEST_true(BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19"
447 "181D9C6EFE8141120314088F5013875A"
448 "C656398D8A2ED19D2A85C8EDD3EC2AEF"))
449 || !TEST_true(EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
451 || !TEST_true(BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD74"
452 "6E1D3B628BA79B9859F741E082542A38"
453 "5502F25DBF55296C3A545E3872760AB7"))
454 || !TEST_true(EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1,
456 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
457 || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
458 "FFFFFFFFFFFFFFFFC7634D81F4372DDF"
459 "581A0DB248B0A77AECEC196ACCC52973"))
460 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
461 || !TEST_true(EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)))
464 TEST_info("NIST curve P-384 -- Generator");
465 test_output_bignum("x", x);
466 test_output_bignum("y", y);
467 /* G_y value taken from the standard: */
468 if (!TEST_true(BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29"
469 "F8F41DBD289A147CE9DA3113B5F0B8C0"
470 "0A60B1CE1D7E819D7A431D7C90EA0E5F"))
472 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
474 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
475 * and therefore setting the coordinates should fail.
477 || !TEST_false(EC_POINT_set_affine_coordinates_GFp(group, P, x,
479 || !TEST_int_eq(EC_GROUP_get_degree(group), 384)
480 || !group_order_tests(group)
481 || !TEST_ptr(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))
482 || !TEST_true(EC_GROUP_copy(P_384, group))
484 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
485 || !TEST_true(BN_hex2bn(&p, "1FF"
486 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
487 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
488 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
489 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
490 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
491 || !TEST_true(BN_hex2bn(&a, "1FF"
492 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
493 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
494 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
495 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC"))
496 || !TEST_true(BN_hex2bn(&b, "051"
497 "953EB9618E1C9A1F929A21A0B68540EE"
498 "A2DA725B99B315F3B8B489918EF109E1"
499 "56193951EC7E937B1652C0BD3BB1BF07"
500 "3573DF883D2C34F1EF451FD46B503F00"))
501 || !TEST_true(EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
502 || !TEST_true(BN_hex2bn(&x, "C6"
503 "858E06B70404E9CD9E3ECB662395B442"
504 "9C648139053FB521F828AF606B4D3DBA"
505 "A14B5E77EFE75928FE1DC127A2FFA8DE"
506 "3348B3C1856A429BF97E7E31C2E5BD66"))
507 || !TEST_true(EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0,
509 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
510 || !TEST_true(BN_hex2bn(&z, "1FF"
511 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
512 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA"
513 "51868783BF2F966B7FCC0148F709A5D0"
514 "3BB5C9B8899C47AEBB6FB71E91386409"))
515 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
516 || !TEST_true(EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)))
519 TEST_info("NIST curve P-521 -- Generator");
520 test_output_bignum("x", x);
521 test_output_bignum("y", y);
522 /* G_y value taken from the standard: */
523 if (!TEST_true(BN_hex2bn(&z, "118"
524 "39296A789A3BC0045C8A5FB42C7D1BD9"
525 "98F54449579B446817AFBD17273E662C"
526 "97EE72995EF42640C550B9013FAD0761"
527 "353C7086A272C24088BE94769FD16650"))
529 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
531 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
532 * and therefore setting the coordinates should fail.
