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 Apache License 2.0 (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
12 #include "internal/nelem.h"
16 # include <openssl/ec.h>
17 # ifndef OPENSSL_NO_ENGINE
18 # include <openssl/engine.h>
20 # include <openssl/err.h>
21 # include <openssl/obj_mac.h>
22 # include <openssl/objects.h>
23 # include <openssl/rand.h>
24 # include <openssl/bn.h>
25 # include <openssl/opensslconf.h>
27 static size_t crv_len = 0;
28 static EC_builtin_curve *curves = NULL;
30 /* test multiplication with group order, long and negative scalars */
31 static int group_order_tests(EC_GROUP *group)
33 BIGNUM *n1 = NULL, *n2 = NULL, *order = NULL;
34 EC_POINT *P = NULL, *Q = NULL, *R = NULL, *S = NULL;
35 const EC_POINT *G = NULL;
39 if (!TEST_ptr(n1 = BN_new())
40 || !TEST_ptr(n2 = BN_new())
41 || !TEST_ptr(order = BN_new())
42 || !TEST_ptr(ctx = BN_CTX_new())
43 || !TEST_ptr(G = EC_GROUP_get0_generator(group))
44 || !TEST_ptr(P = EC_POINT_new(group))
45 || !TEST_ptr(Q = EC_POINT_new(group))
46 || !TEST_ptr(R = EC_POINT_new(group))
47 || !TEST_ptr(S = EC_POINT_new(group)))
50 if (!TEST_true(EC_GROUP_get_order(group, order, ctx))
51 || !TEST_true(EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
52 || !TEST_true(EC_POINT_is_at_infinity(group, Q))
53 || !TEST_true(EC_GROUP_precompute_mult(group, ctx))
54 || !TEST_true(EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
55 || !TEST_true(EC_POINT_is_at_infinity(group, Q))
56 || !TEST_true(EC_POINT_copy(P, G))
57 || !TEST_true(BN_one(n1))
58 || !TEST_true(EC_POINT_mul(group, Q, n1, NULL, NULL, ctx))
59 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
60 || !TEST_true(BN_sub(n1, order, n1))
61 || !TEST_true(EC_POINT_mul(group, Q, n1, NULL, NULL, ctx))
62 || !TEST_true(EC_POINT_invert(group, Q, ctx))
63 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx)))
66 for (i = 1; i <= 2; i++) {
67 const BIGNUM *scalars[6];
68 const EC_POINT *points[6];
70 if (!TEST_true(BN_set_word(n1, i))
72 * If i == 1, P will be the predefined generator for which
73 * EC_GROUP_precompute_mult has set up precomputation.
75 || !TEST_true(EC_POINT_mul(group, P, n1, NULL, NULL, ctx))
76 || (i == 1 && !TEST_int_eq(0, EC_POINT_cmp(group, P, G, ctx)))
77 || !TEST_true(BN_one(n1))
79 || !TEST_true(BN_sub(n1, n1, order))
80 || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n1, ctx))
81 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
84 || !TEST_true(BN_add(n2, order, BN_value_one()))
85 || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
86 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
88 /* n2 = (1 - order) * (1 + order) = 1 - order^2 */
89 || !TEST_true(BN_mul(n2, n1, n2, ctx))
90 || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
91 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx)))
94 /* n2 = order^2 - 1 */
95 BN_set_negative(n2, 0);
96 if (!TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
97 /* Add P to verify the result. */
98 || !TEST_true(EC_POINT_add(group, Q, Q, P, ctx))
99 || !TEST_true(EC_POINT_is_at_infinity(group, Q))
101 /* Exercise EC_POINTs_mul, including corner cases. */
102 || !TEST_false(EC_POINT_is_at_infinity(group, P)))
105 scalars[0] = scalars[1] = BN_value_one();
106 points[0] = points[1] = P;
108 if (!TEST_true(EC_POINTs_mul(group, R, NULL, 2, points, scalars, ctx))
109 || !TEST_true(EC_POINT_dbl(group, S, points[0], ctx))
110 || !TEST_int_eq(0, EC_POINT_cmp(group, R, S, ctx)))
114 points[0] = Q; /* => infinity */
116 points[1] = P; /* => -P */
118 points[2] = Q; /* => infinity */
120 points[3] = Q; /* => infinity */
122 points[4] = P; /* => P */
124 points[5] = Q; /* => infinity */
125 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 6, points, scalars, ctx))
126 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
132 if (r == 0 && i != 0)
133 TEST_info(i == 1 ? "allowing precomputation" :
134 "without precomputation");
146 static int prime_field_tests(void)
149 BIGNUM *p = NULL, *a = NULL, *b = NULL, *scalar3 = NULL;
150 EC_GROUP *group = NULL, *tmp = NULL;
151 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL,
152 *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
153 EC_POINT *P = NULL, *Q = NULL, *R = NULL;
154 BIGNUM *x = NULL, *y = NULL, *z = NULL, *yplusone = NULL;
155 const EC_POINT *points[4];
156 const BIGNUM *scalars[4];
157 unsigned char buf[100];
161 if (!TEST_ptr(ctx = BN_CTX_new())
162 || !TEST_ptr(p = BN_new())
163 || !TEST_ptr(a = BN_new())
164 || !TEST_ptr(b = BN_new())
165 || !TEST_true(BN_hex2bn(&p, "17"))
166 || !TEST_true(BN_hex2bn(&a, "1"))
167 || !TEST_true(BN_hex2bn(&b, "1"))
169 * applications should use EC_GROUP_new_curve_GFp so
170 * that the library gets to choose the EC_METHOD
172 || !TEST_ptr(group = EC_GROUP_new(EC_GFp_mont_method()))
173 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
174 || !TEST_ptr(tmp = EC_GROUP_new(EC_GROUP_method_of(group)))
175 || !TEST_true(EC_GROUP_copy(tmp, group)))
177 EC_GROUP_free(group);
181 if (!TEST_true(EC_GROUP_get_curve(group, p, a, b, ctx)))
184 TEST_info("Curve defined by Weierstrass equation");
185 TEST_note(" y^2 = x^3 + a*x + b (mod p)");
186 test_output_bignum("a", a);
187 test_output_bignum("b", b);
188 test_output_bignum("p", p);
191 if (!TEST_ptr(P = EC_POINT_new(group))
192 || !TEST_ptr(Q = EC_POINT_new(group))
193 || !TEST_ptr(R = EC_POINT_new(group))
194 || !TEST_true(EC_POINT_set_to_infinity(group, P))
195 || !TEST_true(EC_POINT_is_at_infinity(group, P))
196 || !TEST_true(EC_POINT_oct2point(group, Q, buf, 1, ctx))
197 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx))
198 || !TEST_true(EC_POINT_is_at_infinity(group, P))
199 || !TEST_ptr(x = BN_new())
200 || !TEST_ptr(y = BN_new())
201 || !TEST_ptr(z = BN_new())
202 || !TEST_ptr(yplusone = BN_new())
203 || !TEST_true(BN_hex2bn(&x, "D"))
204 || !TEST_true(EC_POINT_set_compressed_coordinates(group, Q, x, 1, ctx)))
207 if (!TEST_int_gt(EC_POINT_is_on_curve(group, Q, ctx), 0)) {
208 if (!TEST_true(EC_POINT_get_affine_coordinates(group, Q, x, y, ctx)))
210 TEST_info("Point is not on curve");
211 test_output_bignum("x", x);
212 test_output_bignum("y", y);
216 TEST_note("A cyclic subgroup:");
219 if (!TEST_int_ne(k--, 0))
222 if (EC_POINT_is_at_infinity(group, P)) {
223 TEST_note(" point at infinity");
225 if (!TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y,
229 test_output_bignum("x", x);
230 test_output_bignum("y", y);
233 if (!TEST_true(EC_POINT_copy(R, P))
234 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx)))
237 } while (!EC_POINT_is_at_infinity(group, P));
239 if (!TEST_true(EC_POINT_add(group, P, Q, R, ctx))
240 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
244 EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf,
246 if (!TEST_size_t_ne(len, 0)
247 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
248 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
250 test_output_memory("Generator as octet string, compressed form:",
253 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED,
254 buf, sizeof(buf), ctx);
255 if (!TEST_size_t_ne(len, 0)
256 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
257 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
259 test_output_memory("Generator as octet string, uncompressed form:",
262 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID,
263 buf, sizeof(buf), ctx);
264 if (!TEST_size_t_ne(len, 0)
265 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
266 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
268 test_output_memory("Generator as octet string, hybrid form:",
271 if (!TEST_true(EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z,
274 TEST_info("A representation of the inverse of that generator in");
275 TEST_note("Jacobian projective coordinates");
276 test_output_bignum("x", x);
277 test_output_bignum("y", y);
278 test_output_bignum("z", z);
280 if (!TEST_true(EC_POINT_invert(group, P, ctx))
281 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
284 * Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2,
285 * 2000) -- not a NIST curve, but commonly used
288 || !TEST_true(BN_hex2bn(&p, "FFFFFFFF"
289 "FFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"))
290 || !TEST_int_eq(1, BN_check_prime(p, ctx, NULL))
291 || !TEST_true(BN_hex2bn(&a, "FFFFFFFF"
292 "FFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"))
293 || !TEST_true(BN_hex2bn(&b, "1C97BEFC"
294 "54BD7A8B65ACF89F81D4D4ADC565FA45"))
295 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
296 || !TEST_true(BN_hex2bn(&x, "4A96B568"
297 "8EF573284664698968C38BB913CBFC82"))
298 || !TEST_true(BN_hex2bn(&y, "23a62855"
299 "3168947d59dcc912042351377ac5fb32"))
300 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
302 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
303 * and therefore setting the coordinates should fail.
305 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
307 || !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
308 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
309 || !TEST_true(BN_hex2bn(&z, "0100000000"
310 "000000000001F4C8F927AED3CA752257"))
311 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
312 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
314 TEST_info("SEC2 curve secp160r1 -- Generator");
315 test_output_bignum("x", x);
316 test_output_bignum("y", y);
317 /* G_y value taken from the standard: */
318 if (!TEST_true(BN_hex2bn(&z, "23a62855"
319 "3168947d59dcc912042351377ac5fb32"))
321 || !TEST_int_eq(EC_GROUP_get_degree(group), 160)
322 || !group_order_tests(group)
323 || !TEST_ptr(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))
324 || !TEST_true(EC_GROUP_copy(P_160, group))
326 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
328 || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFF"
329 "FFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"))
330 || !TEST_int_eq(1, BN_check_prime(p, ctx, NULL))
331 || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFF"
332 "FFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"))
333 || !TEST_true(BN_hex2bn(&b, "64210519E59C80E7"
334 "0FA7E9AB72243049FEB8DEECC146B9B1"))
335 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
336 || !TEST_true(BN_hex2bn(&x, "188DA80EB03090F6"
337 "7CBF20EB43A18800F4FF0AFD82FF1012"))
338 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx))
339 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
340 || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFF"
341 "FFFFFFFF99DEF836146BC9B1B4D22831"))
342 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
343 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
346 TEST_info("NIST curve P-192 -- Generator");
347 test_output_bignum("x", x);
348 test_output_bignum("y", y);
349 /* G_y value taken from the standard: */
350 if (!TEST_true(BN_hex2bn(&z, "07192B95FFC8DA78"
351 "631011ED6B24CDD573F977A11E794811"))
353 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
355 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
356 * and therefore setting the coordinates should fail.
