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;
34 const EC_POINT *G = NULL;
38 if (!TEST_ptr(n1 = BN_new())
39 || !TEST_ptr(n2 = BN_new())
40 || !TEST_ptr(order = BN_new())
41 || !TEST_ptr(ctx = BN_CTX_new())
42 || !TEST_ptr(G = EC_GROUP_get0_generator(group))
43 || !TEST_ptr(P = EC_POINT_new(group))
44 || !TEST_ptr(Q = EC_POINT_new(group))
45 || !TEST_ptr(R = EC_POINT_new(group))
46 || !TEST_ptr(S = EC_POINT_new(group)))
49 if (!TEST_true(EC_GROUP_get_order(group, order, ctx))
50 || !TEST_true(EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
51 || !TEST_true(EC_POINT_is_at_infinity(group, Q))
52 || !TEST_true(EC_GROUP_precompute_mult(group, ctx))
53 || !TEST_true(EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
54 || !TEST_true(EC_POINT_is_at_infinity(group, Q))
55 || !TEST_true(EC_POINT_copy(P, G))
56 || !TEST_true(BN_one(n1))
57 || !TEST_true(EC_POINT_mul(group, Q, n1, NULL, NULL, ctx))
58 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
59 || !TEST_true(BN_sub(n1, order, n1))
60 || !TEST_true(EC_POINT_mul(group, Q, n1, NULL, NULL, ctx))
61 || !TEST_true(EC_POINT_invert(group, Q, ctx))
62 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx)))
65 for (i = 1; i <= 2; i++) {
66 const BIGNUM *scalars[6];
67 const EC_POINT *points[6];
69 if (!TEST_true(BN_set_word(n1, i))
71 * If i == 1, P will be the predefined generator for which
72 * EC_GROUP_precompute_mult has set up precomputation.
74 || !TEST_true(EC_POINT_mul(group, P, n1, NULL, NULL, ctx))
75 || (i == 1 && !TEST_int_eq(0, EC_POINT_cmp(group, P, G, ctx)))
76 || !TEST_true(BN_one(n1))
78 || !TEST_true(BN_sub(n1, n1, order))
79 || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n1, ctx))
80 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
83 || !TEST_true(BN_add(n2, order, BN_value_one()))
84 || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
85 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
87 /* n2 = (1 - order) * (1 + order) = 1 - order^2 */
88 || !TEST_true(BN_mul(n2, n1, n2, ctx))
89 || !TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
90 || !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx)))
93 /* n2 = order^2 - 1 */
94 BN_set_negative(n2, 0);
95 if (!TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
96 /* Add P to verify the result. */
97 || !TEST_true(EC_POINT_add(group, Q, Q, P, ctx))
98 || !TEST_true(EC_POINT_is_at_infinity(group, Q))
100 /* Exercise EC_POINTs_mul, including corner cases. */
101 || !TEST_false(EC_POINT_is_at_infinity(group, P)))
104 scalars[0] = scalars[1] = BN_value_one();
105 points[0] = points[1] = P;
107 if (!TEST_true(EC_POINTs_mul(group, R, NULL, 2, points, scalars, ctx))
108 || !TEST_true(EC_POINT_dbl(group, S, points[0], ctx))
109 || !TEST_int_eq(0, EC_POINT_cmp(group, R, S, ctx)))
113 points[0] = Q; /* => infinity */
115 points[1] = P; /* => -P */
117 points[2] = Q; /* => infinity */
119 points[3] = Q; /* => infinity */
121 points[4] = P; /* => P */
123 points[5] = Q; /* => infinity */
124 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 6, points, scalars, ctx))
125 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
131 if (r == 0 && i != 0)
132 TEST_info(i == 1 ? "allowing precomputation" :
133 "without precomputation");
145 static int prime_field_tests(void)
148 BIGNUM *p = NULL, *a = NULL, *b = NULL, *scalar3 = NULL;
149 EC_GROUP *group = NULL, *tmp = NULL;
150 EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL,
151 *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
152 EC_POINT *P = NULL, *Q = NULL, *R = NULL;
153 BIGNUM *x = NULL, *y = NULL, *z = NULL, *yplusone = NULL;
154 const EC_POINT *points[4];
155 const BIGNUM *scalars[4];
156 unsigned char buf[100];
160 if (!TEST_ptr(ctx = BN_CTX_new())
161 || !TEST_ptr(p = BN_new())
162 || !TEST_ptr(a = BN_new())
163 || !TEST_ptr(b = BN_new())
164 || !TEST_true(BN_hex2bn(&p, "17"))
165 || !TEST_true(BN_hex2bn(&a, "1"))
166 || !TEST_true(BN_hex2bn(&b, "1"))
168 * applications should use EC_GROUP_new_curve_GFp so
169 * that the library gets to choose the EC_METHOD
171 || !TEST_ptr(group = EC_GROUP_new(EC_GFp_mont_method()))
172 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
173 || !TEST_ptr(tmp = EC_GROUP_new(EC_GROUP_method_of(group)))
174 || !TEST_true(EC_GROUP_copy(tmp, group)))
176 EC_GROUP_free(group);
180 if (!TEST_true(EC_GROUP_get_curve(group, p, a, b, ctx)))
183 TEST_info("Curve defined by Weierstrass equation");
184 TEST_note(" y^2 = x^3 + a*x + b (mod p)");
185 test_output_bignum("a", a);
186 test_output_bignum("b", b);
187 test_output_bignum("p", p);
190 if (!TEST_ptr(P = EC_POINT_new(group))
191 || !TEST_ptr(Q = EC_POINT_new(group))
192 || !TEST_ptr(R = EC_POINT_new(group))
193 || !TEST_true(EC_POINT_set_to_infinity(group, P))
194 || !TEST_true(EC_POINT_is_at_infinity(group, P))
195 || !TEST_true(EC_POINT_oct2point(group, Q, buf, 1, ctx))
196 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx))
197 || !TEST_true(EC_POINT_is_at_infinity(group, P))
198 || !TEST_ptr(x = BN_new())
