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ectest.c
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/*
* Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved.
* Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
*
* Licensed under the Apache License 2.0 (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
#include <string.h>
#include "internal/nelem.h"
#include "testutil.h"
#ifndef OPENSSL_NO_EC
# include <openssl/ec.h>
# ifndef OPENSSL_NO_ENGINE
# include <openssl/engine.h>
# endif
# include <openssl/err.h>
# include <openssl/obj_mac.h>
# include <openssl/objects.h>
# include <openssl/rand.h>
# include <openssl/bn.h>
# include <openssl/opensslconf.h>
static size_t crv_len = 0;
static EC_builtin_curve *curves = NULL;
/* test multiplication with group order, long and negative scalars */
static int group_order_tests(EC_GROUP *group)
{
BIGNUM *n1 = NULL, *n2 = NULL, *order = NULL;
EC_POINT *P = NULL, *Q = NULL, *R = NULL, *S = NULL;
const EC_POINT *G = NULL;
BN_CTX *ctx = NULL;
int i = 0, r = 0;
if (!TEST_ptr(n1 = BN_new())
|| !TEST_ptr(n2 = BN_new())
|| !TEST_ptr(order = BN_new())
|| !TEST_ptr(ctx = BN_CTX_new())
|| !TEST_ptr(G = EC_GROUP_get0_generator(group))
|| !TEST_ptr(P = EC_POINT_new(group))
|| !TEST_ptr(Q = EC_POINT_new(group))
|| !TEST_ptr(R = EC_POINT_new(group))
|| !TEST_ptr(S = EC_POINT_new(group)))
goto err;
if (!TEST_true(EC_GROUP_get_order(group, order, ctx))
|| !TEST_true(EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, Q))
|| !TEST_true(EC_GROUP_precompute_mult(group, ctx))
|| !TEST_true(EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, Q))
|| !TEST_true(EC_POINT_copy(P, G))
|| !TEST_true(BN_one(n1))
|| !TEST_true(EC_POINT_mul(group, Q, n1, NULL, NULL, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
|| !TEST_true(BN_sub(n1, order, n1))
|| !TEST_true(EC_POINT_mul(group, Q, n1, NULL, NULL, ctx))
|| !TEST_true(EC_POINT_invert(group, Q, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx)))
goto err;
for (i = 1; i <= 2; i++) {
const BIGNUM *scalars[6];
const EC_POINT *points[6];
if (!TEST_true(BN_set_word(n1, i))
/*
* If i == 1, P will be the predefined generator for which
* EC_GROUP_precompute_mult has set up precomputation.
*/
|| !TEST_true(EC_POINT_mul(group, P, n1, NULL, NULL, ctx))
|| (i == 1 && !TEST_int_eq(0, EC_POINT_cmp(group, P, G, ctx)))
|| !TEST_true(BN_one(n1))
/* n1 = 1 - order */
|| !TEST_true(BN_sub(n1, n1, order))
|| !TEST_true(EC_POINT_mul(group, Q, NULL, P, n1, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
/* n2 = 1 + order */
|| !TEST_true(BN_add(n2, order, BN_value_one()))
|| !TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx))
/* n2 = (1 - order) * (1 + order) = 1 - order^2 */
|| !TEST_true(BN_mul(n2, n1, n2, ctx))
|| !TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, Q, P, ctx)))
goto err;
/* n2 = order^2 - 1 */
BN_set_negative(n2, 0);
if (!TEST_true(EC_POINT_mul(group, Q, NULL, P, n2, ctx))
/* Add P to verify the result. */
|| !TEST_true(EC_POINT_add(group, Q, Q, P, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, Q))
/* Exercise EC_POINTs_mul, including corner cases. */
|| !TEST_false(EC_POINT_is_at_infinity(group, P)))
goto err;
scalars[0] = scalars[1] = BN_value_one();
points[0] = points[1] = P;
if (!TEST_true(EC_POINTs_mul(group, R, NULL, 2, points, scalars, ctx))
|| !TEST_true(EC_POINT_dbl(group, S, points[0], ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, R, S, ctx)))
goto err;
scalars[0] = n1;
points[0] = Q; /* => infinity */
scalars[1] = n2;
points[1] = P; /* => -P */
scalars[2] = n1;
points[2] = Q; /* => infinity */
scalars[3] = n2;
points[3] = Q; /* => infinity */
scalars[4] = n1;
points[4] = P; /* => P */
scalars[5] = n2;
points[5] = Q; /* => infinity */