358 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
360 || !TEST_int_eq(EC_GROUP_get_degree(group), 192)
361 || !group_order_tests(group)
362 || !TEST_ptr(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))
363 || !TEST_true(EC_GROUP_copy(P_192, group))
365 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
367 || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFF"
368 "FFFFFFFF000000000000000000000001"))
369 || !TEST_int_eq(1, BN_check_prime(p, ctx, NULL))
370 || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFF"
371 "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"))
372 || !TEST_true(BN_hex2bn(&b, "B4050A850C04B3ABF5413256"
373 "5044B0B7D7BFD8BA270B39432355FFB4"))
374 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
375 || !TEST_true(BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B9"
376 "4A03C1D356C21122343280D6115C1D21"))
377 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 0, ctx))
378 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
379 || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF"
380 "FFFF16A2E0B8F03E13DD29455C5C2A3D"))
381 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
382 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
385 TEST_info("NIST curve P-224 -- Generator");
386 test_output_bignum("x", x);
387 test_output_bignum("y", y);
388 /* G_y value taken from the standard: */
389 if (!TEST_true(BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6"
390 "CD4375A05A07476444D5819985007E34"))
392 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
394 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
395 * and therefore setting the coordinates should fail.
397 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
399 || !TEST_int_eq(EC_GROUP_get_degree(group), 224)
400 || !group_order_tests(group)
401 || !TEST_ptr(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))
402 || !TEST_true(EC_GROUP_copy(P_224, group))
404 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
406 || !TEST_true(BN_hex2bn(&p, "FFFFFFFF000000010000000000000000"
407 "00000000FFFFFFFFFFFFFFFFFFFFFFFF"))
408 || !TEST_int_eq(1, BN_check_prime(p, ctx, NULL))
409 || !TEST_true(BN_hex2bn(&a, "FFFFFFFF000000010000000000000000"
410 "00000000FFFFFFFFFFFFFFFFFFFFFFFC"))
411 || !TEST_true(BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC"
412 "651D06B0CC53B0F63BCE3C3E27D2604B"))
413 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
415 || !TEST_true(BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F2"
416 "77037D812DEB33A0F4A13945D898C296"))
417 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx))
418 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
419 || !TEST_true(BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFF"
420 "BCE6FAADA7179E84F3B9CAC2FC632551"))
421 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
422 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
425 TEST_info("NIST curve P-256 -- Generator");
426 test_output_bignum("x", x);
427 test_output_bignum("y", y);
428 /* G_y value taken from the standard: */
429 if (!TEST_true(BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E16"
430 "2BCE33576B315ECECBB6406837BF51F5"))
432 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
434 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
435 * and therefore setting the coordinates should fail.
437 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
439 || !TEST_int_eq(EC_GROUP_get_degree(group), 256)
440 || !group_order_tests(group)
441 || !TEST_ptr(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))
442 || !TEST_true(EC_GROUP_copy(P_256, group))
444 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
446 || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
447 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
448 "FFFFFFFF0000000000000000FFFFFFFF"))
449 || !TEST_int_eq(1, BN_check_prime(p, ctx, NULL))
450 || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
451 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
452 "FFFFFFFF0000000000000000FFFFFFFC"))
453 || !TEST_true(BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19"
454 "181D9C6EFE8141120314088F5013875A"
455 "C656398D8A2ED19D2A85C8EDD3EC2AEF"))
456 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
458 || !TEST_true(BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD74"
459 "6E1D3B628BA79B9859F741E082542A38"
460 "5502F25DBF55296C3A545E3872760AB7"))
461 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx))
462 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
463 || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
464 "FFFFFFFFFFFFFFFFC7634D81F4372DDF"
465 "581A0DB248B0A77AECEC196ACCC52973"))
466 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
467 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
470 TEST_info("NIST curve P-384 -- Generator");
471 test_output_bignum("x", x);
472 test_output_bignum("y", y);
473 /* G_y value taken from the standard: */
474 if (!TEST_true(BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29"
475 "F8F41DBD289A147CE9DA3113B5F0B8C0"
476 "0A60B1CE1D7E819D7A431D7C90EA0E5F"))
478 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
480 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
481 * and therefore setting the coordinates should fail.
483 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
485 || !TEST_int_eq(EC_GROUP_get_degree(group), 384)
486 || !group_order_tests(group)
487 || !TEST_ptr(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))
488 || !TEST_true(EC_GROUP_copy(P_384, group))
490 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
491 || !TEST_true(BN_hex2bn(&p, "1FF"
492 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
493 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
494 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
495 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
496 || !TEST_int_eq(1, BN_check_prime(p, ctx, NULL))
497 || !TEST_true(BN_hex2bn(&a, "1FF"
498 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
499 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
500 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
501 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC"))
502 || !TEST_true(BN_hex2bn(&b, "051"
503 "953EB9618E1C9A1F929A21A0B68540EE"
504 "A2DA725B99B315F3B8B489918EF109E1"
505 "56193951EC7E937B1652C0BD3BB1BF07"
506 "3573DF883D2C34F1EF451FD46B503F00"))
507 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
508 || !TEST_true(BN_hex2bn(&x, "C6"
509 "858E06B70404E9CD9E3ECB662395B442"
510 "9C648139053FB521F828AF606B4D3DBA"
511 "A14B5E77EFE75928FE1DC127A2FFA8DE"
512 "3348B3C1856A429BF97E7E31C2E5BD66"))
513 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 0, ctx))
514 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
515 || !TEST_true(BN_hex2bn(&z, "1FF"
516 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
517 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA"
518 "51868783BF2F966B7FCC0148F709A5D0"
519 "3BB5C9B8899C47AEBB6FB71E91386409"))
520 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
521 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
524 TEST_info("NIST curve P-521 -- Generator");
525 test_output_bignum("x", x);
526 test_output_bignum("y", y);
527 /* G_y value taken from the standard: */
528 if (!TEST_true(BN_hex2bn(&z, "118"
529 "39296A789A3BC0045C8A5FB42C7D1BD9"
530 "98F54449579B446817AFBD17273E662C"
531 "97EE72995EF42640C550B9013FAD0761"
532 "353C7086A272C24088BE94769FD16650"))
534 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
536 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
537 * and therefore setting the coordinates should fail.
539 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
541 || !TEST_int_eq(EC_GROUP_get_degree(group), 521)
542 || !group_order_tests(group)
543 || !TEST_ptr(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))
544 || !TEST_true(EC_GROUP_copy(P_521, group))
546 /* more tests using the last curve */
548 /* Restore the point that got mangled in the (x, y + 1) test. */
549 || !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
550 || !TEST_true(EC_POINT_copy(Q, P))
551 || !TEST_false(EC_POINT_is_at_infinity(group, Q))
552 || !TEST_true(EC_POINT_dbl(group, P, P, ctx))
553 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
554 || !TEST_true(EC_POINT_invert(group, Q, ctx)) /* P = -2Q */
555 || !TEST_true(EC_POINT_add(group, R, P, Q, ctx))
556 || !TEST_true(EC_POINT_add(group, R, R, Q, ctx))
557 || !TEST_true(EC_POINT_is_at_infinity(group, R)) /* R = P + 2Q */
558 || !TEST_false(EC_POINT_is_at_infinity(group, Q)))
565 if (!TEST_true(EC_GROUP_get_order(group, z, ctx))
566 || !TEST_true(BN_add(y, z, BN_value_one()))
568 || !TEST_true(BN_rshift1(y, y)))
570 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
573 TEST_note("combined multiplication ...");
575 /* z is still the group order */
576 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
577 || !TEST_true(EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
578 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
579 || !TEST_int_eq(0, EC_POINT_cmp(group, R, Q, ctx))
580 || !TEST_true(BN_rand(y, BN_num_bits(y), 0, 0))
581 || !TEST_true(BN_add(z, z, y)))
583 BN_set_negative(z, 1);
585 scalars[1] = z; /* z = -(order + y) */
587 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
588 || !TEST_true(EC_POINT_is_at_infinity(group, P))
589 || !TEST_true(BN_rand(x, BN_num_bits(y) - 1, 0, 0))
590 || !TEST_true(BN_add(z, x, y)))
592 BN_set_negative(z, 1);
595 scalars[2] = z; /* z = -(x+y) */
597 if (!TEST_ptr(scalar3 = BN_new()))
600 scalars[3] = scalar3;
602 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx))
603 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
615 EC_GROUP_free(group);
626 EC_GROUP_free(P_160);
627 EC_GROUP_free(P_192);
628 EC_GROUP_free(P_224);
629 EC_GROUP_free(P_256);
630 EC_GROUP_free(P_384);
631 EC_GROUP_free(P_521);
635 # ifndef OPENSSL_NO_EC2M
637 static struct c2_curve_test {
648 } char2_curve_tests[] = {
649 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
652 "0800000000000000000000000000000000000000C9",
655 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
656 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
657 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163
659 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
662 "0800000000000000000000000000000000000000C9",
664 "020A601907B8C953CA1481EB10512F78744A3205FD",
665 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
666 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
667 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163
669 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
672 "020000000000000000000000000000000000000004000000000000000001",
675 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
676 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
678 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
681 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
684 "020000000000000000000000000000000000000004000000000000000001",
685 "000000000000000000000000000000000000000000000000000000000001",
686 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
687 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
688 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
690 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
693 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
697 "00000000000000000000000000000000000000000000000000000000000010A1",
701 "78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
703 "0F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
706 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
709 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
713 "00000000000000000000000000000000000000000000000000000000000010A1",
715 "0000000000000000000000000000000000000000000000000000000000000001",
717 "C8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
719 "8DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
721 "FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
724 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
727 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
730 "0200000000000000000000000000000000000000"
731 "0000000000000000000000000000000000000000008000000000000000000001",
734 "0060F05F658F49C1AD3AB1890F7184210EFD0987"
735 "E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
736 "01E369050B7C4E42ACBA1DACBF04299C3460782F"
737 "918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
739 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
740 "FFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
743 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
746 "0200000000000000000000000000000000000000"
747 "0000000000000000000000000000000000000000008000000000000000000001",
748 "0000000000000000000000000000000000000000"
749 "0000000000000000000000000000000000000000000000000000000000000001",
750 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422E"
751 "F1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
752 "015D4860D088DDB3496B0C6064756260441CDE4A"
753 "F1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
754 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5"
755 "A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
757 "0100000000000000000000000000000000000000"
758 "00000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
761 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
765 "0000000000000000000000000000000000000000000000000000000000000000"
766 "0000000000000000000000000000000000000000000000000000000000000425",
770 "82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E6"
771 "47DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
773 "4F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA7"
774 "4FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
777 "00000000000000000000000000000000000000000000000000000000131850E1"
778 "F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
781 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
785 "0000000000000000000000000000000000000000000000000000000000000000"
786 "0000000000000000000000000000000000000000000000000000000000000425",
788 "0000000000000000000000000000000000000000000000000000000000000000"
789 "0000000000000000000000000000000000000000000000000000000000000001",
791 "DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA5933"
792 "2BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
794 "6C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293"
795 "CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
797 "6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A57"
798 "6291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
801 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18"
802 "FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
807 static int char2_curve_test(int n)
811 BIGNUM *p = NULL, *a = NULL, *b = NULL;
812 BIGNUM *x = NULL, *y = NULL, *z = NULL, *cof = NULL, *yplusone = NULL;
813 EC_GROUP *group = NULL, *variable = NULL;
814 EC_POINT *P = NULL, *Q = NULL, *R = NULL;
815 const EC_POINT *points[3];
816 const BIGNUM *scalars[3];
817 struct c2_curve_test *const test = char2_curve_tests + n;
819 if (!TEST_ptr(ctx = BN_CTX_new())
820 || !TEST_ptr(p = BN_new())
821 || !TEST_ptr(a = BN_new())
822 || !TEST_ptr(b = BN_new())
823 || !TEST_ptr(x = BN_new())
824 || !TEST_ptr(y = BN_new())
825 || !TEST_ptr(z = BN_new())
826 || !TEST_ptr(yplusone = BN_new())
827 || !TEST_true(BN_hex2bn(&p, test->p))
828 || !TEST_true(BN_hex2bn(&a, test->a))
829 || !TEST_true(BN_hex2bn(&b, test->b))
830 || !TEST_true(group = EC_GROUP_new(EC_GF2m_simple_method()))
831 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
832 || !TEST_ptr(P = EC_POINT_new(group))
833 || !TEST_ptr(Q = EC_POINT_new(group))
834 || !TEST_ptr(R = EC_POINT_new(group))
835 || !TEST_true(BN_hex2bn(&x, test->x))
836 || !TEST_true(BN_hex2bn(&y, test->y))
837 || !TEST_true(BN_add(yplusone, y, BN_value_one())))
840 /* Change test based on whether binary point compression is enabled or not. */
841 # ifdef OPENSSL_EC_BIN_PT_COMP
843 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
844 * and therefore setting the coordinates should fail.
