text: /* crypto/ec/ectest.c */
  /*
   * 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>
  #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
  
  #if 0
  static void timings(EC_GROUP *group, int type, BN_CTX *ctx)
  	{
  	clock_t clck;
  	int i, j;
  	BIGNUM *s;
  	BIGNUM *r[10], *r0[10];
  	EC_POINT *P;
  		
  	s = BN_new();
  	if (s == NULL) ABORT;
  
  	fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group));
  	if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
  	fprintf(stdout, "%d-bit scalars ", (int)BN_num_bits(s));
  	fflush(stdout);
  
  	P = EC_POINT_new(group);
  	if (P == NULL) ABORT;
  	EC_POINT_copy(P, EC_GROUP_get0_generator(group));
  
  	for (i = 0; i < 10; i++)
  		{
  		if ((r[i] = BN_new()) == NULL) ABORT;
  		if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT;
  		if (type != TIMING_BASE_PT)
  			{
  			if ((r0[i] = BN_new()) == NULL) ABORT;
  			if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT;
  			}
  		}
  
  	clck = clock();
  	for (i = 0; i < 10; i++)
  		{
  		for (j = 0; j < 10; j++)
  			{
  			if (!EC_POINT_mul(group, P, (type != TIMING_RAND_PT) ? r[i] : NULL, 
  				(type != TIMING_BASE_PT) ? P : NULL, (type != TIMING_BASE_PT) ? r0[i] : NULL, ctx)) ABORT;
  			}
  		}
  	clck = clock() - clck;
  
  	fprintf(stdout, "\n");
  
  #ifdef CLOCKS_PER_SEC
  	/* "To determine the time in seconds, the value returned
  	 * by the clock function should be divided by the value
  	 * of the macro CLOCKS_PER_SEC."
  	 *                                       -- ISO/IEC 9899 */
  #	define UNIT "s"
  #else
  	/* "`CLOCKS_PER_SEC' undeclared (first use this function)"
  	 *                            -- cc on NeXTstep/OpenStep */
  #	define UNIT "units"
  #	define CLOCKS_PER_SEC 1
  #endif
  
  	if (type == TIMING_BASE_PT) {
  		fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
  			"base point multiplications", (double)clck/CLOCKS_PER_SEC);
  	} else if (type == TIMING_RAND_PT) {
  		fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
  			"random point multiplications", (double)clck/CLOCKS_PER_SEC);
  	} else if (type == TIMING_SIMUL) {
  		fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
  			"s*P+t*Q operations", (double)clck/CLOCKS_PER_SEC);
  	}
  	fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
  
  	EC_POINT_free(P);
  	BN_free(s);
  	for (i = 0; i < 10; i++)
  		{
  		BN_free(r[i]);
  		if (type != TIMING_BASE_PT) BN_free(r0[i]);
  		}
  	}
  #endif
  
  /* 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);
  	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] = 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);
  	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;
  	unsigned char buf[100];
  	size_t i, len;
  	int k;
  	
  #if 1 /* optional */
  	ctx = BN_CTX_new();
  	if (!ctx) ABORT;
  #endif
  
  	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();
  	if (!x || !y || !z) 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))
  		{
  		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;
  
  #if 0 /* optional */
  		{
  			EC_POINT *points[3];
  		
  			points[0] = R;
  			points[1] = Q;
  			points[2] = P;
  			if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
  		}
  #endif
  
  		}
  	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 (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
  	if (!EC_POINT_is_on_curve(group, P, ctx)) 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)))) 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)) 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;
  
  	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)))) 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)) 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;
  	
  	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)))) 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)) 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;
  	
  	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)))) 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)) 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;
  	
  	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)))) 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)) 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;
  	
  	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)))) ABORT;
  	if (!EC_GROUP_copy(P_521, group)) ABORT;
  
  
  	/* more tests using the last curve */
  
  	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)) 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) */
  
  		BN_init(&scalar3);
  		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);
  	}
  