199 || !TEST_ptr(y = BN_new())
200 || !TEST_ptr(z = BN_new())
201 || !TEST_ptr(yplusone = BN_new())
202 || !TEST_true(BN_hex2bn(&x, "D"))
203 || !TEST_true(EC_POINT_set_compressed_coordinates(group, Q, x, 1, ctx)))
206 if (!TEST_int_gt(EC_POINT_is_on_curve(group, Q, ctx), 0)) {
207 if (!TEST_true(EC_POINT_get_affine_coordinates(group, Q, x, y, ctx)))
209 TEST_info("Point is not on curve");
210 test_output_bignum("x", x);
211 test_output_bignum("y", y);
215 TEST_note("A cyclic subgroup:");
218 if (!TEST_int_ne(k--, 0))
221 if (EC_POINT_is_at_infinity(group, P)) {
222 TEST_note(" point at infinity");
224 if (!TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y,
228 test_output_bignum("x", x);
229 test_output_bignum("y", y);
232 if (!TEST_true(EC_POINT_copy(R, P))
233 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx)))
236 } while (!EC_POINT_is_at_infinity(group, P));
238 if (!TEST_true(EC_POINT_add(group, P, Q, R, ctx))
239 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
243 EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf,
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, compressed form:",
252 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED,
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, uncompressed form:",
261 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID,
262 buf, sizeof(buf), ctx);
263 if (!TEST_size_t_ne(len, 0)
264 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
265 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
267 test_output_memory("Generator as octet string, hybrid form:",
270 if (!TEST_true(EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z,
273 TEST_info("A representation of the inverse of that generator in");
274 TEST_note("Jacobian projective coordinates");
275 test_output_bignum("x", x);
276 test_output_bignum("y", y);
277 test_output_bignum("z", z);
279 if (!TEST_true(EC_POINT_invert(group, P, ctx))
280 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
283 * Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2,
284 * 2000) -- not a NIST curve, but commonly used
287 || !TEST_true(BN_hex2bn(&p, "FFFFFFFF"
288 "FFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"))
289 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
290 || !TEST_true(BN_hex2bn(&a, "FFFFFFFF"
291 "FFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"))
292 || !TEST_true(BN_hex2bn(&b, "1C97BEFC"
293 "54BD7A8B65ACF89F81D4D4ADC565FA45"))
294 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
295 || !TEST_true(BN_hex2bn(&x, "4A96B568"
296 "8EF573284664698968C38BB913CBFC82"))
297 || !TEST_true(BN_hex2bn(&y, "23a62855"
298 "3168947d59dcc912042351377ac5fb32"))
299 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
301 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
302 * and therefore setting the coordinates should fail.
304 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
306 || !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
307 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
308 || !TEST_true(BN_hex2bn(&z, "0100000000"
309 "000000000001F4C8F927AED3CA752257"))
310 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
311 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
313 TEST_info("SEC2 curve secp160r1 -- Generator");
314 test_output_bignum("x", x);
315 test_output_bignum("y", y);
316 /* G_y value taken from the standard: */
317 if (!TEST_true(BN_hex2bn(&z, "23a62855"
318 "3168947d59dcc912042351377ac5fb32"))
320 || !TEST_int_eq(EC_GROUP_get_degree(group), 160)
321 || !group_order_tests(group)
322 || !TEST_ptr(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))
323 || !TEST_true(EC_GROUP_copy(P_160, group))
325 /* Curve P-192 (FIPS PUB 186-2, App. 6) */
327 || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFF"
328 "FFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"))
329 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
330 || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFF"
331 "FFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"))
332 || !TEST_true(BN_hex2bn(&b, "64210519E59C80E7"
333 "0FA7E9AB72243049FEB8DEECC146B9B1"))
334 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
335 || !TEST_true(BN_hex2bn(&x, "188DA80EB03090F6"
336 "7CBF20EB43A18800F4FF0AFD82FF1012"))
337 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx))
338 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
339 || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFF"
340 "FFFFFFFF99DEF836146BC9B1B4D22831"))
341 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
342 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
345 TEST_info("NIST curve P-192 -- Generator");
346 test_output_bignum("x", x);
347 test_output_bignum("y", y);
348 /* G_y value taken from the standard: */
349 if (!TEST_true(BN_hex2bn(&z, "07192B95FFC8DA78"
350 "631011ED6B24CDD573F977A11E794811"))
352 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
354 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
355 * and therefore setting the coordinates should fail.