846 if (!TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx))
847 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x,
850 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
851 || !TEST_true(BN_hex2bn(&z, test->order))
852 || !TEST_true(BN_hex2bn(&cof, test->cof))
853 || !TEST_true(EC_GROUP_set_generator(group, P, z, cof))
854 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
856 TEST_info("%s -- Generator", test->name);
857 test_output_bignum("x", x);
858 test_output_bignum("y", y);
859 /* G_y value taken from the standard: */
860 if (!TEST_true(BN_hex2bn(&z, test->y))
861 || !TEST_BN_eq(y, z))
865 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
866 * and therefore setting the coordinates should fail.
868 if (!TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx))
869 || !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
870 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
871 || !TEST_true(BN_hex2bn(&z, test->order))
872 || !TEST_true(BN_hex2bn(&cof, test->cof))
873 || !TEST_true(EC_GROUP_set_generator(group, P, z, cof)))
875 TEST_info("%s -- Generator:", test->name);
876 test_output_bignum("x", x);
877 test_output_bignum("y", y);
880 if (!TEST_int_eq(EC_GROUP_get_degree(group), test->degree)
881 || !group_order_tests(group)
882 || !TEST_ptr(variable = EC_GROUP_new(EC_GROUP_method_of(group)))
883 || !TEST_true(EC_GROUP_copy(variable, group)))
886 /* more tests using the last curve */
887 if (n == OSSL_NELEM(char2_curve_tests) - 1) {
888 if (!TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
889 || !TEST_true(EC_POINT_copy(Q, P))
890 || !TEST_false(EC_POINT_is_at_infinity(group, Q))
891 || !TEST_true(EC_POINT_dbl(group, P, P, ctx))
892 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
893 || !TEST_true(EC_POINT_invert(group, Q, ctx)) /* P = -2Q */
894 || !TEST_true(EC_POINT_add(group, R, P, Q, ctx))
895 || !TEST_true(EC_POINT_add(group, R, R, Q, ctx))
896 || !TEST_true(EC_POINT_is_at_infinity(group, R)) /* R = P + 2Q */
897 || !TEST_false(EC_POINT_is_at_infinity(group, Q)))
904 if (!TEST_true(BN_add(y, z, BN_value_one()))
906 || !TEST_true(BN_rshift1(y, y)))
908 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
911 TEST_note("combined multiplication ...");
913 /* z is still the group order */
914 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
915 || !TEST_true(EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
916 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
917 || !TEST_int_eq(0, EC_POINT_cmp(group, R, Q, ctx)))
920 if (!TEST_true(BN_rand(y, BN_num_bits(y), 0, 0))
921 || !TEST_true(BN_add(z, z, y)))
923 BN_set_negative(z, 1);
925 scalars[1] = z; /* z = -(order + y) */
927 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
928 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
931 if (!TEST_true(BN_rand(x, BN_num_bits(y) - 1, 0, 0))
932 || !TEST_true(BN_add(z, x, y)))
934 BN_set_negative(z, 1);
937 scalars[2] = z; /* z = -(x+y) */
939 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx))
940 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
958 EC_GROUP_free(group);
959 EC_GROUP_free(variable);
963 static int char2_field_tests(void)
966 BIGNUM *p = NULL, *a = NULL, *b = NULL;
967 EC_GROUP *group = NULL, *tmp = NULL;
968 EC_POINT *P = NULL, *Q = NULL, *R = NULL;
969 BIGNUM *x = NULL, *y = NULL, *z = NULL, *cof = NULL, *yplusone = NULL;
970 unsigned char buf[100];
974 if (!TEST_ptr(ctx = BN_CTX_new())
975 || !TEST_ptr(p = BN_new())
976 || !TEST_ptr(a = BN_new())
977 || !TEST_ptr(b = BN_new())
978 || !TEST_true(BN_hex2bn(&p, "13"))
979 || !TEST_true(BN_hex2bn(&a, "3"))
980 || !TEST_true(BN_hex2bn(&b, "1")))
983 group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use
984 * EC_GROUP_new_curve_GF2m
985 * so that the library gets
986 * to choose the EC_METHOD */
988 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
989 || !TEST_ptr(tmp = EC_GROUP_new(EC_GROUP_method_of(group)))
990 || !TEST_true(EC_GROUP_copy(tmp, group)))
992 EC_GROUP_free(group);
996 if (!TEST_true(EC_GROUP_get_curve(group, p, a, b, ctx)))
999 TEST_info("Curve defined by Weierstrass equation");
1000 TEST_note(" y^2 + x*y = x^3 + a*x^2 + b (mod p)");
1001 test_output_bignum("a", a);
1002 test_output_bignum("b", b);
1003 test_output_bignum("p", p);
1005 if (!TEST_ptr(P = EC_POINT_new(group))
1006 || !TEST_ptr(Q = EC_POINT_new(group))
1007 || !TEST_ptr(R = EC_POINT_new(group))
1008 || !TEST_true(EC_POINT_set_to_infinity(group, P))
1009 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
1013 if (!TEST_true(EC_POINT_oct2point(group, Q, buf, 1, ctx))
1014 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx))
1015 || !TEST_true(EC_POINT_is_at_infinity(group, P))
1016 || !TEST_ptr(x = BN_new())
1017 || !TEST_ptr(y = BN_new())
1018 || !TEST_ptr(z = BN_new())
1019 || !TEST_ptr(cof = BN_new())
1020 || !TEST_ptr(yplusone = BN_new())
1021 || !TEST_true(BN_hex2bn(&x, "6"))
1022 /* Change test based on whether binary point compression is enabled or not. */
1023 # ifdef OPENSSL_EC_BIN_PT_COMP
1024 || !TEST_true(EC_POINT_set_compressed_coordinates(group, Q, x, 1, ctx))
1026 || !TEST_true(BN_hex2bn(&y, "8"))
1027 || !TEST_true(EC_POINT_set_affine_coordinates(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(group, Q, x, y, ctx)))
1037 TEST_info("Point is not on curve");
1038 test_output_bignum("x", x);
1039 test_output_bignum("y", y);
1043 TEST_note("A cyclic subgroup:");
1046 if (!TEST_int_ne(k--, 0))
1049 if (EC_POINT_is_at_infinity(group, P))
1050 TEST_note(" point at infinity");
1052 if (!TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y,
1056 test_output_bignum("x", x);
1057 test_output_bignum("y", y);
1060 if (!TEST_true(EC_POINT_copy(R, P))
1061 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx)))
1064 while (!EC_POINT_is_at_infinity(group, P));
1066 if (!TEST_true(EC_POINT_add(group, P, Q, R, ctx))
1067 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
1070 /* Change test based on whether binary point compression is enabled or not. */
1071 # ifdef OPENSSL_EC_BIN_PT_COMP
1072 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED,
1073 buf, sizeof(buf), ctx);
1074 if (!TEST_size_t_ne(len, 0)
1075 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
1076 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
1078 test_output_memory("Generator as octet string, compressed form:",
1082 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED,
1083 buf, sizeof(buf), ctx);
1084 if (!TEST_size_t_ne(len, 0)
1085 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
1086 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
1088 test_output_memory("Generator as octet string, uncompressed form:",
1091 /* Change test based on whether binary point compression is enabled or not. */
1092 # ifdef OPENSSL_EC_BIN_PT_COMP
1094 EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof(buf),
1096 if (!TEST_size_t_ne(len, 0)
1097 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
1098 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
1100 test_output_memory("Generator as octet string, hybrid form:",
1104 if (!TEST_true(EC_POINT_invert(group, P, ctx))
1105 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx)))
1116 EC_GROUP_free(group);
1130 static int internal_curve_test(int n)
1132 EC_GROUP *group = NULL;
1133 int nid = curves[n].nid;
1135 if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))) {
1136 TEST_info("EC_GROUP_new_curve_name() failed with curve %s\n",
1140 if (!TEST_true(EC_GROUP_check(group, NULL))) {
1141 TEST_info("EC_GROUP_check() failed with curve %s\n", OBJ_nid2sn(nid));
1142 EC_GROUP_free(group);
1145 EC_GROUP_free(group);
1149 static int internal_curve_test_method(int n)
1151 int r, nid = curves[n].nid;
1154 if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))) {
1155 TEST_info("Curve %s failed\n", OBJ_nid2sn(nid));
1158 r = group_order_tests(group);
1159 EC_GROUP_free(group);
1163 static int group_field_test(void)
1166 BIGNUM *secp521r1_field = NULL;
1167 BIGNUM *sect163r2_field = NULL;
1168 EC_GROUP *secp521r1_group = NULL;
1169 EC_GROUP *sect163r2_group = NULL;
1171 BN_hex2bn(&secp521r1_field,
1172 "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
1173 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
1174 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
1175 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
1179 BN_hex2bn(§163r2_field,
1180 "08000000000000000000000000000000"
1183 secp521r1_group = EC_GROUP_new_by_curve_name(NID_secp521r1);
1184 if (BN_cmp(secp521r1_field, EC_GROUP_get0_field(secp521r1_group)))
1187 # ifndef OPENSSL_NO_EC2M
1188 sect163r2_group = EC_GROUP_new_by_curve_name(NID_sect163r2);
1189 if (BN_cmp(sect163r2_field, EC_GROUP_get0_field(sect163r2_group)))
1193 EC_GROUP_free(secp521r1_group);
1194 EC_GROUP_free(sect163r2_group);
1195 BN_free(secp521r1_field);
1196 BN_free(sect163r2_field);
1200 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1202 * nistp_test_params contains magic numbers for testing our optimized
1203 * implementations of several NIST curves with characteristic > 3.