534 || !TEST_false(EC_POINT_set_affine_coordinates_GFp(group, P, x,
536 || !TEST_int_eq(EC_GROUP_get_degree(group), 521)
537 || !group_order_tests(group)
538 || !TEST_ptr(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))
539 || !TEST_true(EC_GROUP_copy(P_521, group))
541 /* more tests using the last curve */
543 /* Restore the point that got mangled in the (x, y + 1) test. */
544 || !TEST_true(EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx))
545 || !TEST_true(EC_POINT_copy(Q, P))
546 || !TEST_false(EC_POINT_is_at_infinity(group, Q))
547 || !TEST_true(EC_POINT_dbl(group, P, P, ctx))
548 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
549 || !TEST_true(EC_POINT_invert(group, Q, ctx)) /* P = -2Q */
550 || !TEST_true(EC_POINT_add(group, R, P, Q, ctx))
551 || !TEST_true(EC_POINT_add(group, R, R, Q, ctx))
552 || !TEST_true(EC_POINT_is_at_infinity(group, R)) /* R = P + 2Q */
553 || !TEST_false(EC_POINT_is_at_infinity(group, Q)))
560 if (!TEST_true(EC_GROUP_get_order(group, z, ctx))
561 || !TEST_true(BN_add(y, z, BN_value_one()))
563 || !TEST_true(BN_rshift1(y, y)))
565 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
568 TEST_note("combined multiplication ...");
570 /* z is still the group order */
571 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
572 || !TEST_true(EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
573 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
574 || !TEST_int_eq(0, EC_POINT_cmp(group, R, Q, ctx))
575 || !TEST_true(BN_rand(y, BN_num_bits(y), 0, 0))
576 || !TEST_true(BN_add(z, z, y)))
578 BN_set_negative(z, 1);
580 scalars[1] = z; /* z = -(order + y) */
582 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
583 || !TEST_true(EC_POINT_is_at_infinity(group, P))
584 || !TEST_true(BN_rand(x, BN_num_bits(y) - 1, 0, 0))
585 || !TEST_true(BN_add(z, x, y)))
587 BN_set_negative(z, 1);
590 scalars[2] = z; /* z = -(x+y) */
592 if (!TEST_ptr(scalar3 = BN_new()))
595 scalars[3] = scalar3;
597 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx))
598 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
610 EC_GROUP_free(group);
621 EC_GROUP_free(P_160);
622 EC_GROUP_free(P_192);
623 EC_GROUP_free(P_224);
624 EC_GROUP_free(P_256);
625 EC_GROUP_free(P_384);
626 EC_GROUP_free(P_521);
630 # ifndef OPENSSL_NO_EC2M
632 static struct c2_curve_test {
643 } char2_curve_tests[] = {
644 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
647 "0800000000000000000000000000000000000000C9",
650 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
651 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
652 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163
654 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
657 "0800000000000000000000000000000000000000C9",
659 "020A601907B8C953CA1481EB10512F78744A3205FD",
660 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
661 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
662 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163
664 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
667 "020000000000000000000000000000000000000004000000000000000001",
670 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
671 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
673 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
676 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
679 "020000000000000000000000000000000000000004000000000000000001",
680 "000000000000000000000000000000000000000000000000000000000001",
681 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
682 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
683 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
685 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
688 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
692 "00000000000000000000000000000000000000000000000000000000000010A1",
696 "78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
698 "0F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
701 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
704 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
708 "00000000000000000000000000000000000000000000000000000000000010A1",
710 "0000000000000000000000000000000000000000000000000000000000000001",
712 "C8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
714 "8DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
716 "FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
719 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
722 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
725 "0200000000000000000000000000000000000000"
726 "0000000000000000000000000000000000000000008000000000000000000001",