357 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
359 || !TEST_int_eq(EC_GROUP_get_degree(group), 192)
360 || !group_order_tests(group)
361 || !TEST_ptr(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))
362 || !TEST_true(EC_GROUP_copy(P_192, group))
364 /* Curve P-224 (FIPS PUB 186-2, App. 6) */
366 || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFF"
367 "FFFFFFFF000000000000000000000001"))
368 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
369 || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFF"
370 "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"))
371 || !TEST_true(BN_hex2bn(&b, "B4050A850C04B3ABF5413256"
372 "5044B0B7D7BFD8BA270B39432355FFB4"))
373 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
374 || !TEST_true(BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B9"
375 "4A03C1D356C21122343280D6115C1D21"))
376 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 0, ctx))
377 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
378 || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF"
379 "FFFF16A2E0B8F03E13DD29455C5C2A3D"))
380 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
381 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
384 TEST_info("NIST curve P-224 -- Generator");
385 test_output_bignum("x", x);
386 test_output_bignum("y", y);
387 /* G_y value taken from the standard: */
388 if (!TEST_true(BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6"
389 "CD4375A05A07476444D5819985007E34"))
391 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
393 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
394 * and therefore setting the coordinates should fail.
396 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
398 || !TEST_int_eq(EC_GROUP_get_degree(group), 224)
399 || !group_order_tests(group)
400 || !TEST_ptr(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))
401 || !TEST_true(EC_GROUP_copy(P_224, group))
403 /* Curve P-256 (FIPS PUB 186-2, App. 6) */
405 || !TEST_true(BN_hex2bn(&p, "FFFFFFFF000000010000000000000000"
406 "00000000FFFFFFFFFFFFFFFFFFFFFFFF"))
407 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
408 || !TEST_true(BN_hex2bn(&a, "FFFFFFFF000000010000000000000000"
409 "00000000FFFFFFFFFFFFFFFFFFFFFFFC"))
410 || !TEST_true(BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC"
411 "651D06B0CC53B0F63BCE3C3E27D2604B"))
412 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
414 || !TEST_true(BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F2"
415 "77037D812DEB33A0F4A13945D898C296"))
416 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx))
417 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
418 || !TEST_true(BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFF"
419 "BCE6FAADA7179E84F3B9CAC2FC632551"))
420 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
421 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
424 TEST_info("NIST curve P-256 -- Generator");
425 test_output_bignum("x", x);
426 test_output_bignum("y", y);
427 /* G_y value taken from the standard: */
428 if (!TEST_true(BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E16"
429 "2BCE33576B315ECECBB6406837BF51F5"))
431 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
433 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
434 * and therefore setting the coordinates should fail.
436 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
438 || !TEST_int_eq(EC_GROUP_get_degree(group), 256)
439 || !group_order_tests(group)
440 || !TEST_ptr(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))
441 || !TEST_true(EC_GROUP_copy(P_256, group))
443 /* Curve P-384 (FIPS PUB 186-2, App. 6) */
445 || !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
446 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
447 "FFFFFFFF0000000000000000FFFFFFFF"))
448 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
449 || !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
450 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
451 "FFFFFFFF0000000000000000FFFFFFFC"))
452 || !TEST_true(BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19"
453 "181D9C6EFE8141120314088F5013875A"
454 "C656398D8A2ED19D2A85C8EDD3EC2AEF"))
455 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
457 || !TEST_true(BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD74"
458 "6E1D3B628BA79B9859F741E082542A38"
459 "5502F25DBF55296C3A545E3872760AB7"))
460 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx))
461 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
462 || !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
463 "FFFFFFFFFFFFFFFFC7634D81F4372DDF"
464 "581A0DB248B0A77AECEC196ACCC52973"))
465 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
466 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
469 TEST_info("NIST curve P-384 -- Generator");
470 test_output_bignum("x", x);
471 test_output_bignum("y", y);
472 /* G_y value taken from the standard: */
473 if (!TEST_true(BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29"
474 "F8F41DBD289A147CE9DA3113B5F0B8C0"
475 "0A60B1CE1D7E819D7A431D7C90EA0E5F"))
477 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
479 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
480 * and therefore setting the coordinates should fail.