1205 struct nistp_test_params {
1206 const EC_METHOD *(*meth) (void);
1209 * Qx, Qy and D are taken from
1210 * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
1211 * Otherwise, values are standard curve parameters from FIPS 180-3
1213 const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d;
1216 static const struct nistp_test_params nistp_tests_params[] = {
1219 EC_GFp_nistp224_method,
1222 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
1224 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
1226 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
1228 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E",
1230 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555",
1232 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
1234 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
1236 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
1238 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8",
1242 EC_GFp_nistp256_method,
1245 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
1247 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc",
1249 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
1251 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19",
1253 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09",
1255 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
1257 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5",
1259 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
1261 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96",
1265 EC_GFp_nistp521_method,
1269 "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
1270 "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
1273 "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
1274 "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc",
1277 "953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e1"
1278 "56193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00",
1281 "e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e"
1282 "59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4",
1285 "350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8"
1286 "554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e",
1289 "858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dba"
1290 "a14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66",
1293 "39296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c"
1294 "97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650",
1297 "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa"
1298 "51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409",
1301 "085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eee"
1302 "df09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722",
1306 static int nistp_single_test(int idx)
1308 const struct nistp_test_params *test = nistp_tests_params + idx;
1310 BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL;
1311 BIGNUM *n = NULL, *m = NULL, *order = NULL, *yplusone = NULL;
1312 EC_GROUP *NISTP = NULL;
1313 EC_POINT *G = NULL, *P = NULL, *Q = NULL, *Q_CHECK = NULL;
1316 TEST_note("NIST curve P-%d (optimised implementation):",
1318 if (!TEST_ptr(ctx = BN_CTX_new())
1319 || !TEST_ptr(p = BN_new())
1320 || !TEST_ptr(a = BN_new())
1321 || !TEST_ptr(b = BN_new())
1322 || !TEST_ptr(x = BN_new())
1323 || !TEST_ptr(y = BN_new())
1324 || !TEST_ptr(m = BN_new())
1325 || !TEST_ptr(n = BN_new())
1326 || !TEST_ptr(order = BN_new())
1327 || !TEST_ptr(yplusone = BN_new())
1329 || !TEST_ptr(NISTP = EC_GROUP_new(test->meth()))
1330 || !TEST_true(BN_hex2bn(&p, test->p))
1331 || !TEST_int_eq(1, BN_check_prime(p, ctx, NULL))
1332 || !TEST_true(BN_hex2bn(&a, test->a))
1333 || !TEST_true(BN_hex2bn(&b, test->b))
1334 || !TEST_true(EC_GROUP_set_curve(NISTP, p, a, b, ctx))
1335 || !TEST_ptr(G = EC_POINT_new(NISTP))
1336 || !TEST_ptr(P = EC_POINT_new(NISTP))
1337 || !TEST_ptr(Q = EC_POINT_new(NISTP))
1338 || !TEST_ptr(Q_CHECK = EC_POINT_new(NISTP))
1339 || !TEST_true(BN_hex2bn(&x, test->Qx))
1340 || !TEST_true(BN_hex2bn(&y, test->Qy))
1341 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
1343 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
1344 * and therefore setting the coordinates should fail.
1346 || !TEST_false(EC_POINT_set_affine_coordinates(NISTP, Q_CHECK, x,
1348 || !TEST_true(EC_POINT_set_affine_coordinates(NISTP, Q_CHECK, x, y,
1350 || !TEST_true(BN_hex2bn(&x, test->Gx))
1351 || !TEST_true(BN_hex2bn(&y, test->Gy))
1352 || !TEST_true(EC_POINT_set_affine_coordinates(NISTP, G, x, y, ctx))
1353 || !TEST_true(BN_hex2bn(&order, test->order))
1354 || !TEST_true(EC_GROUP_set_generator(NISTP, G, order, BN_value_one()))
1355 || !TEST_int_eq(EC_GROUP_get_degree(NISTP), test->degree))
1358 TEST_note("NIST test vectors ... ");
1359 if (!TEST_true(BN_hex2bn(&n, test->d)))
1361 /* fixed point multiplication */
1362 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1363 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1365 /* random point multiplication */
1366 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1367 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1369 /* set generator to P = 2*G, where G is the standard generator */
1370 || !TEST_true(EC_POINT_dbl(NISTP, P, G, ctx))
1371 || !TEST_true(EC_GROUP_set_generator(NISTP, P, order, BN_value_one()))
1372 /* set the scalar to m=n/2, where n is the NIST test scalar */
1373 || !TEST_true(BN_rshift(m, n, 1)))
1376 /* test the non-standard generator */
1377 /* fixed point multiplication */
1378 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1379 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1381 /* random point multiplication */
1382 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1383 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1386 * We have not performed precomputation so have_precompute mult should be
1389 || !TEST_false(EC_GROUP_have_precompute_mult(NISTP))
1391 /* now repeat all tests with precomputation */
1392 || !TEST_true(EC_GROUP_precompute_mult(NISTP, ctx))
1393 || !TEST_true(EC_GROUP_have_precompute_mult(NISTP)))
1396 /* fixed point multiplication */
1397 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1398 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1400 /* random point multiplication */
1401 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1402 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1404 /* reset generator */
1405 || !TEST_true(EC_GROUP_set_generator(NISTP, G, order, BN_value_one())))
1407 /* fixed point multiplication */
1408 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1409 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1411 /* random point multiplication */
1412 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1413 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1416 /* regression test for felem_neg bug */
1417 if (!TEST_true(BN_set_word(m, 32))
1418 || !TEST_true(BN_set_word(n, 31))
1419 || !TEST_true(EC_POINT_copy(P, G))
1420 || !TEST_true(EC_POINT_invert(NISTP, P, ctx))
1421 || !TEST_true(EC_POINT_mul(NISTP, Q, m, P, n, ctx))
1422 || !TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, G, ctx)))
1425 r = group_order_tests(NISTP);
1427 EC_GROUP_free(NISTP);
1431 EC_POINT_free(Q_CHECK);
1446 * Tests a point known to cause an incorrect underflow in an old version of
1449 static int underflow_test(void)
1452 EC_GROUP *grp = NULL;
1453 EC_POINT *P = NULL, *Q = NULL, *R = NULL;
1454 BIGNUM *x1 = NULL, *y1 = NULL, *z1 = NULL, *x2 = NULL, *y2 = NULL;
1458 "1534f0077fffffe87e9adcfe000000000000000000003e05a21d2400002e031b1f4"
1459 "b80000c6fafa4f3c1288798d624a247b5e2ffffffffffffffefe099241900004";
1460 const char *p521m1 =
1461 "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
1462 "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe";
1469 x1 = BN_CTX_get(ctx);
1470 y1 = BN_CTX_get(ctx);
1471 z1 = BN_CTX_get(ctx);
1472 x2 = BN_CTX_get(ctx);
1473 y2 = BN_CTX_get(ctx);
1474 k = BN_CTX_get(ctx);
1478 grp = EC_GROUP_new_by_curve_name(NID_secp521r1);
1479 P = EC_POINT_new(grp);
1480 Q = EC_POINT_new(grp);
1481 R = EC_POINT_new(grp);
1482 if (!TEST_ptr(grp) || !TEST_ptr(P) || !TEST_ptr(Q) || !TEST_ptr(R))
1485 if (!TEST_int_gt(BN_hex2bn(&x1, x1str), 0)
1486 || !TEST_int_gt(BN_hex2bn(&y1, p521m1), 0)
1487 || !TEST_int_gt(BN_hex2bn(&z1, p521m1), 0)
1488 || !TEST_int_gt(BN_hex2bn(&k, "02"), 0)
1489 || !TEST_true(EC_POINT_set_Jprojective_coordinates_GFp(grp, P, x1,
1491 || !TEST_true(EC_POINT_mul(grp, Q, NULL, P, k, ctx))
1492 || !TEST_true(EC_POINT_get_affine_coordinates(grp, Q, x1, y1, ctx))
1493 || !TEST_true(EC_POINT_dbl(grp, R, P, ctx))
1494 || !TEST_true(EC_POINT_get_affine_coordinates(grp, R, x2, y2, ctx)))
1497 if (!TEST_int_eq(BN_cmp(x1, x2), 0)
1498 || !TEST_int_eq(BN_cmp(y1, y2), 0))
1515 static const unsigned char p521_named[] = {
1516 0x06, 0x05, 0x2b, 0x81, 0x04, 0x00, 0x23,
1519 static const unsigned char p521_explicit[] = {
1520 0x30, 0x82, 0x01, 0xc3, 0x02, 0x01, 0x01, 0x30, 0x4d, 0x06, 0x07, 0x2a,
1521 0x86, 0x48, 0xce, 0x3d, 0x01, 0x01, 0x02, 0x42, 0x01, 0xff, 0xff, 0xff,
1522 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1523 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1524 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1525 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1526 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1527 0xff, 0xff, 0x30, 0x81, 0x9f, 0x04, 0x42, 0x01, 0xff, 0xff, 0xff, 0xff,
1528 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1529 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1530 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1531 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1532 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1533 0xfc, 0x04, 0x42, 0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, 0x9a,
1534 0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85, 0x40, 0xee, 0xa2, 0xda, 0x72,
1535 0x5b, 0x99, 0xb3, 0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, 0x09,
1536 0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e, 0x93, 0x7b, 0x16, 0x52, 0xc0,
1537 0xbd, 0x3b, 0xb1, 0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, 0x34,
1538 0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50, 0x3f, 0x00, 0x03, 0x15, 0x00,
1539 0xd0, 0x9e, 0x88, 0x00, 0x29, 0x1c, 0xb8, 0x53, 0x96, 0xcc, 0x67, 0x17,
1540 0x39, 0x32, 0x84, 0xaa, 0xa0, 0xda, 0x64, 0xba, 0x04, 0x81, 0x85, 0x04,
1541 0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, 0xe9, 0xcd, 0x9e, 0x3e,
1542 0xcb, 0x66, 0x23, 0x95, 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f,
1543 0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d, 0x3d, 0xba, 0xa1, 0x4b,
1544 0x5e, 0x77, 0xef, 0xe7, 0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff,
1545 0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a, 0x42, 0x9b, 0xf9, 0x7e,
1546 0x7e, 0x31, 0xc2, 0xe5, 0xbd, 0x66, 0x01, 0x18, 0x39, 0x29, 0x6a, 0x78,
1547 0x9a, 0x3b, 0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, 0x1b, 0xd9,
1548 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17,
1549 0x27, 0x3e, 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, 0x26, 0x40,
1550 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86,
1551 0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50,
1552 0x02, 0x42, 0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1553 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1554 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfa,
1555 0x51, 0x86, 0x87, 0x83, 0xbf, 0x2f, 0x96, 0x6b, 0x7f, 0xcc, 0x01, 0x48,
1556 0xf7, 0x09, 0xa5, 0xd0, 0x3b, 0xb5, 0xc9, 0xb8, 0x89, 0x9c, 0x47, 0xae,
1557 0xbb, 0x6f, 0xb7, 0x1e, 0x91, 0x38, 0x64, 0x09, 0x02, 0x01, 0x01,
1561 * This test validates a named curve's group parameters using
1562 * EC_GROUP_check_named_curve(). It also checks that modifying any of the
1563 * group parameters results in the curve not being valid.