  
  #if 0
  	timings(P_160, TIMING_BASE_PT, ctx);
  	timings(P_160, TIMING_RAND_PT, ctx);
  	timings(P_160, TIMING_SIMUL, ctx);
  	timings(P_192, TIMING_BASE_PT, ctx);
  	timings(P_192, TIMING_RAND_PT, ctx);
  	timings(P_192, TIMING_SIMUL, ctx);
  	timings(P_224, TIMING_BASE_PT, ctx);
  	timings(P_224, TIMING_RAND_PT, ctx);
  	timings(P_224, TIMING_SIMUL, ctx);
  	timings(P_256, TIMING_BASE_PT, ctx);
  	timings(P_256, TIMING_RAND_PT, ctx);
  	timings(P_256, TIMING_SIMUL, ctx);
  	timings(P_384, TIMING_BASE_PT, ctx);
  	timings(P_384, TIMING_RAND_PT, ctx);
  	timings(P_384, TIMING_SIMUL, ctx);
  	timings(P_521, TIMING_BASE_PT, ctx);
  	timings(P_521, TIMING_RAND_PT, ctx);
  	timings(P_521, TIMING_SIMUL, ctx);
  #endif
  
  
  	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);
  
  	if (P_160) EC_GROUP_free(P_160);
  	if (P_192) EC_GROUP_free(P_192);
  	if (P_224) EC_GROUP_free(P_224);
  	if (P_256) EC_GROUP_free(P_256);
  	if (P_384) EC_GROUP_free(P_384);
  	if (P_521) 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 (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
  	if (!EC_POINT_is_on_curve(group, P, ctx)) 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 (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
  	if (!EC_POINT_is_on_curve(group, P, ctx)) 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)))) 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;
  	unsigned char buf[100];
  	size_t i, len;
  	int k;
  	
  #if 1 /* optional */
  	ctx = BN_CTX_new();
  	if (!ctx) ABORT;
  #endif
  
  	p = BN_new();
  	a = BN_new();
  	b = BN_new();
  	if (!p || !a || !b) 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;
  	if (!EC_GROUP_set_curve_GF2m(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_GF2m(group, p, a, b, ctx)) ABORT;
  
  	fprintf(stdout, "Curve defined by Weierstrass equation\n     y^2 + x*y = x^3 + a*x^2 + 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(0x... means binary polynomial)\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();
  	cof = BN_new();
  	if (!x || !y || !z || !cof) ABORT;
  
  	if (!BN_hex2bn(&x, "6")) ABORT;
  /* Change test based on whether binary point compression is enabled or not. */
  #ifdef OPENSSL_EC_BIN_PT_COMP
  	if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT;
  #else
  	if (!BN_hex2bn(&y, "8")) ABORT;
  	if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
  #endif
  	if (!EC_POINT_is_on_curve(group, Q, ctx))
  		{
  /* Change test based on whether binary point compression is enabled or not. */
  #ifdef OPENSSL_EC_BIN_PT_COMP
  		if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
  #endif
  		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_GF2m(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;
  
  /* Change test based on whether binary point compression is enabled or not. */
  #ifdef OPENSSL_EC_BIN_PT_COMP
  	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]);
  #endif
  	
  	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]);
  	
  /* Change test based on whether binary point compression is enabled or not. */
  #ifdef OPENSSL_EC_BIN_PT_COMP
  	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]);
  #endif
  
  	fprintf(stdout, "\n");
  	
  	if (!EC_POINT_invert(group, P, ctx)) ABORT;
  	if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
  
  
  	/* Curve K-163 (FIPS PUB 186-2, App. 6) */
  	CHAR2_CURVE_TEST
  		(
  		"NIST curve K-163",
  		"0800000000000000000000000000000000000000C9",
  		"1",
  		"1",
  		"02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
  		"0289070FB05D38FF58321F2E800536D538CCDAA3D9",
  		1,
  		"04000000000000000000020108A2E0CC0D99F8A5EF",
  		"2",
  		163,
  		C2_K163
  		);
  
  	/* Curve B-163 (FIPS PUB 186-2, App. 6) */
  	CHAR2_CURVE_TEST
  		(
  		"NIST curve B-163",
  		"0800000000000000000000000000000000000000C9",
  		"1",
  		"020A601907B8C953CA1481EB10512F78744A3205FD",
  		"03F0EBA16286A2D57EA0991168D4994637E8343E36",
  		"00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
  		1,
  		"040000000000000000000292FE77E70C12A4234C33",
  		"2",
  		163,
  		C2_B163
  		);
  
  	/* Curve K-233 (FIPS PUB 186-2, App. 6) */
  	CHAR2_CURVE_TEST
  		(
  		"NIST curve K-233",
  		"020000000000000000000000000000000000000004000000000000000001",
  		"0",
  		"1",
  		"017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
  		"01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
  		0,
  		"008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
  		"4",
  		233,
  		C2_K233
  		);
  
