xref: /openbsd-src/regress/lib/libcrypto/ec/ectest.c (revision 3370674dae15185c1b94d00aa72a322aa6aea569)

/*	$OpenBSD: ectest.c,v 1.35 2025/01/24 11:49:13 tb Exp $	*/
/*
 * Originally written by Bodo Moeller for the OpenSSL project.
 */
/* ====================================================================
 * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 *
 * 3. All advertising materials mentioning features or use of this
 *    software must display the following acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 * OF THE POSSIBILITY OF SUCH DAMAGE.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */
/* ====================================================================
 * 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>
#include <string.h>
#include <time.h>

#include <openssl/ec.h>
#include <openssl/err.h>
#include <openssl/obj_mac.h>
#include <openssl/objects.h>
#include <openssl/bn.h>
#include <openssl/opensslconf.h>

#define ABORT do { \
	fflush(stdout); \
	fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
	ERR_print_errors_fp(stderr); \
	exit(1); \
} while (0)

/* test multiplication with group order, long and negative scalars */
static void
group_order_tests(EC_GROUP *group, BN_CTX *ctx)
{
	BIGNUM *n1, *n2, *order;
	EC_POINT *P = EC_POINT_new(group);
	EC_POINT *Q = EC_POINT_new(group);

	if (P == NULL || Q == NULL)
		ABORT;

	BN_CTX_start(ctx);

	if ((n1 = BN_CTX_get(ctx)) == NULL)
		ABORT;
	if ((n2 = BN_CTX_get(ctx)) == NULL)
		ABORT;
	if ((order = BN_CTX_get(ctx)) == NULL)
		ABORT;
	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_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 ... ");
	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) */
	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;
	fprintf(stdout, "ok\n");
	EC_POINT_free(P);
	EC_POINT_free(Q);
	BN_CTX_end(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;
	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;

	if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL)
		ABORT;

	{
		EC_GROUP *tmp;

		if ((tmp = EC_GROUP_dup(group)) == NULL)
			ABORT;
		EC_GROUP_free(group);
		group = tmp;
	}

	if (!EC_GROUP_get_curve(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();
	if (!x || !y || !z)
		ABORT;

	if (!BN_hex2bn(&x, "D"))
		ABORT;
	if (!EC_POINT_set_compressed_coordinates(group, Q, x, 1, ctx))
		ABORT;
	if (EC_POINT_is_on_curve(group, Q, ctx) <= 0) {
		if (!EC_POINT_get_affine_coordinates(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 = 0;
	do {
		fprintf(stderr, "     %d - ", k);
		if (EC_POINT_is_at_infinity(group, P))
			fprintf(stdout, "point at infinity\n");
		else {
			if (!EC_POINT_get_affine_coordinates(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;
		if (k++ > 99)
			ABORT;
	} while (!EC_POINT_is_at_infinity(group, P));

	if (k != 7) {
		fprintf(stderr, "cycled in %d iterations, want 7\n", k);
		ABORT;
	}

	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_affine_coordinates(group, R, x, y, ctx))
		ABORT;
	fprintf(stdout, "\nThe inverse of that generator:\n     X = 0x");
	BN_print_fp(stdout, x);
	fprintf(stdout, ", Y = 0x");
	BN_print_fp(stdout, y);
	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(group, p, a, b, ctx))
		ABORT;

	if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82"))
		ABORT;
	if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32"))
		ABORT;
	if (!EC_POINT_set_affine_coordinates(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(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, ctx);

	if ((P_160 = EC_GROUP_dup(group)) == NULL)
		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(group, p, a, b, ctx))
		ABORT;

	if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"))
		ABORT;
	if (!EC_POINT_set_compressed_coordinates(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(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;

	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 192)
		ABORT;
	fprintf(stdout, " ok\n");

	group_order_tests(group, ctx);

	if ((P_192 = EC_GROUP_dup(group)) == NULL)
		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(group, p, a, b, ctx))
		ABORT;

	if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"))
		ABORT;
	if (!EC_POINT_set_compressed_coordinates(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(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;

	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 224)
		ABORT;
	fprintf(stdout, " ok\n");

	group_order_tests(group, ctx);

	if ((P_224 = EC_GROUP_dup(group)) == NULL)
		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(group, p, a, b, ctx))
		ABORT;

	if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"))
		ABORT;
	if (!EC_POINT_set_compressed_coordinates(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(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;

	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 256)
		ABORT;
	fprintf(stdout, " ok\n");

	group_order_tests(group, ctx);

	if ((P_256 = EC_GROUP_dup(group)) == NULL)
		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(group, p, a, b, ctx))
		ABORT;

	if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
	    "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
	if (!EC_POINT_set_compressed_coordinates(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(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;

	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 384)
		ABORT;
	fprintf(stdout, " ok\n");

	group_order_tests(group, ctx);

	if ((P_384 = EC_GROUP_dup(group)) == NULL)
		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(group, p, a, b, ctx))
		ABORT;

	if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
	    "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
	    "3C1856A429BF97E7E31C2E5BD66")) ABORT;
	if (!EC_POINT_set_compressed_coordinates(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(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;

	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 521)
		ABORT;
	fprintf(stdout, " ok\n");

	group_order_tests(group, ctx);

	if ((P_521 = EC_GROUP_dup(group)) == NULL)
		ABORT;

	/* more tests using the last curve */
	fprintf(stdout, "infinity tests ...");
	fflush(stdout);
	if (!EC_POINT_copy(Q, P))
		ABORT;
	if (EC_POINT_is_at_infinity(group, Q))
		ABORT;
	/* P := 2P */
	if (!EC_POINT_dbl(group, P, P, ctx))
		ABORT;
	if (EC_POINT_is_on_curve(group, P, ctx) <= 0)
		ABORT;
	/* Q := -P */
	if (!EC_POINT_invert(group, Q, ctx))
		ABORT;
	/* R := 2P - P = P */
	if (!EC_POINT_add(group, R, P, Q, ctx))
		ABORT;
	/* R := R + Q = P - P = infty */
	if (!EC_POINT_add(group, R, R, Q, ctx))
		ABORT;
	if (!EC_POINT_is_at_infinity(group, R))
		ABORT;
	fprintf(stdout, " ok\n\n");

	if (ctx)
		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);

	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);
}

int
main(int argc, char *argv[])
{
	ERR_load_crypto_strings();

	prime_field_tests();

	CRYPTO_cleanup_all_ex_data();
	ERR_free_strings();
	ERR_remove_thread_state(NULL);

	return 0;
}