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ectest.c
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/*
* Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the OpenSSL license (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
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the OpenSSL open source
* license provided above.
*
* The elliptic curve binary polynomial software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
*
*/
#include <stdio.h>
#include <stdlib.h>
#ifdef FLAT_INC
# include "e_os.h"
#else
# include "../e_os.h"
#endif
#include <string.h>
#include <time.h>
#ifdef OPENSSL_NO_EC
int main(int argc, char *argv[])
{
puts("Elliptic curves are disabled.");
return 0;
}
#else
# 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>
# if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12)
/* suppress "too big too optimize" warning */
# pragma warning(disable:4959)
# endif
# define ABORT do { \
fflush(stdout); \
fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
ERR_print_errors_fp(stderr); \
EXIT(1); \
} while (0)
# define TIMING_BASE_PT 0
# define TIMING_RAND_PT 1
# define TIMING_SIMUL 2
/* test multiplication with group order, long and negative scalars */
static void group_order_tests(EC_GROUP *group)
{
BIGNUM *n1, *n2, *order;
EC_POINT *P = EC_POINT_new(group);
EC_POINT *Q = EC_POINT_new(group);
EC_POINT *R = EC_POINT_new(group);
EC_POINT *S = EC_POINT_new(group);
BN_CTX *ctx = BN_CTX_new();
int i;
n1 = BN_new();
n2 = BN_new();
order = BN_new();
fprintf(stdout, "verify group order ...");
fflush(stdout);
if (!EC_GROUP_get_order(group, order, ctx))
ABORT;
if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
ABORT;
if (!EC_POINT_is_at_infinity(group, Q))
ABORT;
fprintf(stdout, ".");
fflush(stdout);
if (!EC_GROUP_precompute_mult(group, ctx))
ABORT;
if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx))
ABORT;
if (!EC_POINT_is_at_infinity(group, Q))
ABORT;
fprintf(stdout, " ok\n");
fprintf(stdout, "long/negative scalar tests ");
for (i = 1; i <= 2; i++) {
const BIGNUM *scalars[6];
const EC_POINT *points[6];
fprintf(stdout, i == 1 ?
"allowing precomputation ... " :
"without precomputation ... ");
if (!BN_set_word(n1, i))
ABORT;
/*
* If i == 1, P will be the predefined generator for which
* EC_GROUP_precompute_mult has set up precomputation.
*/
if (!EC_POINT_mul(group, P, n1, NULL, NULL, ctx))
ABORT;
if (!BN_one(n1))
ABORT;
/* n1 = 1 - order */
if (!BN_sub(n1, n1, order))
ABORT;
if (!EC_POINT_mul(group, Q, NULL, P, n1, ctx))
ABORT;
if (0 != EC_POINT_cmp(group, Q, P, ctx))
ABORT;
/* n2 = 1 + order */
if (!BN_add(n2, order, BN_value_one()))
ABORT;
if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx))
ABORT;
if (0 != EC_POINT_cmp(group, Q, P, ctx))
ABORT;
/* n2 = (1 - order) * (1 + order) = 1 - order^2 */
if (!BN_mul(n2, n1, n2, ctx))
ABORT;
if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx))
ABORT;
if (0 != EC_POINT_cmp(group, Q, P, ctx))
ABORT;
/* n2 = order^2 - 1 */
BN_set_negative(n2, 0);
if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx))
ABORT;
/* Add P to verify the result. */
if (!EC_POINT_add(group, Q, Q, P, ctx))
ABORT;
if (!EC_POINT_is_at_infinity(group, Q))
ABORT;
/* Exercise EC_POINTs_mul, including corner cases. */
if (EC_POINT_is_at_infinity(group, P))
ABORT;
scalars[0] = scalars[1] = BN_value_one();
points[0] = points[1] = P;
if (!EC_POINTs_mul(group, R, NULL, 2, points, scalars, ctx))
ABORT;
if (!EC_POINT_dbl(group, S, points[0], ctx))
ABORT;
if (0 != EC_POINT_cmp(group, R, S, ctx))
ABORT;
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 (!EC_POINTs_mul(group, P, NULL, 6, points, scalars, ctx))
ABORT;
if (!EC_POINT_is_at_infinity(group, P))
ABORT;
}
fprintf(stdout, "ok\n");
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);
}
static void prime_field_tests(void)
{
BN_CTX *ctx = NULL;
BIGNUM *p, *a, *b;
EC_GROUP *group;
EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 =
NULL, *P_384 = NULL, *P_521 = NULL;
EC_POINT *P, *Q, *R;
BIGNUM *x, *y, *z, *yplusone;
unsigned char buf[100];