if (!TEST_true(EC_POINTs_mul(group, P, NULL, 6, points, scalars, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, P)))
goto err;
}
r = 1;
err:
if (r == 0 && i != 0)
TEST_info(i == 1 ? "allowing precomputation" :
"without precomputation");
EC_POINT_free(P);
EC_POINT_free(Q);
EC_POINT_free(R);
EC_POINT_free(S);
BN_free(n1);
BN_free(n2);
BN_free(order);
BN_CTX_free(ctx);
return r;
}
static int prime_field_tests(void)
{
BN_CTX *ctx = NULL;
BIGNUM *p = NULL, *a = NULL, *b = NULL, *scalar3 = NULL;
EC_GROUP *group = NULL, *tmp = NULL;
EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL,
*P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
EC_POINT *P = NULL, *Q = NULL, *R = NULL;
BIGNUM *x = NULL, *y = NULL, *z = NULL, *yplusone = NULL;
const EC_POINT *points[4];
const BIGNUM *scalars[4];
unsigned char buf[100];
size_t len, r = 0;
int k;
if (!TEST_ptr(ctx = BN_CTX_new())
|| !TEST_ptr(p = BN_new())
|| !TEST_ptr(a = BN_new())
|| !TEST_ptr(b = BN_new())
|| !TEST_true(BN_hex2bn(&p, "17"))
|| !TEST_true(BN_hex2bn(&a, "1"))
|| !TEST_true(BN_hex2bn(&b, "1"))
/*
* applications should use EC_GROUP_new_curve_GFp so
* that the library gets to choose the EC_METHOD
*/
|| !TEST_ptr(group = EC_GROUP_new(EC_GFp_mont_method()))
|| !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
|| !TEST_ptr(tmp = EC_GROUP_new(EC_GROUP_method_of(group)))
|| !TEST_true(EC_GROUP_copy(tmp, group)))
goto err;
EC_GROUP_free(group);
group = tmp;
tmp = NULL;
if (!TEST_true(EC_GROUP_get_curve(group, p, a, b, ctx)))
goto err;
TEST_info("Curve defined by Weierstrass equation");
TEST_note(" y^2 = x^3 + a*x + b (mod p)");
test_output_bignum("a", a);
test_output_bignum("b", b);
test_output_bignum("p", p);
buf[0] = 0;
if (!TEST_ptr(P = EC_POINT_new(group))
|| !TEST_ptr(Q = EC_POINT_new(group))
|| !TEST_ptr(R = EC_POINT_new(group))
|| !TEST_true(EC_POINT_set_to_infinity(group, P))
|| !TEST_true(EC_POINT_is_at_infinity(group, P))
|| !TEST_true(EC_POINT_oct2point(group, Q, buf, 1, ctx))
|| !TEST_true(EC_POINT_add(group, P, P, Q, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, P))
|| !TEST_ptr(x = BN_new())
|| !TEST_ptr(y = BN_new())
|| !TEST_ptr(z = BN_new())
|| !TEST_ptr(yplusone = BN_new())
|| !TEST_true(BN_hex2bn(&x, "D"))
|| !TEST_true(EC_POINT_set_compressed_coordinates(group, Q, x, 1, ctx)))
goto err;
if (!TEST_int_gt(EC_POINT_is_on_curve(group, Q, ctx), 0)) {
if (!TEST_true(EC_POINT_get_affine_coordinates(group, Q, x, y, ctx)))
goto err;
TEST_info("Point is not on curve");
test_output_bignum("x", x);
test_output_bignum("y", y);
goto err;
}
TEST_note("A cyclic subgroup:");
k = 100;
do {
if (!TEST_int_ne(k--, 0))
goto err;
if (EC_POINT_is_at_infinity(group, P)) {
TEST_note(" point at infinity");
} else {
if (!TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y,
ctx)))
goto err;
test_output_bignum("x", x);
test_output_bignum("y", y);
}
if (!TEST_true(EC_POINT_copy(R, P))
|| !TEST_true(EC_POINT_add(group, P, P, Q, ctx)))
goto err;
} while (!EC_POINT_is_at_infinity(group, P));
if (!TEST_true(EC_POINT_add(group, P, Q, R, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, P)))
goto err;
len =
EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf,
sizeof(buf), ctx);
if (!TEST_size_t_ne(len, 0)
|| !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
goto err;
test_output_memory("Generator as octet string, compressed form:",
buf, len);
len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED,
buf, sizeof(buf), ctx);
if (!TEST_size_t_ne(len, 0)
|| !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
goto err;
test_output_memory("Generator as octet string, uncompressed form:",
buf, len);
len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID,
buf, sizeof(buf), ctx);
if (!TEST_size_t_ne(len, 0)
|| !TEST_true(EC_POINT_oct2point(group, P, buf, len, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, P, Q, ctx)))