729 "0060F05F658F49C1AD3AB1890F7184210EFD0987"
730 "E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
731 "01E369050B7C4E42ACBA1DACBF04299C3460782F"
732 "918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
734 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
735 "FFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
738 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
741 "0200000000000000000000000000000000000000"
742 "0000000000000000000000000000000000000000008000000000000000000001",
743 "0000000000000000000000000000000000000000"
744 "0000000000000000000000000000000000000000000000000000000000000001",
745 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422E"
746 "F1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
747 "015D4860D088DDB3496B0C6064756260441CDE4A"
748 "F1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
749 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5"
750 "A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
752 "0100000000000000000000000000000000000000"
753 "00000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
756 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
760 "0000000000000000000000000000000000000000000000000000000000000000"
761 "0000000000000000000000000000000000000000000000000000000000000425",
765 "82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E6"
766 "47DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
768 "4F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA7"
769 "4FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
772 "00000000000000000000000000000000000000000000000000000000131850E1"
773 "F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
776 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
780 "0000000000000000000000000000000000000000000000000000000000000000"
781 "0000000000000000000000000000000000000000000000000000000000000425",
783 "0000000000000000000000000000000000000000000000000000000000000000"
784 "0000000000000000000000000000000000000000000000000000000000000001",
786 "DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA5933"
787 "2BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
789 "6C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293"
790 "CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
792 "6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A57"
793 "6291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
796 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18"
797 "FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
802 static int char2_curve_test(int n)
806 BIGNUM *p = NULL, *a = NULL, *b = NULL;
807 BIGNUM *x = NULL, *y = NULL, *z = NULL, *cof = NULL, *yplusone = NULL;
808 EC_GROUP *group = NULL, *variable = NULL;
809 EC_POINT *P = NULL, *Q = NULL, *R = NULL;
810 const EC_POINT *points[3];
811 const BIGNUM *scalars[3];
812 struct c2_curve_test *const test = char2_curve_tests + n;
814 if (!TEST_ptr(ctx = BN_CTX_new())
815 || !TEST_ptr(p = BN_new())
816 || !TEST_ptr(a = BN_new())
817 || !TEST_ptr(b = BN_new())
818 || !TEST_ptr(x = BN_new())
819 || !TEST_ptr(y = BN_new())
820 || !TEST_ptr(z = BN_new())
821 || !TEST_ptr(yplusone = BN_new())
822 || !TEST_true(BN_hex2bn(&p, test->p))
823 || !TEST_true(BN_hex2bn(&a, test->a))
824 || !TEST_true(BN_hex2bn(&b, test->b))
825 || !TEST_true(group = EC_GROUP_new(EC_GF2m_simple_method()))
826 || !TEST_true(EC_GROUP_set_curve_GF2m(group, p, a, b, ctx))
827 || !TEST_ptr(P = EC_POINT_new(group))
828 || !TEST_ptr(Q = EC_POINT_new(group))
829 || !TEST_ptr(R = EC_POINT_new(group))
830 || !TEST_true(BN_hex2bn(&x, test->x))
831 || !TEST_true(BN_hex2bn(&y, test->y))
832 || !TEST_true(BN_add(yplusone, y, BN_value_one())))
835 /* Change test based on whether binary point compression is enabled or not. */
836 # ifdef OPENSSL_EC_BIN_PT_COMP
838 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
839 * and therefore setting the coordinates should fail.
841 if (!TEST_false(EC_POINT_set_affine_coordinates_GF2m(group, P, x, yplusone,
843 || !TEST_true(EC_POINT_set_compressed_coordinates_GF2m(group, P, x,
846 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
847 || !TEST_true(BN_hex2bn(&z, test->order))
848 || !TEST_true(BN_hex2bn(&cof, test->cof))
849 || !TEST_true(EC_GROUP_set_generator(group, P, z, cof))
850 || !TEST_true(EC_POINT_get_affine_coordinates_GF2m(group, P, x, y,
853 TEST_info("%s -- Generator", test->name);
854 test_output_bignum("x", x);
855 test_output_bignum("y", y);
856 /* G_y value taken from the standard: */
857 if (!TEST_true(BN_hex2bn(&z, test->y))
858 || !TEST_BN_eq(y, z))
862 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
863 * and therefore setting the coordinates should fail.