482 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
484 || !TEST_int_eq(EC_GROUP_get_degree(group), 384)
485 || !group_order_tests(group)
486 || !TEST_ptr(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))
487 || !TEST_true(EC_GROUP_copy(P_384, group))
489 /* Curve P-521 (FIPS PUB 186-2, App. 6) */
490 || !TEST_true(BN_hex2bn(&p, "1FF"
491 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
492 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
493 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
494 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
495 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
496 || !TEST_true(BN_hex2bn(&a, "1FF"
497 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
498 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
499 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
500 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC"))
501 || !TEST_true(BN_hex2bn(&b, "051"
502 "953EB9618E1C9A1F929A21A0B68540EE"
503 "A2DA725B99B315F3B8B489918EF109E1"
504 "56193951EC7E937B1652C0BD3BB1BF07"
505 "3573DF883D2C34F1EF451FD46B503F00"))
506 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
507 || !TEST_true(BN_hex2bn(&x, "C6"
508 "858E06B70404E9CD9E3ECB662395B442"
509 "9C648139053FB521F828AF606B4D3DBA"
510 "A14B5E77EFE75928FE1DC127A2FFA8DE"
511 "3348B3C1856A429BF97E7E31C2E5BD66"))
512 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 0, ctx))
513 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
514 || !TEST_true(BN_hex2bn(&z, "1FF"
515 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
516 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA"
517 "51868783BF2F966B7FCC0148F709A5D0"
518 "3BB5C9B8899C47AEBB6FB71E91386409"))
519 || !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
520 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
523 TEST_info("NIST curve P-521 -- Generator");
524 test_output_bignum("x", x);
525 test_output_bignum("y", y);
526 /* G_y value taken from the standard: */
527 if (!TEST_true(BN_hex2bn(&z, "118"
528 "39296A789A3BC0045C8A5FB42C7D1BD9"
529 "98F54449579B446817AFBD17273E662C"
530 "97EE72995EF42640C550B9013FAD0761"
531 "353C7086A272C24088BE94769FD16650"))
533 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
535 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
536 * and therefore setting the coordinates should fail.
538 || !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
540 || !TEST_int_eq(EC_GROUP_get_degree(group), 521)
541 || !group_order_tests(group)
542 || !TEST_ptr(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))
543 || !TEST_true(EC_GROUP_copy(P_521, group))
545 /* more tests using the last curve */
547 /* Restore the point that got mangled in the (x, y + 1) test. */
548 || !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
549 || !TEST_true(EC_POINT_copy(Q, P))
550 || !TEST_false(EC_POINT_is_at_infinity(group, Q))
551 || !TEST_true(EC_POINT_dbl(group, P, P, ctx))
552 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
553 || !TEST_true(EC_POINT_invert(group, Q, ctx)) /* P = -2Q */
554 || !TEST_true(EC_POINT_add(group, R, P, Q, ctx))
555 || !TEST_true(EC_POINT_add(group, R, R, Q, ctx))
556 || !TEST_true(EC_POINT_is_at_infinity(group, R)) /* R = P + 2Q */
557 || !TEST_false(EC_POINT_is_at_infinity(group, Q)))
564 if (!TEST_true(EC_GROUP_get_order(group, z, ctx))
565 || !TEST_true(BN_add(y, z, BN_value_one()))
567 || !TEST_true(BN_rshift1(y, y)))
569 scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
572 TEST_note("combined multiplication ...");
574 /* z is still the group order */
575 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
576 || !TEST_true(EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
577 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
578 || !TEST_int_eq(0, EC_POINT_cmp(group, R, Q, ctx))
579 || !TEST_true(BN_rand(y, BN_num_bits(y), 0, 0))
580 || !TEST_true(BN_add(z, z, y)))
582 BN_set_negative(z, 1);
584 scalars[1] = z; /* z = -(order + y) */
586 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
587 || !TEST_true(EC_POINT_is_at_infinity(group, P))
588 || !TEST_true(BN_rand(x, BN_num_bits(y) - 1, 0, 0))
589 || !TEST_true(BN_add(z, x, y)))
591 BN_set_negative(z, 1);
594 scalars[2] = z; /* z = -(x+y) */
596 if (!TEST_ptr(scalar3 = BN_new()))
599 scalars[3] = scalar3;
601 if (!TEST_true(EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx))
602 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
614 EC_GROUP_free(group);
625 EC_GROUP_free(P_160);
626 EC_GROUP_free(P_192);
627 EC_GROUP_free(P_224);
628 EC_GROUP_free(P_256);
629 EC_GROUP_free(P_384);
630 EC_GROUP_free(P_521);
634 # ifndef OPENSSL_NO_EC2M
636 static struct c2_curve_test {
647 } char2_curve_tests[] = {
648 /* Curve K-163 (FIPS PUB 186-2, App. 6) */
651 "0800000000000000000000000000000000000000C9",
654 "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
655 "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
656 1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163
658 /* Curve B-163 (FIPS PUB 186-2, App. 6) */
661 "0800000000000000000000000000000000000000C9",
663 "020A601907B8C953CA1481EB10512F78744A3205FD",
664 "03F0EBA16286A2D57EA0991168D4994637E8343E36",
665 "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
666 1, "040000000000000000000292FE77E70C12A4234C33", "2", 163
668 /* Curve K-233 (FIPS PUB 186-2, App. 6) */
671 "020000000000000000000000000000000000000004000000000000000001",
674 "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
675 "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
677 "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
680 /* Curve B-233 (FIPS PUB 186-2, App. 6) */
683 "020000000000000000000000000000000000000004000000000000000001",
684 "000000000000000000000000000000000000000000000000000000000001",