goto err;
test_output_memory("Generator as octet string, hybrid form:",
buf, len);
if (!TEST_true(EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z,
ctx)))
goto err;
TEST_info("A representation of the inverse of that generator in");
TEST_note("Jacobian projective coordinates");
test_output_bignum("x", x);
test_output_bignum("y", y);
test_output_bignum("z", z);
if (!TEST_true(EC_POINT_invert(group, P, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
/*
* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2,
* 2000) -- not a NIST curve, but commonly used
*/
|| !TEST_true(BN_hex2bn(&p, "FFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"))
|| !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
|| !TEST_true(BN_hex2bn(&a, "FFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"))
|| !TEST_true(BN_hex2bn(&b, "1C97BEFC"
"54BD7A8B65ACF89F81D4D4ADC565FA45"))
|| !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
|| !TEST_true(BN_hex2bn(&x, "4A96B568"
"8EF573284664698968C38BB913CBFC82"))
|| !TEST_true(BN_hex2bn(&y, "23a62855"
"3168947d59dcc912042351377ac5fb32"))
|| !TEST_true(BN_add(yplusone, y, BN_value_one()))
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
|| !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
ctx))
|| !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
|| !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
|| !TEST_true(BN_hex2bn(&z, "0100000000"
"000000000001F4C8F927AED3CA752257"))
|| !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
|| !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
goto err;
TEST_info("SEC2 curve secp160r1 -- Generator");
test_output_bignum("x", x);
test_output_bignum("y", y);
/* G_y value taken from the standard: */
if (!TEST_true(BN_hex2bn(&z, "23a62855"
"3168947d59dcc912042351377ac5fb32"))
|| !TEST_BN_eq(y, z)
|| !TEST_int_eq(EC_GROUP_get_degree(group), 160)
|| !group_order_tests(group)
|| !TEST_ptr(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))
|| !TEST_true(EC_GROUP_copy(P_160, group))
/* Curve P-192 (FIPS PUB 186-2, App. 6) */
|| !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"))
|| !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
|| !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"))
|| !TEST_true(BN_hex2bn(&b, "64210519E59C80E7"
"0FA7E9AB72243049FEB8DEECC146B9B1"))
|| !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
|| !TEST_true(BN_hex2bn(&x, "188DA80EB03090F6"
"7CBF20EB43A18800F4FF0AFD82FF1012"))
|| !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx))
|| !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
|| !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFF"
"FFFFFFFF99DEF836146BC9B1B4D22831"))
|| !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
|| !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
goto err;
TEST_info("NIST curve P-192 -- Generator");
test_output_bignum("x", x);
test_output_bignum("y", y);
/* G_y value taken from the standard: */
if (!TEST_true(BN_hex2bn(&z, "07192B95FFC8DA78"
"631011ED6B24CDD573F977A11E794811"))
|| !TEST_BN_eq(y, z)
|| !TEST_true(BN_add(yplusone, y, BN_value_one()))
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
|| !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
ctx))
|| !TEST_int_eq(EC_GROUP_get_degree(group), 192)
|| !group_order_tests(group)
|| !TEST_ptr(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))
|| !TEST_true(EC_GROUP_copy(P_192, group))
/* Curve P-224 (FIPS PUB 186-2, App. 6) */
|| !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFF000000000000000000000001"))
|| !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
|| !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"))
|| !TEST_true(BN_hex2bn(&b, "B4050A850C04B3ABF5413256"
"5044B0B7D7BFD8BA270B39432355FFB4"))
|| !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