865 if (!TEST_false(EC_POINT_set_affine_coordinates_GF2m(group, P, x, yplusone,
867 || !TEST_true(EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx))
868 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
869 || !TEST_true(BN_hex2bn(&z, test->order))
870 || !TEST_true(BN_hex2bn(&cof, test->cof))
871 || !TEST_true(EC_GROUP_set_generator(group, P, z, cof)))
873 TEST_info("%s -- Generator:", test->name);
874 test_output_bignum("x", x);
875 test_output_bignum("y", y);
878 if (!TEST_int_eq(EC_GROUP_get_degree(group), test->degree)
879 || !group_order_tests(group)
880 || !TEST_ptr(variable = EC_GROUP_new(EC_GROUP_method_of(group)))
881 || !TEST_true(EC_GROUP_copy(variable, group)))
884 /* more tests using the last curve */
885 if (n == OSSL_NELEM(char2_curve_tests) - 1) {
886 if (!TEST_true(EC_POINT_set_affine_coordinates_GF2m(group, P, x, y,
888 || !TEST_true(EC_POINT_copy(Q, P))
889 || !TEST_false(EC_POINT_is_at_infinity(group, Q))
890 || !TEST_true(EC_POINT_dbl(group, P, P, ctx))
891 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
892 || !TEST_true(EC_POINT_invert(group, Q, ctx)) /* P = -2Q */
893 || !TEST_true(EC_POINT_add(group, R, P, Q, ctx))
894 || !TEST_true(EC_POINT_add(group, R, R, Q, ctx))
895 || !TEST_true(EC_POINT_is_at_infinity(group, R)) /* R = P + 2Q */
896 || !TEST_false(EC_POINT_is_at_infinity(group, Q)))
903 if (!TEST_true(BN_add(y, z, BN_value_one()))
905 || !TEST_true(BN_rshift1(y, y)))
907 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
910 TEST_note("combined multiplication ...");
912 /* z is still the group order */
913 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
914 || !TEST_true(EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
915 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
916 || !TEST_int_eq(0, EC_POINT_cmp(group, R, Q, ctx)))
919 if (!TEST_true(BN_rand(y, BN_num_bits(y), 0, 0))
920 || !TEST_true(BN_add(z, z, y)))
922 BN_set_negative(z, 1);
924 scalars[1] = z; /* z = -(order + y) */
926 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
927 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
930 if (!TEST_true(BN_rand(x, BN_num_bits(y) - 1, 0, 0))
931 || !TEST_true(BN_add(z, x, y)))
933 BN_set_negative(z, 1);
936 scalars[2] = z; /* z = -(x+y) */
938 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx))
939 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
957 EC_GROUP_free(group);
958 EC_GROUP_free(variable);
962 static int char2_field_tests(void)
965 BIGNUM *p = NULL, *a = NULL, *b = NULL;
966 EC_GROUP *group = NULL, *tmp = NULL;
967 EC_POINT *P = NULL, *Q = NULL, *R = NULL;
968 BIGNUM *x = NULL, *y = NULL, *z = NULL, *cof = NULL, *yplusone = NULL;
969 unsigned char buf[100];
973 if (!TEST_ptr(ctx = BN_CTX_new())
974 || !TEST_ptr(p = BN_new())
975 || !TEST_ptr(a = BN_new())
976 || !TEST_ptr(b = BN_new())
977 || !TEST_true(BN_hex2bn(&p, "13"))
978 || !TEST_true(BN_hex2bn(&a, "3"))
979 || !TEST_true(BN_hex2bn(&b, "1")))
982 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use
983 * EC_GROUP_new_curve_GF2m
984 * so that the library gets
985 * to choose the EC_METHOD */
987 || !TEST_true(EC_GROUP_set_curve_GF2m(group, p, a, b, ctx))
988 || !TEST_ptr(tmp = EC_GROUP_new(EC_GROUP_method_of(group)))
989 || !TEST_true(EC_GROUP_copy(tmp, group)))
991 EC_GROUP_free(group);
995 if (!TEST_true(EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)))
998 TEST_info("Curve defined by Weierstrass equation");
999 TEST_note(" y^2 + x*y = x^3 + a*x^2 + b (mod p)");
1000 test_output_bignum("a", a);
1001 test_output_bignum("b", b);
1002 test_output_bignum("p", p);
1004 if (!TEST_ptr(P = EC_POINT_new(group))
1005 || !TEST_ptr(Q = EC_POINT_new(group))
1006 || !TEST_ptr(R = EC_POINT_new(group))
1007 || !TEST_true(EC_POINT_set_to_infinity(group, P))