685 "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
686 "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
687 "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
689 "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
692 /* Curve K-283 (FIPS PUB 186-2, App. 6) */
696 "00000000000000000000000000000000000000000000000000000000000010A1",
700 "78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
702 "0F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
705 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
708 /* Curve B-283 (FIPS PUB 186-2, App. 6) */
712 "00000000000000000000000000000000000000000000000000000000000010A1",
714 "0000000000000000000000000000000000000000000000000000000000000001",
716 "C8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
718 "8DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
720 "FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
723 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
726 /* Curve K-409 (FIPS PUB 186-2, App. 6) */
729 "0200000000000000000000000000000000000000"
730 "0000000000000000000000000000000000000000008000000000000000000001",
733 "0060F05F658F49C1AD3AB1890F7184210EFD0987"
734 "E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
735 "01E369050B7C4E42ACBA1DACBF04299C3460782F"
736 "918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
738 "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
739 "FFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
742 /* Curve B-409 (FIPS PUB 186-2, App. 6) */
745 "0200000000000000000000000000000000000000"
746 "0000000000000000000000000000000000000000008000000000000000000001",
747 "0000000000000000000000000000000000000000"
748 "0000000000000000000000000000000000000000000000000000000000000001",
749 "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422E"
750 "F1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
751 "015D4860D088DDB3496B0C6064756260441CDE4A"
752 "F1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
753 "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5"
754 "A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
756 "0100000000000000000000000000000000000000"
757 "00000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
760 /* Curve K-571 (FIPS PUB 186-2, App. 6) */
764 "0000000000000000000000000000000000000000000000000000000000000000"
765 "0000000000000000000000000000000000000000000000000000000000000425",
769 "82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E6"
770 "47DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
772 "4F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA7"
773 "4FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
776 "00000000000000000000000000000000000000000000000000000000131850E1"
777 "F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
780 /* Curve B-571 (FIPS PUB 186-2, App. 6) */
784 "0000000000000000000000000000000000000000000000000000000000000000"
785 "0000000000000000000000000000000000000000000000000000000000000425",
787 "0000000000000000000000000000000000000000000000000000000000000000"
788 "0000000000000000000000000000000000000000000000000000000000000001",
790 "DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA5933"
791 "2BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
793 "6C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293"
794 "CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
796 "6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A57"
797 "6291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
800 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18"
801 "FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
806 static int char2_curve_test(int n)
810 BIGNUM *p = NULL, *a = NULL, *b = NULL;
811 BIGNUM *x = NULL, *y = NULL, *z = NULL, *cof = NULL, *yplusone = NULL;
812 EC_GROUP *group = NULL, *variable = NULL;
813 EC_POINT *P = NULL, *Q = NULL, *R = NULL;
814 const EC_POINT *points[3];
815 const BIGNUM *scalars[3];
816 struct c2_curve_test *const test = char2_curve_tests + n;
818 if (!TEST_ptr(ctx = BN_CTX_new())
819 || !TEST_ptr(p = BN_new())
820 || !TEST_ptr(a = BN_new())
821 || !TEST_ptr(b = BN_new())
822 || !TEST_ptr(x = BN_new())
823 || !TEST_ptr(y = BN_new())
824 || !TEST_ptr(z = BN_new())
825 || !TEST_ptr(yplusone = BN_new())
826 || !TEST_true(BN_hex2bn(&p, test->p))
827 || !TEST_true(BN_hex2bn(&a, test->a))
828 || !TEST_true(BN_hex2bn(&b, test->b))
829 || !TEST_true(group = EC_GROUP_new(EC_GF2m_simple_method()))
830 || !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
831 || !TEST_ptr(P = EC_POINT_new(group))
832 || !TEST_ptr(Q = EC_POINT_new(group))
833 || !TEST_ptr(R = EC_POINT_new(group))
834 || !TEST_true(BN_hex2bn(&x, test->x))
835 || !TEST_true(BN_hex2bn(&y, test->y))
836 || !TEST_true(BN_add(yplusone, y, BN_value_one())))
839 /* Change test based on whether binary point compression is enabled or not. */
840 # ifdef OPENSSL_EC_BIN_PT_COMP
842 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
843 * and therefore setting the coordinates should fail.
845 if (!TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx))
846 || !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x,
849 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
850 || !TEST_true(BN_hex2bn(&z, test->order))
851 || !TEST_true(BN_hex2bn(&cof, test->cof))
852 || !TEST_true(EC_GROUP_set_generator(group, P, z, cof))
853 || !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
855 TEST_info("%s -- Generator", test->name);
856 test_output_bignum("x", x);
857 test_output_bignum("y", y);
858 /* G_y value taken from the standard: */
859 if (!TEST_true(BN_hex2bn(&z, test->y))
860 || !TEST_BN_eq(y, z))
864 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
865 * and therefore setting the coordinates should fail.