size_t i, len;
int k;
ctx = BN_CTX_new();
if (!ctx)
ABORT;
p = BN_new();
a = BN_new();
b = BN_new();
if (!p || !a || !b)
ABORT;
if (!BN_hex2bn(&p, "17"))
ABORT;
if (!BN_hex2bn(&a, "1"))
ABORT;
if (!BN_hex2bn(&b, "1"))
ABORT;
group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use
* EC_GROUP_new_curve_GFp so
* that the library gets to
* choose the EC_METHOD */
if (!group)
ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
ABORT;
{
EC_GROUP *tmp;
tmp = EC_GROUP_new(EC_GROUP_method_of(group));
if (!tmp)
ABORT;
if (!EC_GROUP_copy(tmp, group))
ABORT;
EC_GROUP_free(group);
group = tmp;
}
if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx))
ABORT;
fprintf(stdout,
"Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
BN_print_fp(stdout, p);
fprintf(stdout, ")\n a = 0x");
BN_print_fp(stdout, a);
fprintf(stdout, "\n b = 0x");
BN_print_fp(stdout, b);
fprintf(stdout, "\n");
P = EC_POINT_new(group);
Q = EC_POINT_new(group);
R = EC_POINT_new(group);
if (!P || !Q || !R)
ABORT;
if (!EC_POINT_set_to_infinity(group, P))
ABORT;
if (!EC_POINT_is_at_infinity(group, P))
ABORT;
buf[0] = 0;
if (!EC_POINT_oct2point(group, Q, buf, 1, ctx))
ABORT;
if (!EC_POINT_add(group, P, P, Q, ctx))
ABORT;
if (!EC_POINT_is_at_infinity(group, P))
ABORT;
x = BN_new();
y = BN_new();
z = BN_new();
yplusone = BN_new();
if (x == NULL || y == NULL || z == NULL || yplusone == NULL)
ABORT;
if (!BN_hex2bn(&x, "D"))
ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx))
ABORT;
if (EC_POINT_is_on_curve(group, Q, ctx) <= 0) {
if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx))
ABORT;
fprintf(stderr, "Point is not on curve: x = 0x");
BN_print_fp(stderr, x);
fprintf(stderr, ", y = 0x");
BN_print_fp(stderr, y);
fprintf(stderr, "\n");
ABORT;
}
fprintf(stdout, "A cyclic subgroup:\n");
k = 100;
do {
if (k-- == 0)
ABORT;
if (EC_POINT_is_at_infinity(group, P))
fprintf(stdout, " point at infinity\n");
else {
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
ABORT;
fprintf(stdout, " x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, ", y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
}
if (!EC_POINT_copy(R, P))
ABORT;
if (!EC_POINT_add(group, P, P, Q, ctx))
ABORT;
}
while (!EC_POINT_is_at_infinity(group, P));
if (!EC_POINT_add(group, P, Q, R, ctx))
ABORT;
if (!EC_POINT_is_at_infinity(group, P))
ABORT;
len =
EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf,
sizeof buf, ctx);
if (len == 0)
ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx))
ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx))
ABORT;
fprintf(stdout, "Generator as octet string, compressed form:\n ");
for (i = 0; i < len; i++)
fprintf(stdout, "%02X", buf[i]);
len =
EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf,
sizeof buf, ctx);
if (len == 0)
ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx))
ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx))
ABORT;
fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
for (i = 0; i < len; i++)
fprintf(stdout, "%02X", buf[i]);
len =
EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf,
ctx);
if (len == 0)
ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx))
ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx))
ABORT;
fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
for (i = 0; i < len; i++)
fprintf(stdout, "%02X", buf[i]);
if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx))
ABORT;
fprintf(stdout,
"\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, ", Y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, ", Z = 0x");
BN_print_fp(stdout, z);
fprintf(stdout, "\n");
if (!EC_POINT_invert(group, P, ctx))
ABORT;
if (0 != EC_POINT_cmp(group, P, R, ctx))
ABORT;
/*
* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2,
* 2000) -- not a NIST curve, but commonly used
*/
if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF"))
ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
ABORT;
if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC"))
ABORT;
if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45"))
ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