|| !TEST_true(BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B9"
"4A03C1D356C21122343280D6115C1D21"))
|| !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 0, ctx))
|| !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
|| !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF"
"FFFF16A2E0B8F03E13DD29455C5C2A3D"))
|| !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
|| !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
goto err;
TEST_info("NIST curve P-224 -- Generator");
test_output_bignum("x", x);
test_output_bignum("y", y);
/* G_y value taken from the standard: */
if (!TEST_true(BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6"
"CD4375A05A07476444D5819985007E34"))
|| !TEST_BN_eq(y, z)
|| !TEST_true(BN_add(yplusone, y, BN_value_one()))
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
|| !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
ctx))
|| !TEST_int_eq(EC_GROUP_get_degree(group), 224)
|| !group_order_tests(group)
|| !TEST_ptr(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))
|| !TEST_true(EC_GROUP_copy(P_224, group))
/* Curve P-256 (FIPS PUB 186-2, App. 6) */
|| !TEST_true(BN_hex2bn(&p, "FFFFFFFF000000010000000000000000"
"00000000FFFFFFFFFFFFFFFFFFFFFFFF"))
|| !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
|| !TEST_true(BN_hex2bn(&a, "FFFFFFFF000000010000000000000000"
"00000000FFFFFFFFFFFFFFFFFFFFFFFC"))
|| !TEST_true(BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC"
"651D06B0CC53B0F63BCE3C3E27D2604B"))
|| !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
|| !TEST_true(BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F2"
"77037D812DEB33A0F4A13945D898C296"))
|| !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx))
|| !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
|| !TEST_true(BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFF"
"BCE6FAADA7179E84F3B9CAC2FC632551"))
|| !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
|| !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
goto err;
TEST_info("NIST curve P-256 -- Generator");
test_output_bignum("x", x);
test_output_bignum("y", y);
/* G_y value taken from the standard: */
if (!TEST_true(BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E16"
"2BCE33576B315ECECBB6406837BF51F5"))
|| !TEST_BN_eq(y, z)
|| !TEST_true(BN_add(yplusone, y, BN_value_one()))
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
|| !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
ctx))
|| !TEST_int_eq(EC_GROUP_get_degree(group), 256)
|| !group_order_tests(group)
|| !TEST_ptr(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))
|| !TEST_true(EC_GROUP_copy(P_256, group))
/* Curve P-384 (FIPS PUB 186-2, App. 6) */
|| !TEST_true(BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
"FFFFFFFF0000000000000000FFFFFFFF"))
|| !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
|| !TEST_true(BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
"FFFFFFFF0000000000000000FFFFFFFC"))
|| !TEST_true(BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19"
"181D9C6EFE8141120314088F5013875A"
"C656398D8A2ED19D2A85C8EDD3EC2AEF"))
|| !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
|| !TEST_true(BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD74"
"6E1D3B628BA79B9859F741E082542A38"
"5502F25DBF55296C3A545E3872760AB7"))
|| !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 1, ctx))
|| !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
|| !TEST_true(BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFC7634D81F4372DDF"
"581A0DB248B0A77AECEC196ACCC52973"))
|| !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
|| !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
goto err;
TEST_info("NIST curve P-384 -- Generator");
test_output_bignum("x", x);
test_output_bignum("y", y);