867 if (!TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx))
868 || !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
869 || !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
870 || !TEST_true(BN_hex2bn(&z, test->order))
871 || !TEST_true(BN_hex2bn(&cof, test->cof))
872 || !TEST_true(EC_GROUP_set_generator(group, P, z, cof)))
874 TEST_info("%s -- Generator:", test->name);
875 test_output_bignum("x", x);
876 test_output_bignum("y", y);
879 if (!TEST_int_eq(EC_GROUP_get_degree(group), test->degree)
880 || !group_order_tests(group)
881 || !TEST_ptr(variable = EC_GROUP_new(EC_GROUP_method_of(group)))
882 || !TEST_true(EC_GROUP_copy(variable, group)))
885 /* more tests using the last curve */
886 if (n == OSSL_NELEM(char2_curve_tests) - 1) {
887 if (!TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
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(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(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(group, Q, x, 1, ctx))
1025 || !TEST_true(BN_hex2bn(&y, "8"))
1026 || !TEST_true(EC_POINT_set_affine_coordinates(group, Q, x, y, ctx))
1030 if (!TEST_int_gt(EC_POINT_is_on_curve(group, Q, ctx), 0)) {
1031 /* Change test based on whether binary point compression is enabled or not. */
1032 # ifdef OPENSSL_EC_BIN_PT_COMP
1033 if (!TEST_true(EC_POINT_get_affine_coordinates(group, Q, x, y, ctx)))
1036 TEST_info("Point is not on curve");
1037 test_output_bignum("x", x);
1038 test_output_bignum("y", y);
1042 TEST_note("A cyclic subgroup:");
1045 if (!TEST_int_ne(k--, 0))
1048 if (EC_POINT_is_at_infinity(group, P))
1049 TEST_note(" point at infinity");
1051 if (!TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y,
1055 test_output_bignum("x", x);
1056 test_output_bignum("y", y);
1059 if (!TEST_true(EC_POINT_copy(R, P))
1060 || !TEST_true(EC_POINT_add(group, P, P, Q, ctx)))
1063 while (!EC_POINT_is_at_infinity(group, P));
1065 if (!TEST_true(EC_POINT_add(group, P, Q, R, ctx))
1066 || !TEST_true(EC_POINT_is_at_infinity(group, P)))
1069 /* Change test based on whether binary point compression is enabled or not. */
1070 # ifdef OPENSSL_EC_BIN_PT_COMP
1071 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED,
1072 buf, sizeof(buf), ctx);
1073 if (!TEST_size_t_ne(len, 0)
1074 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
1075 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
1077 test_output_memory("Generator as octet string, compressed form:",
1081 len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED,
1082 buf, sizeof(buf), ctx);
1083 if (!TEST_size_t_ne(len, 0)
1084 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
1085 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
1087 test_output_memory("Generator as octet string, uncompressed form:",
1090 /* Change test based on whether binary point compression is enabled or not. */
1091 # ifdef OPENSSL_EC_BIN_PT_COMP
1093 EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof(buf),
1095 if (!TEST_size_t_ne(len, 0)
1096 || !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
1097 || !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
1099 test_output_memory("Generator as octet string, hybrid form:",
1103 if (!TEST_true(EC_POINT_invert(group, P, ctx))
1104 || !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx)))
1115 EC_GROUP_free(group);
1129 static int internal_curve_test(int n)
1131 EC_GROUP *group = NULL;
1132 int nid = curves[n].nid;
1134 if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))) {
1135 TEST_info("EC_GROUP_new_curve_name() failed with curve %s\n",
1139 if (!TEST_true(EC_GROUP_check(group, NULL))) {
1140 TEST_info("EC_GROUP_check() failed with curve %s\n", OBJ_nid2sn(nid));
1141 EC_GROUP_free(group);
1144 EC_GROUP_free(group);
1148 static int internal_curve_test_method(int n)
1150 int r, nid = curves[n].nid;
1153 if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(nid))) {
1154 TEST_info("Curve %s failed\n", OBJ_nid2sn(nid));
1157 r = group_order_tests(group);
1158 EC_GROUP_free(group);
1162 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1164 * nistp_test_params contains magic numbers for testing our optimized
1165 * implementations of several NIST curves with characteristic > 3.