1008 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
1012 if (!TEST_true(EC_POINT_oct2point(group, Q, buf, 1, ctx))
1013 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx))
1014 || !TEST_true(EC_POINT_is_at_infinity(group, P))
1015 || !TEST_ptr(x = BN_new())
1016 || !TEST_ptr(y = BN_new())
1017 || !TEST_ptr(z = BN_new())
1018 || !TEST_ptr(cof = BN_new())
1019 || !TEST_ptr(yplusone = BN_new())
1020 || !TEST_true(BN_hex2bn(&x, "6"))
1021 /* Change test based on whether binary point compression is enabled or not. */
1022 # ifdef OPENSSL_EC_BIN_PT_COMP
1023 || !TEST_true(EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1,
1026 || !TEST_true(BN_hex2bn(&y, "8"))
1027 || !TEST_true(EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx))
1031 if (!TEST_int_gt(EC_POINT_is_on_curve(group, Q, ctx), 0)) {
1032 /* Change test based on whether binary point compression is enabled or not. */
1033 # ifdef OPENSSL_EC_BIN_PT_COMP
1034 if (!TEST_true(EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y,
1038 TEST_info("Point is not on curve");
1039 test_output_bignum("x", x);
1040 test_output_bignum("y", y);
1044 TEST_note("A cyclic subgroup:");
1047 if (!TEST_int_ne(k--, 0))
1050 if (EC_POINT_is_at_infinity(group, P))
1051 TEST_note(" point at infinity");
1053 if (!TEST_true(EC_POINT_get_affine_coordinates_GF2m(group, P, x, y,
1057 test_output_bignum("x", x);
1058 test_output_bignum("y", y);
1061 if (!TEST_true(EC_POINT_copy(R, P))
1062 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx)))
1065 while (!EC_POINT_is_at_infinity(group, P));
1067 if (!TEST_true(EC_POINT_add(group, P, Q, R, ctx))
1068 || !TEST_true(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
1073 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED,
1074 buf, sizeof(buf), ctx);
1075 if (!TEST_size_t_ne(len, 0)
1076 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
1077 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
1079 test_output_memory("Generator as octet string, compressed form:",
1083 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED,
1084 buf, sizeof(buf), ctx);
1085 if (!TEST_size_t_ne(len, 0)
1086 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
1087 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
1089 test_output_memory("Generator as octet string, uncompressed form:",
1092 /* Change test based on whether binary point compression is enabled or not. */
1093 # ifdef OPENSSL_EC_BIN_PT_COMP
1095 EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof(buf),
1097 if (!TEST_size_t_ne(len, 0)
1098 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
1099 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
1101 test_output_memory("Generator as octet string, hybrid form:",
1105 if (!TEST_true(EC_POINT_invert(group, P, ctx))
1106 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx)))
1117 EC_GROUP_free(group);
1131 static int internal_curve_test(int n)
1133 EC_GROUP *group = NULL;
1134 int nid = curves[n].nid;
1136 if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))) {
1137 TEST_info("EC_GROUP_new_curve_name() failed with curve %s\n",
1141 if (!TEST_true(EC_GROUP_check(group, NULL))) {
1142 TEST_info("EC_GROUP_check() failed with curve %s\n", OBJ_nid2sn(nid));
1143 EC_GROUP_free(group);
1146 EC_GROUP_free(group);
1150 static int internal_curve_test_method(int n)
1152 int r, nid = curves[n].nid;
1155 if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))) {
1156 TEST_info("Curve %s failed\n", OBJ_nid2sn(nid));
1159 r = group_order_tests(group);
1160 EC_GROUP_free(group);
1164 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1166 * nistp_test_params contains magic numbers for testing our optimized
1167 * implementations of several NIST curves with characteristic > 3.