1565 static int check_named_curve_test(int id)
1567 int ret = 0, nid, field_nid, has_seed;
1568 EC_GROUP *group = NULL, *gtest = NULL;
1569 const EC_POINT *group_gen = NULL;
1570 EC_POINT *other_gen = NULL;
1571 BIGNUM *group_p = NULL, *group_a = NULL, *group_b = NULL;
1572 BIGNUM *other_p = NULL, *other_a = NULL, *other_b = NULL;
1573 BIGNUM *group_cofactor = NULL, *other_cofactor = NULL;
1574 BIGNUM *other_order = NULL;
1575 const BIGNUM *group_order = NULL;
1576 BN_CTX *bn_ctx = NULL;
1577 static const unsigned char invalid_seed[] = "THIS IS NOT A VALID SEED";
1578 static size_t invalid_seed_len = sizeof(invalid_seed);
1581 nid = curves[id].nid;
1582 if (!TEST_ptr(bn_ctx = BN_CTX_new())
1583 || !TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))
1584 || !TEST_ptr(gtest = EC_GROUP_dup(group))
1585 || !TEST_ptr(group_p = BN_new())
1586 || !TEST_ptr(group_a = BN_new())
1587 || !TEST_ptr(group_b = BN_new())
1588 || !TEST_ptr(group_cofactor = BN_new())
1589 || !TEST_ptr(group_gen = EC_GROUP_get0_generator(group))
1590 || !TEST_ptr(group_order = EC_GROUP_get0_order(group))
1591 || !TEST_true(EC_GROUP_get_cofactor(group, group_cofactor, NULL))
1592 || !TEST_true(EC_GROUP_get_curve(group, group_p, group_a, group_b, NULL))
1593 || !TEST_ptr(other_gen = EC_POINT_dup(group_gen, group))
1594 || !TEST_true(EC_POINT_add(group, other_gen, group_gen, group_gen, NULL))
1595 || !TEST_ptr(other_order = BN_dup(group_order))
1596 || !TEST_true(BN_add_word(other_order, 1))
1597 || !TEST_ptr(other_a = BN_dup(group_a))
1598 || !TEST_true(BN_add_word(other_a, 1))
1599 || !TEST_ptr(other_b = BN_dup(group_b))
1600 || !TEST_true(BN_add_word(other_b, 1))
1601 || !TEST_ptr(other_cofactor = BN_dup(group_cofactor))
1602 || !TEST_true(BN_add_word(other_cofactor, 1)))
1605 /* Determine if the built-in curve has a seed field set */
1606 has_seed = (EC_GROUP_get_seed_len(group) > 0);
1607 field_nid = EC_METHOD_get_field_type(EC_GROUP_method_of(group));
1608 if (field_nid == NID_X9_62_characteristic_two_field) {
1609 if (!TEST_ptr(other_p = BN_dup(group_p))
1610 || !TEST_true(BN_lshift1(other_p, other_p)))
1613 if (!TEST_ptr(other_p = BN_dup(group_p)))
1616 * Just choosing any arbitrary prime does not work..
1617 * Setting p via ec_GFp_nist_group_set_curve() needs the prime to be a
1618 * nist prime. So only select one of these as an alternate prime.
1620 if (!TEST_ptr(BN_copy(other_p,
1621 BN_ucmp(BN_get0_nist_prime_192(), other_p) == 0 ?
1622 BN_get0_nist_prime_256() :
1623 BN_get0_nist_prime_192())))
1627 /* Passes because this is a valid curve */
1628 if (!TEST_int_eq(EC_GROUP_check_named_curve(group, 0, NULL), nid)
1629 /* Only NIST curves pass */
1630 || !TEST_int_eq(EC_GROUP_check_named_curve(group, 1, NULL),
1631 EC_curve_nid2nist(nid) != NULL ? nid : NID_undef))
1634 /* Fail if the curve name doesn't match the parameters */
1635 EC_GROUP_set_curve_name(group, nid + 1);
1637 if (!TEST_int_le(EC_GROUP_check_named_curve(group, 0, NULL), 0))
1641 /* Restore curve name and ensure it's passing */
1642 EC_GROUP_set_curve_name(group, nid);
1643 if (!TEST_int_eq(EC_GROUP_check_named_curve(group, 0, NULL), nid))
1646 if (!TEST_int_eq(EC_GROUP_set_seed(group, invalid_seed, invalid_seed_len),
1652 * If the built-in curve has a seed and we set the seed to another value
1653 * then it will fail the check.
1655 if (!TEST_int_eq(EC_GROUP_check_named_curve(group, 0, NULL), 0))
1659 * If the built-in curve does not have a seed then setting the seed will
1660 * pass the check (as the seed is optional).
1662 if (!TEST_int_eq(EC_GROUP_check_named_curve(group, 0, NULL), nid))
1665 /* Pass if the seed is unknown (as it is optional) */
1666 if (!TEST_int_eq(EC_GROUP_set_seed(group, NULL, 0), 1)
1667 || !TEST_int_eq(EC_GROUP_check_named_curve(group, 0, NULL), nid))
1670 /* Check that a duped group passes */
1671 if (!TEST_int_eq(EC_GROUP_check_named_curve(gtest, 0, NULL), nid))
1674 /* check that changing any generator parameter fails */
1675 if (!TEST_true(EC_GROUP_set_generator(gtest, other_gen, group_order,
1677 || !TEST_int_eq(EC_GROUP_check_named_curve(gtest, 0, NULL), 0)
1678 || !TEST_true(EC_GROUP_set_generator(gtest, group_gen, other_order,
1680 || !TEST_int_eq(EC_GROUP_check_named_curve(gtest, 0, NULL), 0)
1681 /* The order is not an optional field, so this should fail */
1682 || !TEST_false(EC_GROUP_set_generator(gtest, group_gen, NULL,
1684 || !TEST_true(EC_GROUP_set_generator(gtest, group_gen, group_order,
1686 || !TEST_int_eq(EC_GROUP_check_named_curve(gtest, 0, NULL), 0)
1687 /* Check that if the cofactor is not set then it still passes */
1688 || !TEST_true(EC_GROUP_set_generator(gtest, group_gen, group_order,
1690 || !TEST_int_eq(EC_GROUP_check_named_curve(gtest, 0, NULL), nid)
1691 /* check that restoring the generator passes */
1692 || !TEST_true(EC_GROUP_set_generator(gtest, group_gen, group_order,
1694 || !TEST_int_eq(EC_GROUP_check_named_curve(gtest, 0, NULL), nid))
1698 * check that changing any curve parameter fails
1700 * Setting arbitrary p, a or b might fail for some EC_GROUPs
1701 * depending on the internal EC_METHOD implementation, hence run
1702 * these tests conditionally to the success of EC_GROUP_set_curve().
1705 if (EC_GROUP_set_curve(gtest, other_p, group_a, group_b, NULL)) {
1706 if (!TEST_int_le(EC_GROUP_check_named_curve(gtest, 0, NULL), 0))
1709 /* clear the error stack if EC_GROUP_set_curve() failed */
1713 if (EC_GROUP_set_curve(gtest, group_p, other_a, group_b, NULL)) {
1714 if (!TEST_int_le(EC_GROUP_check_named_curve(gtest, 0, NULL), 0))
1717 /* clear the error stack if EC_GROUP_set_curve() failed */
1721 if (EC_GROUP_set_curve(gtest, group_p, group_a, other_b, NULL)) {
1722 if (!TEST_int_le(EC_GROUP_check_named_curve(gtest, 0, NULL), 0))
1725 /* clear the error stack if EC_GROUP_set_curve() failed */
1731 /* Check that restoring the curve parameters passes */
1732 if (!TEST_true(EC_GROUP_set_curve(gtest, group_p, group_a, group_b, NULL))
1733 || !TEST_int_eq(EC_GROUP_check_named_curve(gtest, 0, NULL), nid))
1744 BN_free(group_cofactor);
1745 BN_free(other_cofactor);
1746 BN_free(other_order);
1747 EC_POINT_free(other_gen);
1748 EC_GROUP_free(gtest);
1749 EC_GROUP_free(group);
1750 BN_CTX_free(bn_ctx);
1755 * This checks the lookup capability of EC_GROUP_check_named_curve()
1756 * when the given group was created with explicit parameters.