ABORT;
if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82"))
ABORT;
if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32"))
ABORT;
if (!BN_add(yplusone, y, BN_value_one()))
ABORT;
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
ABORT;
if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx))
ABORT;
if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
ABORT;
if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257"))
ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
ABORT;
fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32"))
ABORT;
if (0 != BN_cmp(y, z))
ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 160)
ABORT;
fprintf(stdout, " ok\n");
group_order_tests(group);
if ((P_160 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
ABORT;
if (!EC_GROUP_copy(P_160, group))
ABORT;
/* Curve P-192 (FIPS PUB 186-2, App. 6) */
if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"))
ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
ABORT;
if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"))
ABORT;
if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"))
ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
ABORT;
if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"))
ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx))
ABORT;
if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
ABORT;
if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"))
ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
ABORT;
fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"))
ABORT;
if (0 != BN_cmp(y, z))
ABORT;
if (!BN_add(yplusone, y, BN_value_one()))
ABORT;
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 192)
ABORT;
fprintf(stdout, " ok\n");
group_order_tests(group);
if ((P_192 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
ABORT;
if (!EC_GROUP_copy(P_192, group))
ABORT;
/* Curve P-224 (FIPS PUB 186-2, App. 6) */
if (!BN_hex2bn
(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"))
ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
ABORT;
if (!BN_hex2bn
(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"))
ABORT;
if (!BN_hex2bn
(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"))
ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
ABORT;
if (!BN_hex2bn
(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"))
ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx))
ABORT;
if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
ABORT;
if (!BN_hex2bn
(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"))
ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
ABORT;
fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn
(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"))
ABORT;
if (0 != BN_cmp(y, z))
ABORT;
if (!BN_add(yplusone, y, BN_value_one()))
ABORT;
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 224)
ABORT;
fprintf(stdout, " ok\n");
group_order_tests(group);
if ((P_224 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
ABORT;
if (!EC_GROUP_copy(P_224, group))
ABORT;
/* Curve P-256 (FIPS PUB 186-2, App. 6) */
if (!BN_hex2bn
(&p,
"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"))
ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
ABORT;
if (!BN_hex2bn
(&a,
"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC"))
ABORT;
if (!BN_hex2bn
(&b,
"5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"))
ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
ABORT;
if (!BN_hex2bn
(&x,
"6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"))
ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx))
ABORT;
if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
ABORT;
if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
"84F3B9CAC2FC632551"))
ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
ABORT;
fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn
(&z,
"4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"))
ABORT;
if (0 != BN_cmp(y, z))
ABORT;
if (!BN_add(yplusone, y, BN_value_one()))
ABORT;
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 256)