1169 struct nistp_test_params {
1170 const EC_METHOD *(*meth) ();
1173 * Qx, Qy and D are taken from
1174 * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
1175 * Otherwise, values are standard curve parameters from FIPS 180-3
1177 const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d;
1180 static const struct nistp_test_params nistp_tests_params[] = {
1183 EC_GFp_nistp224_method,
1186 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
1188 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
1190 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
1192 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E",
1194 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555",
1196 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
1198 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
1200 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
1202 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8",
1206 EC_GFp_nistp256_method,
1209 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
1211 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc",
1213 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
1215 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19",
1217 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09",
1219 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
1221 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5",
1223 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
1225 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96",
1229 EC_GFp_nistp521_method,
1233 "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
1234 "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
1237 "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
1238 "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc",
1241 "953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e1"
1242 "56193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00",
1245 "e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e"
1246 "59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4",
1249 "350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8"
1250 "554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e",
1253 "858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dba"
1254 "a14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66",
1257 "39296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c"
1258 "97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650",
1261 "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa"
1262 "51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409",
1265 "085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eee"
1266 "df09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722",
1270 static int nistp_single_test(int idx)
1272 const struct nistp_test_params *test = nistp_tests_params + idx;
1274 BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL;
1275 BIGNUM *n = NULL, *m = NULL, *order = NULL, *yplusone = NULL;
1276 EC_GROUP *NISTP = NULL;
1277 EC_POINT *G = NULL, *P = NULL, *Q = NULL, *Q_CHECK = NULL;
1280 TEST_note("NIST curve P-%d (optimised implementation):",
1282 if (!TEST_ptr(ctx = BN_CTX_new())
1283 || !TEST_ptr(p = BN_new())
1284 || !TEST_ptr(a = BN_new())
1285 || !TEST_ptr(b = BN_new())
1286 || !TEST_ptr(x = BN_new())
1287 || !TEST_ptr(y = BN_new())
1288 || !TEST_ptr(m = BN_new())
1289 || !TEST_ptr(n = BN_new())
1290 || !TEST_ptr(order = BN_new())
1291 || !TEST_ptr(yplusone = BN_new())
1293 || !TEST_ptr(NISTP = EC_GROUP_new(test->meth()))
1294 || !TEST_true(BN_hex2bn(&p, test->p))
1295 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
1296 || !TEST_true(BN_hex2bn(&a, test->a))
1297 || !TEST_true(BN_hex2bn(&b, test->b))
1298 || !TEST_true(EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx))
1299 || !TEST_ptr(G = EC_POINT_new(NISTP))
1300 || !TEST_ptr(P = EC_POINT_new(NISTP))
1301 || !TEST_ptr(Q = EC_POINT_new(NISTP))
1302 || !TEST_ptr(Q_CHECK = EC_POINT_new(NISTP))
1303 || !TEST_true(BN_hex2bn(&x, test->Qx))
1304 || !TEST_true(BN_hex2bn(&y, test->Qy))
1305 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
1307 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
1308 * and therefore setting the coordinates should fail.