1758 * It is possible to retrieve an alternative alias that does not match
1759 * the original nid in this case.
1761 static int check_named_curve_lookup_test(int id)
1763 int ret = 0, nid, rv = 0;
1764 EC_GROUP *g = NULL , *ga = NULL;
1765 ECPARAMETERS *p = NULL, *pa = NULL;
1769 nid = curves[id].nid;
1770 if (!TEST_ptr(ctx = BN_CTX_new())
1771 || !TEST_ptr(g = EC_GROUP_new_by_curve_name(nid))
1772 || !TEST_ptr(p = EC_GROUP_get_ecparameters(g, NULL)))
1775 /* replace with group from explicit parameters */
1777 if (!TEST_ptr(g = EC_GROUP_new_from_ecparameters(p)))
1780 if (!TEST_int_gt(rv = EC_GROUP_check_named_curve(g, 0, NULL), 0))
1785 * fail if the returned nid is not an alias of the original group.
1787 * The comparison here is done by comparing two explicit
1788 * parameter EC_GROUPs with EC_GROUP_cmp(), to ensure the
1789 * comparison happens with unnamed EC_GROUPs using the same
1792 if (!TEST_ptr(ga = EC_GROUP_new_by_curve_name(rv))
1793 || !TEST_ptr(pa = EC_GROUP_get_ecparameters(ga, NULL)))
1796 /* replace with group from explicit parameters, then compare */
1798 if (!TEST_ptr(ga = EC_GROUP_new_from_ecparameters(pa))
1799 || !TEST_int_eq(EC_GROUP_cmp(g, ga, ctx), 0))
1808 ECPARAMETERS_free(p);
1809 ECPARAMETERS_free(pa);
1816 * Sometime we cannot compare nids for equality, as the built-in curve table
1817 * includes aliases with different names for the same curve.
1819 * This function returns TRUE (1) if the checked nids are identical, or if they
1820 * alias to the same curve. FALSE (0) otherwise.
1823 int are_ec_nids_compatible(int n1d, int n2d)
1827 # ifndef OPENSSL_NO_EC2M
1829 case NID_wap_wsg_idm_ecid_wtls4:
1830 ret = (n2d == NID_sect113r1 || n2d == NID_wap_wsg_idm_ecid_wtls4);
1833 case NID_wap_wsg_idm_ecid_wtls3:
1834 ret = (n2d == NID_sect163k1 || n2d == NID_wap_wsg_idm_ecid_wtls3);
1837 case NID_wap_wsg_idm_ecid_wtls10:
1838 ret = (n2d == NID_sect233k1 || n2d == NID_wap_wsg_idm_ecid_wtls10);
1841 case NID_wap_wsg_idm_ecid_wtls11:
1842 ret = (n2d == NID_sect233r1 || n2d == NID_wap_wsg_idm_ecid_wtls11);
1844 case NID_X9_62_c2pnb163v1:
1845 case NID_wap_wsg_idm_ecid_wtls5:
1846 ret = (n2d == NID_X9_62_c2pnb163v1
1847 || n2d == NID_wap_wsg_idm_ecid_wtls5);
1849 # endif /* OPENSSL_NO_EC2M */
1851 case NID_wap_wsg_idm_ecid_wtls6:
1852 ret = (n2d == NID_secp112r1 || n2d == NID_wap_wsg_idm_ecid_wtls6);
1855 case NID_wap_wsg_idm_ecid_wtls7:
1856 ret = (n2d == NID_secp160r2 || n2d == NID_wap_wsg_idm_ecid_wtls7);
1858 # ifdef OPENSSL_NO_EC_NISTP_64_GCC_128
1860 case NID_wap_wsg_idm_ecid_wtls12:
1861 ret = (n2d == NID_secp224r1 || n2d == NID_wap_wsg_idm_ecid_wtls12);
1865 * For SEC P-224 we want to ensure that the SECP nid is returned, as
1866 * that is associated with a specialized method.
1868 case NID_wap_wsg_idm_ecid_wtls12:
1869 ret = (n2d == NID_secp224r1);
1871 # endif /* def(OPENSSL_NO_EC_NISTP_64_GCC_128) */
1880 * This checks that EC_GROUP_bew_from_ecparameters() returns a "named"
1881 * EC_GROUP for built-in curves.
1883 * Note that it is possible to retrieve an alternative alias that does not match
1886 * Ensure that the OPENSSL_EC_EXPLICIT_CURVE ASN1 flag is set.
1888 static int check_named_curve_from_ecparameters(int id)
1890 int ret = 0, nid, tnid;
1891 EC_GROUP *group = NULL, *tgroup = NULL, *tmpg = NULL;
1892 const EC_POINT *group_gen = NULL;
1893 EC_POINT *other_gen = NULL;
1894 BIGNUM *group_cofactor = NULL, *other_cofactor = NULL;
1895 BIGNUM *other_gen_x = NULL, *other_gen_y = NULL;
1896 const BIGNUM *group_order = NULL;
1897 BIGNUM *other_order = NULL;
1898 BN_CTX *bn_ctx = NULL;
1899 static const unsigned char invalid_seed[] = "THIS IS NOT A VALID SEED";
1900 static size_t invalid_seed_len = sizeof(invalid_seed);
1901 ECPARAMETERS *params = NULL, *other_params = NULL;
1902 EC_GROUP *g_ary[8] = {NULL};
1903 EC_GROUP **g_next = &g_ary[0];
1904 ECPARAMETERS *p_ary[8] = {NULL};
1905 ECPARAMETERS **p_next = &p_ary[0];
1908 nid = curves[id].nid;
1909 TEST_note("Curve %s", OBJ_nid2sn(nid));
1910 if (!TEST_ptr(bn_ctx = BN_CTX_new()))
1912 BN_CTX_start(bn_ctx);
1914 if (/* Allocations */
1915 !TEST_ptr(group_cofactor = BN_CTX_get(bn_ctx))
1916 || !TEST_ptr(other_gen_x = BN_CTX_get(bn_ctx))
1917 || !TEST_ptr(other_gen_y = BN_CTX_get(bn_ctx))
1918 || !TEST_ptr(other_order = BN_CTX_get(bn_ctx))
1919 || !TEST_ptr(other_cofactor = BN_CTX_get(bn_ctx))
1920 /* Generate reference group and params */
1921 || !TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))
1922 || !TEST_ptr(params = EC_GROUP_get_ecparameters(group, NULL))
1923 || !TEST_ptr(group_gen = EC_GROUP_get0_generator(group))
1924 || !TEST_ptr(group_order = EC_GROUP_get0_order(group))
1925 || !TEST_true(EC_GROUP_get_cofactor(group, group_cofactor, NULL))
1926 /* compute `other_*` values */
1927 || !TEST_ptr(tmpg = EC_GROUP_dup(group))
1928 || !TEST_ptr(other_gen = EC_POINT_dup(group_gen, group))
1929 || !TEST_true(EC_POINT_add(group, other_gen, group_gen, group_gen, NULL))
1930 || !TEST_true(EC_POINT_get_affine_coordinates(group, other_gen,
1931 other_gen_x, other_gen_y, bn_ctx))
1932 || !TEST_true(BN_copy(other_order, group_order))
1933 || !TEST_true(BN_add_word(other_order, 1))
1934 || !TEST_true(BN_copy(other_cofactor, group_cofactor))
1935 || !TEST_true(BN_add_word(other_cofactor, 1)))
1938 EC_POINT_free(other_gen);
1941 if (!TEST_ptr(other_gen = EC_POINT_new(tmpg))
1942 || !TEST_true(EC_POINT_set_affine_coordinates(tmpg, other_gen,
1943 other_gen_x, other_gen_y,
1948 * ###########################
1949 * # Actual tests start here #
1950 * ###########################
1954 * Creating a group from built-in explicit parameters returns a
1957 if (!TEST_ptr(tgroup = *g_next++ = EC_GROUP_new_from_ecparameters(params))
1958 || !TEST_int_ne((tnid = EC_GROUP_get_curve_name(tgroup)), NID_undef))
1961 * We cannot always guarantee the names match, as the built-in table
1962 * contains aliases for the same curve with different names.
1964 if (!TEST_true(are_ec_nids_compatible(nid, tnid))) {
1965 TEST_info("nid = %s, tnid = %s", OBJ_nid2sn(nid), OBJ_nid2sn(tnid));
1968 /* Ensure that the OPENSSL_EC_EXPLICIT_CURVE ASN1 flag is set. */
1969 if (!TEST_int_eq(EC_GROUP_get_asn1_flag(tgroup), OPENSSL_EC_EXPLICIT_CURVE))
1973 * An invalid seed in the parameters should be ignored: expect a "named"
1976 if (!TEST_int_eq(EC_GROUP_set_seed(tmpg, invalid_seed, invalid_seed_len),
1978 || !TEST_ptr(other_params = *p_next++ =
1979 EC_GROUP_get_ecparameters(tmpg, NULL))
1980 || !TEST_ptr(tgroup = *g_next++ =
1981 EC_GROUP_new_from_ecparameters(other_params))
1982 || !TEST_int_ne((tnid = EC_GROUP_get_curve_name(tgroup)), NID_undef)
1983 || !TEST_true(are_ec_nids_compatible(nid, tnid))
1984 || !TEST_int_eq(EC_GROUP_get_asn1_flag(tgroup),
1985 OPENSSL_EC_EXPLICIT_CURVE)) {
1986 TEST_info("nid = %s, tnid = %s", OBJ_nid2sn(nid), OBJ_nid2sn(tnid));
1991 * A null seed in the parameters should be ignored, as it is optional:
1992 * expect a "named" group.