1167 struct nistp_test_params {
1168 const EC_METHOD *(*meth) (void);
1171 * Qx, Qy and D are taken from
1172 * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
1173 * Otherwise, values are standard curve parameters from FIPS 180-3
1175 const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d;
1178 static const struct nistp_test_params nistp_tests_params[] = {
1181 EC_GFp_nistp224_method,
1184 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
1186 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
1188 "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
1190 "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E",
1192 "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555",
1194 "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
1196 "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
1198 "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
1200 "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8",
1204 EC_GFp_nistp256_method,
1207 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
1209 "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc",
1211 "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
1213 "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19",
1215 "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09",
1217 "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
1219 "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5",
1221 "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
1223 "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96",
1227 EC_GFp_nistp521_method,
1231 "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
1232 "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
1235 "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
1236 "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc",
1239 "953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e1"
1240 "56193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00",
1243 "e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e"
1244 "59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4",
1247 "350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8"
1248 "554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e",
1251 "858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dba"
1252 "a14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66",
1255 "39296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c"
1256 "97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650",
1259 "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa"
1260 "51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409",
1263 "085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eee"
1264 "df09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722",
1268 static int nistp_single_test(int idx)
1270 const struct nistp_test_params *test = nistp_tests_params + idx;
1272 BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL;
1273 BIGNUM *n = NULL, *m = NULL, *order = NULL, *yplusone = NULL;
1274 EC_GROUP *NISTP = NULL;
1275 EC_POINT *G = NULL, *P = NULL, *Q = NULL, *Q_CHECK = NULL;
1278 TEST_note("NIST curve P-%d (optimised implementation):",
1280 if (!TEST_ptr(ctx = BN_CTX_new())
1281 || !TEST_ptr(p = BN_new())
1282 || !TEST_ptr(a = BN_new())
1283 || !TEST_ptr(b = BN_new())
1284 || !TEST_ptr(x = BN_new())
1285 || !TEST_ptr(y = BN_new())
1286 || !TEST_ptr(m = BN_new())
1287 || !TEST_ptr(n = BN_new())
1288 || !TEST_ptr(order = BN_new())
1289 || !TEST_ptr(yplusone = BN_new())
1291 || !TEST_ptr(NISTP = EC_GROUP_new(test->meth()))
1292 || !TEST_true(BN_hex2bn(&p, test->p))
1293 || !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
1294 || !TEST_true(BN_hex2bn(&a, test->a))
1295 || !TEST_true(BN_hex2bn(&b, test->b))
1296 || !TEST_true(EC_GROUP_set_curve(NISTP, p, a, b, ctx))
1297 || !TEST_ptr(G = EC_POINT_new(NISTP))
1298 || !TEST_ptr(P = EC_POINT_new(NISTP))
1299 || !TEST_ptr(Q = EC_POINT_new(NISTP))
1300 || !TEST_ptr(Q_CHECK = EC_POINT_new(NISTP))
1301 || !TEST_true(BN_hex2bn(&x, test->Qx))
1302 || !TEST_true(BN_hex2bn(&y, test->Qy))
1303 || !TEST_true(BN_add(yplusone, y, BN_value_one()))
1305 * When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
1306 * and therefore setting the coordinates should fail.
1308 || !TEST_false(EC_POINT_set_affine_coordinates(NISTP, Q_CHECK, x,
1310 || !TEST_true(EC_POINT_set_affine_coordinates(NISTP, Q_CHECK, x, y,
1312 || !TEST_true(BN_hex2bn(&x, test->Gx))
1313 || !TEST_true(BN_hex2bn(&y, test->Gy))
1314 || !TEST_true(EC_POINT_set_affine_coordinates(NISTP, G, x, y, ctx))
1315 || !TEST_true(BN_hex2bn(&order, test->order))
1316 || !TEST_true(EC_GROUP_set_generator(NISTP, G, order, BN_value_one()))
1317 || !TEST_int_eq(EC_GROUP_get_degree(NISTP), test->degree))
1320 TEST_note("NIST test vectors ... ");
1321 if (!TEST_true(BN_hex2bn(&n, test->d)))
1323 /* fixed point multiplication */
1324 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1325 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1327 /* random point multiplication */
1328 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1329 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1331 /* set generator to P = 2*G, where G is the standard generator */
1332 || !TEST_true(EC_POINT_dbl(NISTP, P, G, ctx))
1333 || !TEST_true(EC_GROUP_set_generator(NISTP, P, order, BN_value_one()))
1334 /* set the scalar to m=n/2, where n is the NIST test scalar */
1335 || !TEST_true(BN_rshift(m, n, 1)))
1338 /* test the non-standard generator */
1339 /* fixed point multiplication */
1340 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1341 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1343 /* random point multiplication */
1344 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1345 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1348 * We have not performed precomputation so have_precompute mult should be
1351 || !TEST_false(EC_GROUP_have_precompute_mult(NISTP))
1353 /* now repeat all tests with precomputation */
1354 || !TEST_true(EC_GROUP_precompute_mult(NISTP, ctx))