1310 || !TEST_false(EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x,
1312 || !TEST_true(EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y,
1314 || !TEST_true(BN_hex2bn(&x, test->Gx))
1315 || !TEST_true(BN_hex2bn(&y, test->Gy))
1316 || !TEST_true(EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx))
1317 || !TEST_true(BN_hex2bn(&order, test->order))
1318 || !TEST_true(EC_GROUP_set_generator(NISTP, G, order, BN_value_one()))
1319 || !TEST_int_eq(EC_GROUP_get_degree(NISTP), test->degree))
1322 TEST_note("NIST test vectors ... ");
1323 if (!TEST_true(BN_hex2bn(&n, test->d)))
1325 /* fixed point multiplication */
1326 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1327 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1329 /* random point multiplication */
1330 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1331 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1333 /* set generator to P = 2*G, where G is the standard generator */
1334 || !TEST_true(EC_POINT_dbl(NISTP, P, G, ctx))
1335 || !TEST_true(EC_GROUP_set_generator(NISTP, P, order, BN_value_one()))
1336 /* set the scalar to m=n/2, where n is the NIST test scalar */
1337 || !TEST_true(BN_rshift(m, n, 1)))
1340 /* test the non-standard generator */
1341 /* fixed point multiplication */
1342 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1343 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1345 /* random point multiplication */
1346 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1347 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1350 * We have not performed precomputation so have_precompute mult should be
1353 || !TEST_false(EC_GROUP_have_precompute_mult(NISTP))
1355 /* now repeat all tests with precomputation */
1356 || !TEST_true(EC_GROUP_precompute_mult(NISTP, ctx))
1357 || !TEST_true(EC_GROUP_have_precompute_mult(NISTP)))
1360 /* fixed point multiplication */
1361 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1362 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1364 /* random point multiplication */
1365 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1366 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1368 /* reset generator */
1369 || !TEST_true(EC_GROUP_set_generator(NISTP, G, order, BN_value_one())))
1371 /* fixed point multiplication */
1372 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1373 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1375 /* random point multiplication */
1376 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1377 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1380 /* regression test for felem_neg bug */
1381 if (!TEST_true(BN_set_word(m, 32))
1382 || !TEST_true(BN_set_word(n, 31))
1383 || !TEST_true(EC_POINT_copy(P, G))
1384 || !TEST_true(EC_POINT_invert(NISTP, P, ctx))
1385 || !TEST_true(EC_POINT_mul(NISTP, Q, m, P, n, ctx))
1386 || !TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, G, ctx)))
1389 r = group_order_tests(NISTP);
1391 EC_GROUP_free(NISTP);
1395 EC_POINT_free(Q_CHECK);
1410 static int parameter_test(void)
1412 EC_GROUP *group = NULL, *group2 = NULL;
1413 ECPARAMETERS *ecparameters = NULL;
1416 r = TEST_ptr(group = EC_GROUP_new_by_curve_name(NID_secp112r1))
1417 && TEST_ptr(ecparameters = EC_GROUP_get_ecparameters(group, NULL))
1418 && TEST_ptr(group2 = EC_GROUP_new_from_ecparameters(ecparameters))
1419 && TEST_int_eq(EC_GROUP_cmp(group, group2, NULL), 0);
1421 EC_GROUP_free(group);
1422 EC_GROUP_free(group2);
1423 ECPARAMETERS_free(ecparameters);
1428 int setup_tests(void)
1430 #ifndef OPENSSL_NO_EC
1431 crv_len = EC_get_builtin_curves(NULL, 0);
1432 if (!TEST_ptr(curves = OPENSSL_malloc(sizeof(*curves) * crv_len))
1433 || !TEST_true(EC_get_builtin_curves(curves, crv_len)))
1436 ADD_TEST(parameter_test);
1437 ADD_TEST(prime_field_tests);
1438 # ifndef OPENSSL_NO_EC2M
1439 ADD_TEST(char2_field_tests);
1440 ADD_ALL_TESTS(char2_curve_test, OSSL_NELEM(char2_curve_tests));
1442 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1443 ADD_ALL_TESTS(nistp_single_test, OSSL_NELEM(nistp_tests_params));
1445 ADD_ALL_TESTS(internal_curve_test, crv_len);
1446 ADD_ALL_TESTS(internal_curve_test_method, crv_len);
1451 void cleanup_tests(void)
1453 #ifndef OPENSSL_NO_EC
1454 OPENSSL_free(curves);