/* G_y value taken from the standard: */
if (!TEST_true(BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29"
"F8F41DBD289A147CE9DA3113B5F0B8C0"
"0A60B1CE1D7E819D7A431D7C90EA0E5F"))
|| !TEST_BN_eq(y, z)
|| !TEST_true(BN_add(yplusone, y, BN_value_one()))
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
|| !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
ctx))
|| !TEST_int_eq(EC_GROUP_get_degree(group), 384)
|| !group_order_tests(group)
|| !TEST_ptr(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))
|| !TEST_true(EC_GROUP_copy(P_384, group))
/* Curve P-521 (FIPS PUB 186-2, App. 6) */
|| !TEST_true(BN_hex2bn(&p, "1FF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
|| !TEST_int_eq(1, BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
|| !TEST_true(BN_hex2bn(&a, "1FF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC"))
|| !TEST_true(BN_hex2bn(&b, "051"
"953EB9618E1C9A1F929A21A0B68540EE"
"A2DA725B99B315F3B8B489918EF109E1"
"56193951EC7E937B1652C0BD3BB1BF07"
"3573DF883D2C34F1EF451FD46B503F00"))
|| !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
|| !TEST_true(BN_hex2bn(&x, "C6"
"858E06B70404E9CD9E3ECB662395B442"
"9C648139053FB521F828AF606B4D3DBA"
"A14B5E77EFE75928FE1DC127A2FFA8DE"
"3348B3C1856A429BF97E7E31C2E5BD66"))
|| !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x, 0, ctx))
|| !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
|| !TEST_true(BN_hex2bn(&z, "1FF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA"
"51868783BF2F966B7FCC0148F709A5D0"
"3BB5C9B8899C47AEBB6FB71E91386409"))
|| !TEST_true(EC_GROUP_set_generator(group, P, z, BN_value_one()))
|| !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
goto err;
TEST_info("NIST curve P-521 -- Generator");
test_output_bignum("x", x);
test_output_bignum("y", y);
/* G_y value taken from the standard: */
if (!TEST_true(BN_hex2bn(&z, "118"
"39296A789A3BC0045C8A5FB42C7D1BD9"
"98F54449579B446817AFBD17273E662C"
"97EE72995EF42640C550B9013FAD0761"
"353C7086A272C24088BE94769FD16650"))
|| !TEST_BN_eq(y, z)
|| !TEST_true(BN_add(yplusone, y, BN_value_one()))
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
|| !TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone,
ctx))
|| !TEST_int_eq(EC_GROUP_get_degree(group), 521)
|| !group_order_tests(group)
|| !TEST_ptr(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))
|| !TEST_true(EC_GROUP_copy(P_521, group))
/* more tests using the last curve */
/* Restore the point that got mangled in the (x, y + 1) test. */
|| !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
|| !TEST_true(EC_POINT_copy(Q, P))
|| !TEST_false(EC_POINT_is_at_infinity(group, Q))
|| !TEST_true(EC_POINT_dbl(group, P, P, ctx))
|| !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
|| !TEST_true(EC_POINT_invert(group, Q, ctx)) /* P = -2Q */
|| !TEST_true(EC_POINT_add(group, R, P, Q, ctx))
|| !TEST_true(EC_POINT_add(group, R, R, Q, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, R)) /* R = P + 2Q */
|| !TEST_false(EC_POINT_is_at_infinity(group, Q)))
goto err;
points[0] = Q;
points[1] = Q;
points[2] = Q;
points[3] = Q;
if (!TEST_true(EC_GROUP_get_order(group, z, ctx))
|| !TEST_true(BN_add(y, z, BN_value_one()))
|| !TEST_BN_even(y)
|| !TEST_true(BN_rshift1(y, y)))
goto err;
scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
scalars[1] = y;
TEST_note("combined multiplication ...");
/* z is still the group order */
if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
|| !TEST_true(EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, R, Q, ctx))
|| !TEST_true(BN_rand(y, BN_num_bits(y), 0, 0))
|| !TEST_true(BN_add(z, z, y)))
goto err;
BN_set_negative(z, 1);
scalars[0] = y;
scalars[1] = z; /* z = -(order + y) */
if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, P))
|| !TEST_true(BN_rand(x, BN_num_bits(y) - 1, 0, 0))