  	/* Curve B-233 (FIPS PUB 186-2, App. 6) */
  	CHAR2_CURVE_TEST
  		(
  		"NIST curve B-233",
  		"020000000000000000000000000000000000000004000000000000000001",
  		"000000000000000000000000000000000000000000000000000000000001",
  		"0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
  		"00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
  		"01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
  		1,
  		"01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
  		"2",
  		233,
  		C2_B233
  		);
  
  	/* Curve K-283 (FIPS PUB 186-2, App. 6) */
  	CHAR2_CURVE_TEST
  		(
  		"NIST curve K-283",
  		"0800000000000000000000000000000000000000000000000000000000000000000010A1",
  		"0",
  		"1",
  		"0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
  		"01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
  		0,
  		"01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
  		"4",
  		283,
  		C2_K283
  		);
  
  	/* Curve B-283 (FIPS PUB 186-2, App. 6) */
  	CHAR2_CURVE_TEST
  		(
  		"NIST curve B-283",
  		"0800000000000000000000000000000000000000000000000000000000000000000010A1",
  		"000000000000000000000000000000000000000000000000000000000000000000000001",
  		"027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
  		"05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
  		"03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
  		1,
  		"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
  		"2",
  		283,
  		C2_B283
  		);
  
  	/* Curve K-409 (FIPS PUB 186-2, App. 6) */
  	CHAR2_CURVE_TEST
  		(
  		"NIST curve K-409",
  		"02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
  		"0",
  		"1",
  		"0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
  		"01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
  		1,
  		"007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
  		"4",
  		409,
  		C2_K409
  		);
  
  	/* Curve B-409 (FIPS PUB 186-2, App. 6) */
  	CHAR2_CURVE_TEST
  		(
  		"NIST curve B-409",
  		"02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
  		"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
  		"0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
  		"015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
  		"0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
  		1,
  		"010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
  		"2",
  		409,
  		C2_B409
  		);
  
  	/* Curve K-571 (FIPS PUB 186-2, App. 6) */
  	CHAR2_CURVE_TEST
  		(
  		"NIST curve K-571",
  		"80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
  		"0",
  		"1",
  		"026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
  		"0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
  		0,
  		"020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
  		"4",
  		571,
  		C2_K571
  		);
  
  	/* Curve B-571 (FIPS PUB 186-2, App. 6) */
  	CHAR2_CURVE_TEST
  		(
  		"NIST curve B-571",
  		"80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
  		"000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
  		"02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
  		"0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
  		"037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
  		1,
  		"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
  		"2",
  		571,
  		C2_B571
  		);
  
  	/* more tests using the last curve */
  
  	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)) 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[3];
  		const BIGNUM *scalars[3];
  	
  		if (EC_POINT_is_at_infinity(group, Q)) ABORT;
  		points[0] = Q;
  		points[1] = Q;
  		points[2] = Q;
  
  		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) */
  
  		if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
  		if (!EC_POINT_is_at_infinity(group, P)) ABORT;
  
  		fprintf(stdout, " ok\n\n");
  	}
  
  
  #if 0
  	timings(C2_K163, TIMING_BASE_PT, ctx);
  	timings(C2_K163, TIMING_RAND_PT, ctx);
  	timings(C2_K163, TIMING_SIMUL, ctx);
  	timings(C2_B163, TIMING_BASE_PT, ctx);
  	timings(C2_B163, TIMING_RAND_PT, ctx);
  	timings(C2_B163, TIMING_SIMUL, ctx);
  	timings(C2_K233, TIMING_BASE_PT, ctx);
  	timings(C2_K233, TIMING_RAND_PT, ctx);
  	timings(C2_K233, TIMING_SIMUL, ctx);
  	timings(C2_B233, TIMING_BASE_PT, ctx);
  	timings(C2_B233, TIMING_RAND_PT, ctx);
  	timings(C2_B233, TIMING_SIMUL, ctx);
  	timings(C2_K283, TIMING_BASE_PT, ctx);
  	timings(C2_K283, TIMING_RAND_PT, ctx);
  	timings(C2_K283, TIMING_SIMUL, ctx);
  	timings(C2_B283, TIMING_BASE_PT, ctx);
  	timings(C2_B283, TIMING_RAND_PT, ctx);
  	timings(C2_B283, TIMING_SIMUL, ctx);
  	timings(C2_K409, TIMING_BASE_PT, ctx);
  	timings(C2_K409, TIMING_RAND_PT, ctx);
  	timings(C2_K409, TIMING_SIMUL, ctx);
  	timings(C2_B409, TIMING_BASE_PT, ctx);
  	timings(C2_B409, TIMING_RAND_PT, ctx);
  	timings(C2_B409, TIMING_SIMUL, ctx);
  	timings(C2_K571, TIMING_BASE_PT, ctx);
  	timings(C2_K571, TIMING_RAND_PT, ctx);
  	timings(C2_K571, TIMING_SIMUL, ctx);
  	timings(C2_B571, TIMING_BASE_PT, ctx);
  	timings(C2_B571, TIMING_RAND_PT, ctx);
  	timings(C2_B571, TIMING_SIMUL, ctx);
  #endif
  