1355 || !TEST_true(EC_GROUP_have_precompute_mult(NISTP)))
1358 /* fixed point multiplication */
1359 EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
1360 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1362 /* random point multiplication */
1363 EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
1364 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx))
1366 /* reset generator */
1367 || !TEST_true(EC_GROUP_set_generator(NISTP, G, order, BN_value_one())))
1369 /* fixed point multiplication */
1370 EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
1371 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1373 /* random point multiplication */
1374 EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
1375 if (!TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)))
1378 /* regression test for felem_neg bug */
1379 if (!TEST_true(BN_set_word(m, 32))
1380 || !TEST_true(BN_set_word(n, 31))
1381 || !TEST_true(EC_POINT_copy(P, G))
1382 || !TEST_true(EC_POINT_invert(NISTP, P, ctx))
1383 || !TEST_true(EC_POINT_mul(NISTP, Q, m, P, n, ctx))
1384 || !TEST_int_eq(0, EC_POINT_cmp(NISTP, Q, G, ctx)))
1387 r = group_order_tests(NISTP);
1389 EC_GROUP_free(NISTP);
1393 EC_POINT_free(Q_CHECK);
1408 static const unsigned char p521_named[] = {
1409 0x06, 0x05, 0x2b, 0x81, 0x04, 0x00, 0x23,
1412 static const unsigned char p521_explicit[] = {
1413 0x30, 0x82, 0x01, 0xc3, 0x02, 0x01, 0x01, 0x30, 0x4d, 0x06, 0x07, 0x2a,
1414 0x86, 0x48, 0xce, 0x3d, 0x01, 0x01, 0x02, 0x42, 0x01, 0xff, 0xff, 0xff,
1415 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1416 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1417 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1418 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1419 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1420 0xff, 0xff, 0x30, 0x81, 0x9f, 0x04, 0x42, 0x01, 0xff, 0xff, 0xff, 0xff,
1421 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1422 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1423 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1424 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1425 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1426 0xfc, 0x04, 0x42, 0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, 0x9a,
1427 0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85, 0x40, 0xee, 0xa2, 0xda, 0x72,
1428 0x5b, 0x99, 0xb3, 0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, 0x09,
1429 0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e, 0x93, 0x7b, 0x16, 0x52, 0xc0,
1430 0xbd, 0x3b, 0xb1, 0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, 0x34,
1431 0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50, 0x3f, 0x00, 0x03, 0x15, 0x00,
1432 0xd0, 0x9e, 0x88, 0x00, 0x29, 0x1c, 0xb8, 0x53, 0x96, 0xcc, 0x67, 0x17,
1433 0x39, 0x32, 0x84, 0xaa, 0xa0, 0xda, 0x64, 0xba, 0x04, 0x81, 0x85, 0x04,
1434 0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, 0xe9, 0xcd, 0x9e, 0x3e,
1435 0xcb, 0x66, 0x23, 0x95, 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f,
1436 0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d, 0x3d, 0xba, 0xa1, 0x4b,
1437 0x5e, 0x77, 0xef, 0xe7, 0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff,
1438 0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a, 0x42, 0x9b, 0xf9, 0x7e,
1439 0x7e, 0x31, 0xc2, 0xe5, 0xbd, 0x66, 0x01, 0x18, 0x39, 0x29, 0x6a, 0x78,
1440 0x9a, 0x3b, 0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, 0x1b, 0xd9,
1441 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17,
1442 0x27, 0x3e, 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, 0x26, 0x40,
1443 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86,
1444 0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50,
1445 0x02, 0x42, 0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1446 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
1447 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfa,
1448 0x51, 0x86, 0x87, 0x83, 0xbf, 0x2f, 0x96, 0x6b, 0x7f, 0xcc, 0x01, 0x48,
1449 0xf7, 0x09, 0xa5, 0xd0, 0x3b, 0xb5, 0xc9, 0xb8, 0x89, 0x9c, 0x47, 0xae,
1450 0xbb, 0x6f, 0xb7, 0x1e, 0x91, 0x38, 0x64, 0x09, 0x02, 0x01, 0x01,
1453 static int parameter_test(void)
1455 EC_GROUP *group = NULL, *group2 = NULL;
1456 ECPARAMETERS *ecparameters = NULL;
1457 unsigned char *buf = NULL;
1460 if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(NID_secp112r1))
1461 || !TEST_ptr(ecparameters = EC_GROUP_get_ecparameters(group, NULL))
1462 || !TEST_ptr(group2 = EC_GROUP_new_from_ecparameters(ecparameters))
1463 || !TEST_int_eq(EC_GROUP_cmp(group, group2, NULL), 0))
1466 EC_GROUP_free(group);
1469 /* Test the named curve encoding, which should be default. */
1470 if (!TEST_ptr(group = EC_GROUP_new_by_curve_name(NID_secp521r1))
1471 || !TEST_true((len = i2d_ECPKParameters(group, &buf)) >= 0)
1472 || !TEST_mem_eq(buf, len, p521_named, sizeof(p521_named)))
1479 * Test the explicit encoding. P-521 requires correctly zero-padding the
1480 * curve coefficients.
1482 EC_GROUP_set_asn1_flag(group, OPENSSL_EC_EXPLICIT_CURVE);
1483 if (!TEST_true((len = i2d_ECPKParameters(group, &buf)) >= 0)
1484 || !TEST_mem_eq(buf, len, p521_explicit, sizeof(p521_explicit)))
1489 EC_GROUP_free(group);
1490 EC_GROUP_free(group2);
1491 ECPARAMETERS_free(ecparameters);
1497 int setup_tests(void)
1499 #ifndef OPENSSL_NO_EC
1500 crv_len = EC_get_builtin_curves(NULL, 0);
1501 if (!TEST_ptr(curves = OPENSSL_malloc(sizeof(*curves) * crv_len))
1502 || !TEST_true(EC_get_builtin_curves(curves, crv_len)))
1505 ADD_TEST(parameter_test);
1506 ADD_TEST(prime_field_tests);
1507 # ifndef OPENSSL_NO_EC2M
1508 ADD_TEST(char2_field_tests);
1509 ADD_ALL_TESTS(char2_curve_test, OSSL_NELEM(char2_curve_tests));
1511 # ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
1512 ADD_ALL_TESTS(nistp_single_test, OSSL_NELEM(nistp_tests_params));
1514 ADD_ALL_TESTS(internal_curve_test, crv_len);
1515 ADD_ALL_TESTS(internal_curve_test_method, crv_len);
1520 void cleanup_tests(void)
1522 #ifndef OPENSSL_NO_EC
1523 OPENSSL_free(curves);