|| !TEST_true(BN_add(z, x, y)))
goto err;
BN_set_negative(z, 1);
scalars[0] = x;
scalars[1] = y;
scalars[2] = z; /* z = -(x+y) */
if (!TEST_ptr(scalar3 = BN_new()))
goto err;
BN_zero(scalar3);
scalars[3] = scalar3;
if (!TEST_true(EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, P)))
goto err;
TEST_note(" ok\n");
r = 1;
err:
BN_CTX_free(ctx);
BN_free(p);
BN_free(a);
BN_free(b);
EC_GROUP_free(group);
EC_GROUP_free(tmp);
EC_POINT_free(P);
EC_POINT_free(Q);
EC_POINT_free(R);
BN_free(x);
BN_free(y);
BN_free(z);
BN_free(yplusone);
BN_free(scalar3);
EC_GROUP_free(P_160);
EC_GROUP_free(P_192);
EC_GROUP_free(P_224);
EC_GROUP_free(P_256);
EC_GROUP_free(P_384);
EC_GROUP_free(P_521);
return r;
}
# ifndef OPENSSL_NO_EC2M
static struct c2_curve_test {
const char *name;
const char *p;
const char *a;
const char *b;
const char *x;
const char *y;
int ybit;
const char *order;
const char *cof;
int degree;
} char2_curve_tests[] = {
/* Curve K-163 (FIPS PUB 186-2, App. 6) */
{
"NIST curve K-163",
"0800000000000000000000000000000000000000C9",
"1",
"1",
"02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
"0289070FB05D38FF58321F2E800536D538CCDAA3D9",
1, "04000000000000000000020108A2E0CC0D99F8A5EF", "2", 163
},
/* Curve B-163 (FIPS PUB 186-2, App. 6) */
{
"NIST curve B-163",
"0800000000000000000000000000000000000000C9",
"1",
"020A601907B8C953CA1481EB10512F78744A3205FD",
"03F0EBA16286A2D57EA0991168D4994637E8343E36",
"00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
1, "040000000000000000000292FE77E70C12A4234C33", "2", 163
},
/* Curve K-233 (FIPS PUB 186-2, App. 6) */
{
"NIST curve K-233",
"020000000000000000000000000000000000000004000000000000000001",
"0",
"1",
"017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
"01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
0,
"008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
"4", 233
},
/* Curve B-233 (FIPS PUB 186-2, App. 6) */
{
"NIST curve B-233",
"020000000000000000000000000000000000000004000000000000000001",
"000000000000000000000000000000000000000000000000000000000001",
"0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
"00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
"01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1,
"01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
"2", 233
},
/* Curve K-283 (FIPS PUB 186-2, App. 6) */
{
"NIST curve K-283",
"08000000"
"00000000000000000000000000000000000000000000000000000000000010A1",
"0",
"1",
"0503213F"
"78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
"01CCDA38"
"0F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
0,
"01FFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
"4", 283
},
/* Curve B-283 (FIPS PUB 186-2, App. 6) */
{
"NIST curve B-283",
"08000000"
"00000000000000000000000000000000000000000000000000000000000010A1",
"00000000"
"0000000000000000000000000000000000000000000000000000000000000001",
"027B680A"
"C8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
"05F93925"
"8DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
"03676854"
"FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1,
"03FFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
"2", 283
},
/* Curve K-409 (FIPS PUB 186-2, App. 6) */
{
"NIST curve K-409",
"0200000000000000000000000000000000000000"
"0000000000000000000000000000000000000000008000000000000000000001",
"0",
"1",
"0060F05F658F49C1AD3AB1890F7184210EFD0987"
"E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
"01E369050B7C4E42ACBA1DACBF04299C3460782F"
"918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1,
"007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
"4", 409
},
/* Curve B-409 (FIPS PUB 186-2, App. 6) */
{
"NIST curve B-409",
"0200000000000000000000000000000000000000"
"0000000000000000000000000000000000000000008000000000000000000001",