ABORT;
fprintf(stdout, " ok\n");
group_order_tests(group);
if ((P_256 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
ABORT;
if (!EC_GROUP_copy(P_256, group))
ABORT;
/* Curve P-384 (FIPS PUB 186-2, App. 6) */
if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"))
ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
ABORT;
if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC"))
ABORT;
if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
"120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"))
ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
ABORT;
if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
"9859F741E082542A385502F25DBF55296C3A545E3872760AB7"))
ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx))
ABORT;
if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
ABORT;
if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"))
ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
ABORT;
fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
"7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"))
ABORT;
if (0 != BN_cmp(y, z))
ABORT;
if (!BN_add(yplusone, y, BN_value_one()))
ABORT;
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 384)
ABORT;
fprintf(stdout, " ok\n");
group_order_tests(group);
if ((P_384 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
ABORT;
if (!EC_GROUP_copy(P_384, group))
ABORT;
/* Curve P-521 (FIPS PUB 186-2, App. 6) */
if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFF"))
ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL))
ABORT;
if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFC"))
ABORT;
if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
"315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
"DF883D2C34F1EF451FD46B503F00"))
ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx))
ABORT;
if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
"B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
"3C1856A429BF97E7E31C2E5BD66"))
ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx))
ABORT;
if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
ABORT;
if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
"C9B8899C47AEBB6FB71E91386409"))
ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one()))
ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx))
ABORT;
fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
"B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
"7086A272C24088BE94769FD16650"))
ABORT;
if (0 != BN_cmp(y, z))
ABORT;
if (!BN_add(yplusone, y, BN_value_one()))
ABORT;
/*
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not,
* and therefore setting the coordinates should fail.
*/
if (EC_POINT_set_affine_coordinates_GFp(group, P, x, yplusone, ctx))
ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 521)
ABORT;
fprintf(stdout, " ok\n");
group_order_tests(group);
if ((P_521 = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL)
ABORT;
if (!EC_GROUP_copy(P_521, group))
ABORT;
/* more tests using the last curve */
/* Restore the point that got mangled in the (x, y + 1) test. */
if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx))
ABORT;
if (!EC_POINT_copy(Q, P))
ABORT;
if (EC_POINT_is_at_infinity(group, Q))
ABORT;
if (!EC_POINT_dbl(group, P, P, ctx))
ABORT;
if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
ABORT;
if (!EC_POINT_invert(group, Q, ctx))
ABORT; /* P = -2Q */
if (!EC_POINT_add(group, R, P, Q, ctx))
ABORT;
if (!EC_POINT_add(group, R, R, Q, ctx))
ABORT;
if (!EC_POINT_is_at_infinity(group, R))
ABORT; /* R = P + 2Q */
{
const EC_POINT *points[4];
const BIGNUM *scalars[4];
BIGNUM *scalar3;
if (EC_POINT_is_at_infinity(group, Q))
ABORT;
points[0] = Q;
points[1] = Q;
points[2] = Q;
points[3] = Q;
if (!EC_GROUP_get_order(group, z, ctx))
ABORT;
if (!BN_add(y, z, BN_value_one()))
ABORT;
if (BN_is_odd(y))
ABORT;
if (!BN_rshift1(y, y))
ABORT;
scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
scalars[1] = y;
fprintf(stdout, "combined multiplication ...");
fflush(stdout);
/* z is still the group order */