  
  	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); BN_free(cof);
  
  	if (C2_K163) EC_GROUP_free(C2_K163);
  	if (C2_B163) EC_GROUP_free(C2_B163);
  	if (C2_K233) EC_GROUP_free(C2_K233);
  	if (C2_B233) EC_GROUP_free(C2_B233);
  	if (C2_K283) EC_GROUP_free(C2_K283);
  	if (C2_B283) EC_GROUP_free(C2_B283);
  	if (C2_K409) EC_GROUP_free(C2_K409);
  	if (C2_B409) EC_GROUP_free(C2_B409);
  	if (C2_K571) EC_GROUP_free(C2_K571);
  	if (C2_B571) EC_GROUP_free(C2_B571);
  
  	}
  #endif
  
  static void internal_curve_test(void)
  	{
  	EC_builtin_curve *curves = NULL;
  	size_t crv_len = 0, n = 0;
  	int    ok = 1;
  
  	crv_len = EC_get_builtin_curves(NULL, 0);
  
  	curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len);
  
  	if (curves == NULL)
  		return;
  
  	if (!EC_get_builtin_curves(curves, crv_len))
  		{
  		OPENSSL_free(curves);
  		return;
  		}
  
  	fprintf(stdout, "testing internal curves: ");
  		
  	for (n = 0; n < crv_len; n++)
  		{
  		EC_GROUP *group = NULL;
  		int nid = curves[n].nid;
  		if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL)
  			{
  			ok = 0;
  			fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with"
  				" curve %s\n", OBJ_nid2sn(nid));
  			/* try next curve */
  			continue;
  			}
  		if (!EC_GROUP_check(group, NULL))
  			{
  			ok = 0;
  			fprintf(stdout, "\nEC_GROUP_check() failed with"
  				" curve %s\n", OBJ_nid2sn(nid));
  			EC_GROUP_free(group);
  			/* try the next curve */
  			continue;
  			}
  		fprintf(stdout, ".");
  		fflush(stdout);
  		EC_GROUP_free(group);
  		}
  	if (ok)
  		fprintf(stdout, " ok\n\n");
  	else
  		{
  		fprintf(stdout, " failed\n\n");
  		ABORT;
  		}
  	OPENSSL_free(curves);
  	return;
  	}
  
  #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
  /* nistp_test_params contains magic numbers for testing our optimized
   * implementations of several NIST curves with characteristic > 3. */
  struct nistp_test_params
  	{
  	const EC_METHOD* (*meth) ();
  	int degree;
  	/* Qx, Qy and D are taken from
  	 * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
  	 * Otherwise, values are standard curve parameters from FIPS 180-3 */
  	const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d;
  	};
  
  static const struct nistp_test_params nistp_tests_params[] =
  	{
  		{
  		/* P-224 */
  		EC_GFp_nistp224_method,
  		224,
  		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", /* p */
  		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", /* a */
  		"B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", /* b */
  		"E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E", /* Qx */
  		"4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555", /* Qy */
  		"B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", /* Gx */
  		"BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34", /* Gy */
  		"FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", /* order */
  		"3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8", /* d */
  		},
  		{
  		/* P-256 */
  		EC_GFp_nistp256_method,
  		256,
  		"ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", /* p */
  		"ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", /* a */
  		"5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", /* b */
  		"b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19", /* Qx */
  		"3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09", /* Qy */
  		"6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", /* Gx */
  		"4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", /* Gy */
  		"ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", /* order */
  		"c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96", /* d */
  		},
  		{
  		/* P-521 */
  		EC_GFp_nistp521_method,
  		521,
  		"1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", /* p */
  		"1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc", /* a */
  		"051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", /* b */
  		"0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4", /* Qx */
  		"0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e", /* Qy */
  		"c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", /* Gx */
  		"11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", /* Gy */
  		"1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409", /* order */
  		"0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722", /* d */
  		},
  	};
  