"0000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000001",
"0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422E"
"F1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
"015D4860D088DDB3496B0C6064756260441CDE4A"
"F1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
"0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5"
"A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1,
"0100000000000000000000000000000000000000"
"00000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
"2", 409
},
/* Curve K-571 (FIPS PUB 186-2, App. 6) */
{
"NIST curve K-571",
"800000000000000"
"0000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000425",
"0",
"1",
"026EB7A859923FBC"
"82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E6"
"47DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
"0349DC807F4FBF37"
"4F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA7"
"4FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
0,
"0200000000000000"
"00000000000000000000000000000000000000000000000000000000131850E1"
"F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
"4", 571
},
/* Curve B-571 (FIPS PUB 186-2, App. 6) */
{
"NIST curve B-571",
"800000000000000"
"0000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000425",
"0000000000000000"
"0000000000000000000000000000000000000000000000000000000000000000"
"0000000000000000000000000000000000000000000000000000000000000001",
"02F40E7E2221F295"
"DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA5933"
"2BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
"0303001D34B85629"
"6C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293"
"CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
"037BF27342DA639B"
"6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A57"
"6291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1,
"03FFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18"
"FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
"2", 571
}
};
static int char2_curve_test(int n)
{
int r = 0;
BN_CTX *ctx = NULL;
BIGNUM *p = NULL, *a = NULL, *b = NULL;
BIGNUM *x = NULL, *y = NULL, *z = NULL, *cof = NULL, *yplusone = NULL;
EC_GROUP *group = NULL, *variable = NULL;
EC_POINT *P = NULL, *Q = NULL, *R = NULL;
const EC_POINT *points[3];
const BIGNUM *scalars[3];
struct c2_curve_test *const test = char2_curve_tests + n;
if (!TEST_ptr(ctx = BN_CTX_new())
|| !TEST_ptr(p = BN_new())
|| !TEST_ptr(a = BN_new())
|| !TEST_ptr(b = BN_new())
|| !TEST_ptr(x = BN_new())
|| !TEST_ptr(y = BN_new())
|| !TEST_ptr(z = BN_new())
|| !TEST_ptr(yplusone = BN_new())
|| !TEST_true(BN_hex2bn(&p, test->p))
|| !TEST_true(BN_hex2bn(&a, test->a))
|| !TEST_true(BN_hex2bn(&b, test->b))
|| !TEST_true(group = EC_GROUP_new(EC_GF2m_simple_method()))
|| !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
|| !TEST_ptr(P = EC_POINT_new(group))
|| !TEST_ptr(Q = EC_POINT_new(group))
|| !TEST_ptr(R = EC_POINT_new(group))
|| !TEST_true(BN_hex2bn(&x, test->x))
|| !TEST_true(BN_hex2bn(&y, test->y))
|| !TEST_true(BN_add(yplusone, y, BN_value_one())))
goto err;
/* Change test based on whether binary point compression is enabled or not. */
# ifdef OPENSSL_EC_BIN_PT_COMP
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
if (!TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx))
|| !TEST_true(EC_POINT_set_compressed_coordinates(group, P, x,
test->y_bit,
ctx))
|| !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
|| !TEST_true(BN_hex2bn(&z, test->order))
|| !TEST_true(BN_hex2bn(&cof, test->cof))
|| !TEST_true(EC_GROUP_set_generator(group, P, z, cof))
|| !TEST_true(EC_POINT_get_affine_coordinates(group, P, x, y, ctx)))
goto err;
TEST_info("%s -- Generator", test->name);
test_output_bignum("x", x);
test_output_bignum("y", y);
/* G_y value taken from the standard: */