1994 if (!TEST_int_eq(EC_GROUP_set_seed(tmpg, NULL, 0), 1)
1995 || !TEST_ptr(other_params = *p_next++ =
1996 EC_GROUP_get_ecparameters(tmpg, NULL))
1997 || !TEST_ptr(tgroup = *g_next++ =
1998 EC_GROUP_new_from_ecparameters(other_params))
1999 || !TEST_int_ne((tnid = EC_GROUP_get_curve_name(tgroup)), NID_undef)
2000 || !TEST_true(are_ec_nids_compatible(nid, tnid))
2001 || !TEST_int_eq(EC_GROUP_get_asn1_flag(tgroup),
2002 OPENSSL_EC_EXPLICIT_CURVE)) {
2003 TEST_info("nid = %s, tnid = %s", OBJ_nid2sn(nid), OBJ_nid2sn(tnid));
2008 * Check that changing any of the generator parameters does not yield a
2009 * match with the built-in curves
2011 if (/* Other gen, same group order & cofactor */
2012 !TEST_true(EC_GROUP_set_generator(tmpg, other_gen, group_order,
2014 || !TEST_ptr(other_params = *p_next++ =
2015 EC_GROUP_get_ecparameters(tmpg, NULL))
2016 || !TEST_ptr(tgroup = *g_next++ =
2017 EC_GROUP_new_from_ecparameters(other_params))
2018 || !TEST_int_eq((tnid = EC_GROUP_get_curve_name(tgroup)), NID_undef)
2019 /* Same gen & cofactor, different order */
2020 || !TEST_true(EC_GROUP_set_generator(tmpg, group_gen, other_order,
2022 || !TEST_ptr(other_params = *p_next++ =
2023 EC_GROUP_get_ecparameters(tmpg, NULL))
2024 || !TEST_ptr(tgroup = *g_next++ =
2025 EC_GROUP_new_from_ecparameters(other_params))
2026 || !TEST_int_eq((tnid = EC_GROUP_get_curve_name(tgroup)), NID_undef)
2027 /* The order is not an optional field, so this should fail */
2028 || !TEST_false(EC_GROUP_set_generator(tmpg, group_gen, NULL,
2030 /* Check that a wrong cofactor is ignored, and we still match */
2031 || !TEST_true(EC_GROUP_set_generator(tmpg, group_gen, group_order,
2033 || !TEST_ptr(other_params = *p_next++ =
2034 EC_GROUP_get_ecparameters(tmpg, NULL))
2035 || !TEST_ptr(tgroup = *g_next++ =
2036 EC_GROUP_new_from_ecparameters(other_params))
2037 || !TEST_int_ne((tnid = EC_GROUP_get_curve_name(tgroup)), NID_undef)
2038 || !TEST_true(are_ec_nids_compatible(nid, tnid))
2039 || !TEST_int_eq(EC_GROUP_get_asn1_flag(tgroup),
2040 OPENSSL_EC_EXPLICIT_CURVE)
2041 /* Check that if the cofactor is not set then it still matches */
2042 || !TEST_true(EC_GROUP_set_generator(tmpg, group_gen, group_order,
2044 || !TEST_ptr(other_params = *p_next++ =
2045 EC_GROUP_get_ecparameters(tmpg, NULL))
2046 || !TEST_ptr(tgroup = *g_next++ =
2047 EC_GROUP_new_from_ecparameters(other_params))
2048 || !TEST_int_ne((tnid = EC_GROUP_get_curve_name(tgroup)), NID_undef)
2049 || !TEST_true(are_ec_nids_compatible(nid, tnid))
2050 || !TEST_int_eq(EC_GROUP_get_asn1_flag(tgroup),
2051 OPENSSL_EC_EXPLICIT_CURVE)
2052 /* check that restoring the generator passes */
2053 || !TEST_true(EC_GROUP_set_generator(tmpg, group_gen, group_order,
2055 || !TEST_ptr(other_params = *p_next++ =
2056 EC_GROUP_get_ecparameters(tmpg, NULL))
2057 || !TEST_ptr(tgroup = *g_next++ =
2058 EC_GROUP_new_from_ecparameters(other_params))
2059 || !TEST_int_ne((tnid = EC_GROUP_get_curve_name(tgroup)), NID_undef)
2060 || !TEST_true(are_ec_nids_compatible(nid, tnid))
2061 || !TEST_int_eq(EC_GROUP_get_asn1_flag(tgroup),
2062 OPENSSL_EC_EXPLICIT_CURVE))
2067 for (g_next = &g_ary[0]; g_next < g_ary + OSSL_NELEM(g_ary); g_next++)
2068 EC_GROUP_free(*g_next);
2069 for (p_next = &p_ary[0]; p_next < p_ary + OSSL_NELEM(g_ary); p_next++)
2070 ECPARAMETERS_free(*p_next);
2071 ECPARAMETERS_free(params);
2072 EC_POINT_free(other_gen);
2073 EC_GROUP_free(tmpg);
2074 EC_GROUP_free(group);
2076 BN_CTX_free(bn_ctx);
2081 static int parameter_test(void)
2083 EC_GROUP *group = NULL, *group2 = NULL;
2084 ECPARAMETERS *ecparameters = NULL;
2085 unsigned char *buf = NULL;
2088 if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(NID_secp384r1))
2089 || !TEST_ptr(ecparameters = EC_GROUP_get_ecparameters(group, NULL))
2090 || !TEST_ptr(group2 = EC_GROUP_new_from_ecparameters(ecparameters))
2091 || !TEST_int_eq(EC_GROUP_cmp(group, group2, NULL), 0))
2094 EC_GROUP_free(group);
2097 /* Test the named curve encoding, which should be default. */
2098 if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(NID_secp521r1))
2099 || !TEST_true((len = i2d_ECPKParameters(group, &buf)) >= 0)
2100 || !TEST_mem_eq(buf, len, p521_named, sizeof(p521_named)))
2107 * Test the explicit encoding. P-521 requires correctly zero-padding the
2108 * curve coefficients.
2110 EC_GROUP_set_asn1_flag(group, OPENSSL_EC_EXPLICIT_CURVE);
2111 if (!TEST_true((len = i2d_ECPKParameters(group, &buf)) >= 0)
2112 || !TEST_mem_eq(buf, len, p521_explicit, sizeof(p521_explicit)))
2117 EC_GROUP_free(group);
2118 EC_GROUP_free(group2);
2119 ECPARAMETERS_free(ecparameters);
2125 * random 256-bit explicit parameters curve, cofactor absent
2126 * order: 0x0c38d96a9f892b88772ec2e39614a82f4f (132 bit)
2127 * cofactor: 0x12bc94785251297abfafddf1565100da (125 bit)
2129 static const unsigned char params_cf_pass[] = {
2130 0x30, 0x81, 0xcd, 0x02, 0x01, 0x01, 0x30, 0x2c, 0x06, 0x07, 0x2a, 0x86,
2131 0x48, 0xce, 0x3d, 0x01, 0x01, 0x02, 0x21, 0x00, 0xe5, 0x00, 0x1f, 0xc5,
2132 0xca, 0x71, 0x9d, 0x8e, 0xf7, 0x07, 0x4b, 0x48, 0x37, 0xf9, 0x33, 0x2d,
2133 0x71, 0xbf, 0x79, 0xe7, 0xdc, 0x91, 0xc2, 0xff, 0xb6, 0x7b, 0xc3, 0x93,
2134 0x44, 0x88, 0xe6, 0x91, 0x30, 0x44, 0x04, 0x20, 0xe5, 0x00, 0x1f, 0xc5,
2135 0xca, 0x71, 0x9d, 0x8e, 0xf7, 0x07, 0x4b, 0x48, 0x37, 0xf9, 0x33, 0x2d,
2136 0x71, 0xbf, 0x79, 0xe7, 0xdc, 0x91, 0xc2, 0xff, 0xb6, 0x7b, 0xc3, 0x93,
2137 0x44, 0x88, 0xe6, 0x8e, 0x04, 0x20, 0x18, 0x8c, 0x59, 0x57, 0xc4, 0xbc,
2138 0x85, 0x57, 0xc3, 0x66, 0x9f, 0x89, 0xd5, 0x92, 0x0d, 0x7e, 0x42, 0x27,
2139 0x07, 0x64, 0xaa, 0x26, 0xed, 0x89, 0xc4, 0x09, 0x05, 0x4d, 0xc7, 0x23,
2140 0x47, 0xda, 0x04, 0x41, 0x04, 0x1b, 0x6b, 0x41, 0x0b, 0xf9, 0xfb, 0x77,
2141 0xfd, 0x50, 0xb7, 0x3e, 0x23, 0xa3, 0xec, 0x9a, 0x3b, 0x09, 0x31, 0x6b,
2142 0xfa, 0xf6, 0xce, 0x1f, 0xff, 0xeb, 0x57, 0x93, 0x24, 0x70, 0xf3, 0xf4,
2143 0xba, 0x7e, 0xfa, 0x86, 0x6e, 0x19, 0x89, 0xe3, 0x55, 0x6d, 0x5a, 0xe9,
2144 0xc0, 0x3d, 0xbc, 0xfb, 0xaf, 0xad, 0xd4, 0x7e, 0xa6, 0xe5, 0xfa, 0x1a,
2145 0x58, 0x07, 0x9e, 0x8f, 0x0d, 0x3b, 0xf7, 0x38, 0xca, 0x02, 0x11, 0x0c,
2146 0x38, 0xd9, 0x6a, 0x9f, 0x89, 0x2b, 0x88, 0x77, 0x2e, 0xc2, 0xe3, 0x96,
2147 0x14, 0xa8, 0x2f, 0x4f
2151 * random 256-bit explicit parameters curve, cofactor absent
2152 * order: 0x045a75c0c17228ebd9b169a10e34a22101 (131 bit)
2153 * cofactor: 0x2e134b4ede82649f67a2e559d361e5fe (126 bit)
2155 static const unsigned char params_cf_fail[] = {
2156 0x30, 0x81, 0xcd, 0x02, 0x01, 0x01, 0x30, 0x2c, 0x06, 0x07, 0x2a, 0x86,
2157 0x48, 0xce, 0x3d, 0x01, 0x01, 0x02, 0x21, 0x00, 0xc8, 0x95, 0x27, 0x37,
2158 0xe8, 0xe1, 0xfd, 0xcc, 0xf9, 0x6e, 0x0c, 0xa6, 0x21, 0xc1, 0x7d, 0x6b,
2159 0x9d, 0x44, 0x42, 0xea, 0x73, 0x4e, 0x04, 0xb6, 0xac, 0x62, 0x50, 0xd0,
2160 0x33, 0xc2, 0xea, 0x13, 0x30, 0x44, 0x04, 0x20, 0xc8, 0x95, 0x27, 0x37,
2161 0xe8, 0xe1, 0xfd, 0xcc, 0xf9, 0x6e, 0x0c, 0xa6, 0x21, 0xc1, 0x7d, 0x6b,
2162 0x9d, 0x44, 0x42, 0xea, 0x73, 0x4e, 0x04, 0xb6, 0xac, 0x62, 0x50, 0xd0,
2163 0x33, 0xc2, 0xea, 0x10, 0x04, 0x20, 0xbf, 0xa6, 0xa8, 0x05, 0x1d, 0x09,
2164 0xac, 0x70, 0x39, 0xbb, 0x4d, 0xb2, 0x90, 0x8a, 0x15, 0x41, 0x14, 0x1d,
2165 0x11, 0x86, 0x9f, 0x13, 0xa2, 0x63, 0x1a, 0xda, 0x95, 0x22, 0x4d, 0x02,
2166 0x15, 0x0a, 0x04, 0x41, 0x04, 0xaf, 0x16, 0x71, 0xf9, 0xc4, 0xc8, 0x59,
2167 0x1d, 0xa3, 0x6f, 0xe7, 0xc3, 0x57, 0xa1, 0xfa, 0x9f, 0x49, 0x7c, 0x11,
2168 0x27, 0x05, 0xa0, 0x7f, 0xff, 0xf9, 0xe0, 0xe7, 0x92, 0xdd, 0x9c, 0x24,
2169 0x8e, 0xc7, 0xb9, 0x52, 0x71, 0x3f, 0xbc, 0x7f, 0x6a, 0x9f, 0x35, 0x70,
2170 0xe1, 0x27, 0xd5, 0x35, 0x8a, 0x13, 0xfa, 0xa8, 0x33, 0x3e, 0xd4, 0x73,
2171 0x1c, 0x14, 0x58, 0x9e, 0xc7, 0x0a, 0x87, 0x65, 0x8d, 0x02, 0x11, 0x04,
2172 0x5a, 0x75, 0xc0, 0xc1, 0x72, 0x28, 0xeb, 0xd9, 0xb1, 0x69, 0xa1, 0x0e,
2173 0x34, 0xa2, 0x21, 0x01
2177 * Test two random 256-bit explicit parameters curves with absent cofactor.