if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
ABORT;
if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx))
ABORT;
if (0 != EC_POINT_cmp(group, P, R, ctx))
ABORT;
if (0 != EC_POINT_cmp(group, R, Q, ctx))
ABORT;
fprintf(stdout, ".");
fflush(stdout);
if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0))
ABORT;
if (!BN_add(z, z, y))
ABORT;
BN_set_negative(z, 1);
scalars[0] = y;
scalars[1] = z; /* z = -(order + y) */
if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx))
ABORT;
if (!EC_POINT_is_at_infinity(group, P))
ABORT;
fprintf(stdout, ".");
fflush(stdout);
if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0))
ABORT;
if (!BN_add(z, x, y))
ABORT;
BN_set_negative(z, 1);
scalars[0] = x;
scalars[1] = y;
scalars[2] = z; /* z = -(x+y) */
scalar3 = BN_new();
if (!scalar3)
ABORT;
BN_zero(scalar3);
scalars[3] = scalar3;
if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx))
ABORT;
if (!EC_POINT_is_at_infinity(group, P))
ABORT;
fprintf(stdout, " ok\n\n");
BN_free(scalar3);
}
BN_CTX_free(ctx);
BN_free(p);
BN_free(a);
BN_free(b);
EC_GROUP_free(group);
EC_POINT_free(P);
EC_POINT_free(Q);
EC_POINT_free(R);
BN_free(x);
BN_free(y);
BN_free(z);
BN_free(yplusone);
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);
}
/* Change test based on whether binary point compression is enabled or not. */
# ifdef OPENSSL_EC_BIN_PT_COMP
# define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
if (!BN_hex2bn(&x, _x)) ABORT; \
if (!BN_hex2bn(&y, _y)) ABORT; \
if (!BN_add(yplusone, y, BN_value_one())) ABORT; \
/* \
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not, \
* and therefore setting the coordinates should fail. \
*/ \
if (EC_POINT_set_affine_coordinates_GF2m(group, P, x, yplusone, ctx)) ABORT; \
if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \
if (!BN_hex2bn(&z, _order)) ABORT; \
if (!BN_hex2bn(&cof, _cof)) ABORT; \
if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
BN_print_fp(stdout, x); \
fprintf(stdout, "\n y = 0x"); \
BN_print_fp(stdout, y); \
fprintf(stdout, "\n"); \
/* G_y value taken from the standard: */ \
if (!BN_hex2bn(&z, _y)) ABORT; \
if (0 != BN_cmp(y, z)) ABORT;
# else
# define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
if (!BN_hex2bn(&x, _x)) ABORT; \
if (!BN_hex2bn(&y, _y)) ABORT; \
if (!BN_add(yplusone, y, BN_value_one())) ABORT; \
/* \
* When (x, y) is on the curve, (x, y + 1) is, as it happens, not, \
* and therefore setting the coordinates should fail. \
*/ \
if (EC_POINT_set_affine_coordinates_GF2m(group, P, x, yplusone, ctx)) ABORT; \
if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
if (EC_POINT_is_on_curve(group, P, ctx) <= 0) ABORT; \
if (!BN_hex2bn(&z, _order)) ABORT; \
if (!BN_hex2bn(&cof, _cof)) ABORT; \
if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
BN_print_fp(stdout, x); \
fprintf(stdout, "\n y = 0x"); \
BN_print_fp(stdout, y); \
fprintf(stdout, "\n");
# endif
# define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
if (!BN_hex2bn(&p, _p)) ABORT; \
if (!BN_hex2bn(&a, _a)) ABORT; \
if (!BN_hex2bn(&b, _b)) ABORT; \
if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
fprintf(stdout, "verify degree ..."); \
if (EC_GROUP_get_degree(group) != _degree) ABORT; \
fprintf(stdout, " ok\n"); \
group_order_tests(group); \
if ((_variable = EC_GROUP_new(EC_GROUP_method_of(group))) == NULL) ABORT; \
if (!EC_GROUP_copy(_variable, group)) ABORT; \
# ifndef OPENSSL_NO_EC2M
static void char2_field_tests(void)
{
BN_CTX *ctx = NULL;
BIGNUM *p, *a, *b;
EC_GROUP *group;
EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 =
NULL, *C2_K571 = NULL;
EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 =
NULL, *C2_B571 = NULL;
EC_POINT *P, *Q, *R;
BIGNUM *x, *y, *z, *cof, *yplusone;
unsigned char buf[100];
size_t i, len;
int k;
ctx = BN_CTX_new();
if (!ctx)
ABORT;
p = BN_new();
a = BN_new();
b = BN_new();
if (p == NULL || a == NULL || b == NULL)
ABORT;
if (!BN_hex2bn(&p, "13"))
ABORT;
if (!BN_hex2bn(&a, "3"))
ABORT;
if (!BN_hex2bn(&b, "1"))
ABORT;
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 (!group)
ABORT;