if (!TEST_true(BN_hex2bn(&z, test->y))
|| !TEST_BN_eq(y, z))
goto err;
# else
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
if (!TEST_false(EC_POINT_set_affine_coordinates(group, P, x, yplusone, ctx))
|| !TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
|| !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
|| !TEST_true(BN_hex2bn(&z, test->order))
|| !TEST_true(BN_hex2bn(&cof, test->cof))
|| !TEST_true(EC_GROUP_set_generator(group, P, z, cof)))
goto err;
TEST_info("%s -- Generator:", test->name);
test_output_bignum("x", x);
test_output_bignum("y", y);
# endif
if (!TEST_int_eq(EC_GROUP_get_degree(group), test->degree)
|| !group_order_tests(group)
|| !TEST_ptr(variable = EC_GROUP_new(EC_GROUP_method_of(group)))
|| !TEST_true(EC_GROUP_copy(variable, group)))
goto err;
/* more tests using the last curve */
if (n == OSSL_NELEM(char2_curve_tests) - 1) {
if (!TEST_true(EC_POINT_set_affine_coordinates(group, P, x, y, ctx))
|| !TEST_true(EC_POINT_copy(Q, P))
|| !TEST_false(EC_POINT_is_at_infinity(group, Q))
|| !TEST_true(EC_POINT_dbl(group, P, P, ctx))
|| !TEST_int_gt(EC_POINT_is_on_curve(group, P, ctx), 0)
|| !TEST_true(EC_POINT_invert(group, Q, ctx)) /* P = -2Q */
|| !TEST_true(EC_POINT_add(group, R, P, Q, ctx))
|| !TEST_true(EC_POINT_add(group, R, R, Q, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, R)) /* R = P + 2Q */
|| !TEST_false(EC_POINT_is_at_infinity(group, Q)))
goto err;
points[0] = Q;
points[1] = Q;
points[2] = Q;
if (!TEST_true(BN_add(y, z, BN_value_one()))
|| !TEST_BN_even(y)
|| !TEST_true(BN_rshift1(y, y)))
goto err;
scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
scalars[1] = y;
TEST_note("combined multiplication ...");
/* z is still the group order */
if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
|| !TEST_true(EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, P, R, ctx))
|| !TEST_int_eq(0, EC_POINT_cmp(group, R, Q, ctx)))
goto err;
if (!TEST_true(BN_rand(y, BN_num_bits(y), 0, 0))
|| !TEST_true(BN_add(z, z, y)))
goto err;
BN_set_negative(z, 1);
scalars[0] = y;
scalars[1] = z; /* z = -(order + y) */
if (!TEST_true(EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, P)))
goto err;
if (!TEST_true(BN_rand(x, BN_num_bits(y) - 1, 0, 0))
|| !TEST_true(BN_add(z, x, y)))
goto err;
BN_set_negative(z, 1);
scalars[0] = x;
scalars[1] = y;
scalars[2] = z; /* z = -(x+y) */
if (!TEST_true(EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx))
|| !TEST_true(EC_POINT_is_at_infinity(group, P)))
goto err;;
}
r = 1;
err:
BN_CTX_free(ctx);
BN_free(p);
BN_free(a);
BN_free(b);
BN_free(x);
BN_free(y);
BN_free(z);
BN_free(yplusone);
BN_free(cof);
EC_POINT_free(P);
EC_POINT_free(Q);
EC_POINT_free(R);
EC_GROUP_free(group);
EC_GROUP_free(variable);
return r;
}
static int char2_field_tests(void)
{
BN_CTX *ctx = NULL;
BIGNUM *p = NULL, *a = NULL, *b = NULL;
EC_GROUP *group = NULL, *tmp = NULL;
EC_POINT *P = NULL, *Q = NULL, *R = NULL;
BIGNUM *x = NULL, *y = NULL, *z = NULL, *cof = NULL, *yplusone = NULL;
unsigned char buf[100];
size_t len;
int k, r = 0;
if (!TEST_ptr(ctx = BN_CTX_new())
|| !TEST_ptr(p = BN_new())
|| !TEST_ptr(a = BN_new())
|| !TEST_ptr(b = BN_new())
|| !TEST_true(BN_hex2bn(&p, "13"))
|| !TEST_true(BN_hex2bn(&a, "3"))
|| !TEST_true(BN_hex2bn(&b, "1")))
goto err;
group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use
* EC_GROUP_new_curve_GF2m
* so that the library gets
* to choose the EC_METHOD */
if (!TEST_ptr(group)
|| !TEST_true(EC_GROUP_set_curve(group, p, a, b, ctx))
|| !TEST_ptr(tmp = EC_GROUP_new(EC_GROUP_method_of(group)))
|| !TEST_true(EC_GROUP_copy(tmp, group)))
goto err;
EC_GROUP_free(group);
group = tmp;
tmp = NULL;
if (!TEST_true(EC_GROUP_get_curve(group, p, a, b, ctx)))
goto err;
TEST_info("Curve defined by Weierstrass equation");
TEST_note(" y^2 + x*y = x^3 + a*x^2 + b (mod p)");