2178 * The two curves are chosen to roughly straddle the bounds at which the lib
2179 * can compute the cofactor automatically, roughly 4*sqrt(p). So test that:
2181 * - params_cf_pass: order is sufficiently close to p to compute cofactor
2182 * - params_cf_fail: order is too far away from p to compute cofactor
2184 * For standards-compliant curves, cofactor is chosen as small as possible.
2185 * So you can see neither of these curves are fit for cryptographic use.
2187 * Some standards even mandate an upper bound on the cofactor, e.g. SECG1 v2:
2188 * h <= 2**(t/8) where t is the security level of the curve, for which the lib
2189 * will always succeed in computing the cofactor. Neither of these curves
2190 * conform to that -- this is just robustness testing.
2192 static int cofactor_range_test(void)
2194 EC_GROUP *group = NULL;
2197 const unsigned char *b1 = (const unsigned char *)params_cf_fail;
2198 const unsigned char *b2 = (const unsigned char *)params_cf_pass;
2200 if (!TEST_ptr(group = d2i_ECPKParameters(NULL, &b1, sizeof(params_cf_fail)))
2201 || !TEST_BN_eq_zero(EC_GROUP_get0_cofactor(group))
2202 || !TEST_ptr(group = d2i_ECPKParameters(&group, &b2,
2203 sizeof(params_cf_pass)))
2204 || !TEST_int_gt(BN_hex2bn(&cf, "12bc94785251297abfafddf1565100da"), 0)
2205 || !TEST_BN_eq(cf, EC_GROUP_get0_cofactor(group)))
2210 EC_GROUP_free(group);
2215 * For named curves, test that:
2216 * - the lib correctly computes the cofactor if passed a NULL or zero cofactor
2217 * - a nonsensical cofactor throws an error (negative test)
2218 * - nonsensical orders throw errors (negative tests)
2220 static int cardinality_test(int n)
2223 int nid = curves[n].nid;
2225 EC_GROUP *g1 = NULL, *g2 = NULL;
2226 EC_POINT *g2_gen = NULL;
2227 BIGNUM *g1_p = NULL, *g1_a = NULL, *g1_b = NULL, *g1_x = NULL, *g1_y = NULL,
2228 *g1_order = NULL, *g1_cf = NULL, *g2_cf = NULL;
2230 TEST_info("Curve %s cardinality test", OBJ_nid2sn(nid));
2232 if (!TEST_ptr(ctx = BN_CTX_new())
2233 || !TEST_ptr(g1 = EC_GROUP_new_by_curve_name(nid))
2234 || !TEST_ptr(g2 = EC_GROUP_new(EC_GROUP_method_of(g1)))) {
2242 g1_p = BN_CTX_get(ctx);
2243 g1_a = BN_CTX_get(ctx);
2244 g1_b = BN_CTX_get(ctx);
2245 g1_x = BN_CTX_get(ctx);
2246 g1_y = BN_CTX_get(ctx);
2247 g1_order = BN_CTX_get(ctx);
2248 g1_cf = BN_CTX_get(ctx);
2250 if (!TEST_ptr(g2_cf = BN_CTX_get(ctx))
2251 /* pull out the explicit curve parameters */
2252 || !TEST_true(EC_GROUP_get_curve(g1, g1_p, g1_a, g1_b, ctx))
2253 || !TEST_true(EC_POINT_get_affine_coordinates(g1,
2254 EC_GROUP_get0_generator(g1), g1_x, g1_y, ctx))
2255 || !TEST_true(BN_copy(g1_order, EC_GROUP_get0_order(g1)))
2256 || !TEST_true(EC_GROUP_get_cofactor(g1, g1_cf, ctx))
2257 /* construct g2 manually with g1 parameters */
2258 || !TEST_true(EC_GROUP_set_curve(g2, g1_p, g1_a, g1_b, ctx))
2259 || !TEST_ptr(g2_gen = EC_POINT_new(g2))
2260 || !TEST_true(EC_POINT_set_affine_coordinates(g2, g2_gen, g1_x, g1_y, ctx))
2261 /* pass NULL cofactor: lib should compute it */
2262 || !TEST_true(EC_GROUP_set_generator(g2, g2_gen, g1_order, NULL))
2263 || !TEST_true(EC_GROUP_get_cofactor(g2, g2_cf, ctx))
2264 || !TEST_BN_eq(g1_cf, g2_cf)
2265 /* pass zero cofactor: lib should compute it */
2266 || !TEST_true(BN_set_word(g2_cf, 0))
2267 || !TEST_true(EC_GROUP_set_generator(g2, g2_gen, g1_order, g2_cf))
2268 || !TEST_true(EC_GROUP_get_cofactor(g2, g2_cf, ctx))
2269 || !TEST_BN_eq(g1_cf, g2_cf)
2270 /* negative test for invalid cofactor */
2271 || !TEST_true(BN_set_word(g2_cf, 0))
2272 || !TEST_true(BN_sub(g2_cf, g2_cf, BN_value_one()))
2273 || !TEST_false(EC_GROUP_set_generator(g2, g2_gen, g1_order, g2_cf))
2274 /* negative test for NULL order */
2275 || !TEST_false(EC_GROUP_set_generator(g2, g2_gen, NULL, NULL))
2276 /* negative test for zero order */
2277 || !TEST_true(BN_set_word(g1_order, 0))
2278 || !TEST_false(EC_GROUP_set_generator(g2, g2_gen, g1_order, NULL))
2279 /* negative test for negative order */
2280 || !TEST_true(BN_set_word(g2_cf, 0))
2281 || !TEST_true(BN_sub(g2_cf, g2_cf, BN_value_one()))
2282 || !TEST_false(EC_GROUP_set_generator(g2, g2_gen, g1_order, NULL))
2283 /* negative test for too large order */
2284 || !TEST_true(BN_lshift(g1_order, g1_p, 2))
2285 || !TEST_false(EC_GROUP_set_generator(g2, g2_gen, g1_order, NULL)))
2289 EC_POINT_free(g2_gen);
2297 static int check_ec_key_field_public_range_test(int id)
2299 int ret = 0, type = 0;
2300 const EC_POINT *pub = NULL;
2301 const EC_GROUP *group = NULL;
2302 const EC_METHOD *meth = NULL;
2303 const BIGNUM *field = NULL;
2304 BIGNUM *x = NULL, *y = NULL;
2307 if (!TEST_ptr(x = BN_new())
2308 || !TEST_ptr(y = BN_new())
2309 || !TEST_ptr(key = EC_KEY_new_by_curve_name(curves[id].nid))
2310 || !TEST_ptr(group = EC_KEY_get0_group(key))
2311 || !TEST_ptr(meth = EC_GROUP_method_of(group))
2312 || !TEST_ptr(field = EC_GROUP_get0_field(group))
2313 || !TEST_int_gt(EC_KEY_generate_key(key), 0)
2314 || !TEST_int_gt(EC_KEY_check_key(key), 0)
2315 || !TEST_ptr(pub = EC_KEY_get0_public_key(key))
2316 || !TEST_int_gt(EC_POINT_get_affine_coordinates(group, pub, x, y,
2321 * Make the public point out of range by adding the field (which will still
2322 * be the same point on the curve). The add is different for char2 fields.
2324 type = EC_METHOD_get_field_type(meth);
2325 #ifndef OPENSSL_NO_EC2M
2326 if (type == NID_X9_62_characteristic_two_field) {
2327 /* test for binary curves */
2328 if (!TEST_true(BN_GF2m_add(x, x, field)))
2332 if (type == NID_X9_62_prime_field) {
2333 /* test for prime curves */
2334 if (!TEST_true(BN_add(x, x, field)))
2337 /* this should never happen */
2338 TEST_error("Unsupported EC_METHOD field_type");
2341 if (!TEST_int_le(EC_KEY_set_public_key_affine_coordinates(key, x, y), 0))
2351 #endif /* OPENSSL_NO_EC */
2353 int setup_tests(void)
2355 #ifndef OPENSSL_NO_EC
2356 crv_len = EC_get_builtin_curves(NULL, 0);
2357 if (!TEST_ptr(curves = OPENSSL_malloc(sizeof(*curves) * crv_len))
2358 || !TEST_true(EC_get_builtin_curves(curves, crv_len)))
2361 ADD_TEST(parameter_test);
2362 ADD_TEST(cofactor_range_test);
2363 ADD_ALL_TESTS(cardinality_test, crv_len);
2364 ADD_TEST(prime_field_tests);
2365 # ifndef OPENSSL_NO_EC2M
2366 ADD_TEST(char2_field_tests);
2367 ADD_ALL_TESTS(char2_curve_test, OSSL_NELEM(char2_curve_tests));
2369 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
2370 ADD_ALL_TESTS(nistp_single_test, OSSL_NELEM(nistp_tests_params));
2371 ADD_TEST(underflow_test);
2373 ADD_ALL_TESTS(internal_curve_test, crv_len);
2374 ADD_ALL_TESTS(internal_curve_test_method, crv_len);
2375 ADD_TEST(group_field_test);
2376 ADD_ALL_TESTS(check_named_curve_test, crv_len);
2377 ADD_ALL_TESTS(check_named_curve_lookup_test, crv_len);
2378 ADD_ALL_TESTS(check_ec_key_field_public_range_test, crv_len);
2379 ADD_ALL_TESTS(check_named_curve_from_ecparameters, crv_len);
2380 #endif /* OPENSSL_NO_EC */
2384 void cleanup_tests(void)
2386 #ifndef OPENSSL_NO_EC
2387 OPENSSL_free(curves);