  void nistp_single_test(const struct nistp_test_params *test)
  	{
  	BN_CTX *ctx;
  	BIGNUM *p, *a, *b, *x, *y, *n, *m, *order;
  	EC_GROUP *NISTP;
  	EC_POINT *G, *P, *Q, *Q_CHECK;
  
  	fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n", test->degree);
  	ctx = BN_CTX_new();
  	p = BN_new();
  	a = BN_new();
  	b = BN_new();
  	x = BN_new(); y = BN_new();
  	m = BN_new(); n = BN_new(); order = BN_new();
  
  	NISTP = EC_GROUP_new(test->meth());
  	if(!NISTP) ABORT;
  	if (!BN_hex2bn(&p, test->p)) ABORT;
  	if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
  	if (!BN_hex2bn(&a, test->a)) ABORT;
  	if (!BN_hex2bn(&b, test->b)) ABORT;
  	if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx)) ABORT;
  	G = EC_POINT_new(NISTP);
  	P = EC_POINT_new(NISTP);
  	Q = EC_POINT_new(NISTP);
  	Q_CHECK = EC_POINT_new(NISTP);
  	if(!BN_hex2bn(&x, test->Qx)) ABORT;
  	if(!BN_hex2bn(&y, test->Qy)) ABORT;
  	if(!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx)) ABORT;
  	if (!BN_hex2bn(&x, test->Gx)) ABORT;
  	if (!BN_hex2bn(&y, test->Gy)) ABORT;
  	if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx)) ABORT;
  	if (!BN_hex2bn(&order, test->order)) ABORT;
  	if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT;
  
  	fprintf(stdout, "verify degree ... ");
  	if (EC_GROUP_get_degree(NISTP) != test->degree) ABORT;
  	fprintf(stdout, "ok\n");
  
  	fprintf(stdout, "NIST test vectors ... ");
  	if (!BN_hex2bn(&n, test->d)) ABORT;
  	/* fixed point multiplication */
  	EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
  	if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
  	/* random point multiplication */
  	EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
  	if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
  
  	/* set generator to P = 2*G, where G is the standard generator */
  	if (!EC_POINT_dbl(NISTP, P, G, ctx)) ABORT;
  	if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one())) ABORT;
  	/* set the scalar to m=n/2, where n is the NIST test scalar */
  	if (!BN_rshift(m, n, 1)) ABORT;
  
  	/* test the non-standard generator */
  	/* fixed point multiplication */
  	EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
  	if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
  	/* random point multiplication */
  	EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
  	if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
  
  	/* now repeat all tests with precomputation */
  	if (!EC_GROUP_precompute_mult(NISTP, ctx)) ABORT;
  
  	/* fixed point multiplication */
  	EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
  	if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
  	/* random point multiplication */
  	EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
  	if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
  
  	/* reset generator */
  	if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT;
  	/* fixed point multiplication */
  	EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
  	if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
  	/* random point multiplication */
  	EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
  	if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
  
  	fprintf(stdout, "ok\n");
  	group_order_tests(NISTP);
  #if 0
  	timings(NISTP, TIMING_BASE_PT, ctx);
  	timings(NISTP, TIMING_RAND_PT, ctx);
  #endif
  	EC_GROUP_free(NISTP);
  	EC_POINT_free(G);
  	EC_POINT_free(P);
  	EC_POINT_free(Q);
  	EC_POINT_free(Q_CHECK);
  	BN_free(n);
  	BN_free(m);
  	BN_free(p);
  	BN_free(a);
  	BN_free(b);
  	BN_free(x);
  	BN_free(y);
  	BN_free(order);
  	BN_CTX_free(ctx);
  	}
  
  void nistp_tests()
  	{
  	unsigned i;
  
  	for (i = 0; i < sizeof(nistp_tests_params) / sizeof(struct nistp_test_params); i++)
  		{
  		nistp_single_test(&nistp_tests_params[i]);
  		}
  	}
  #endif
  
  static const char rnd_seed[] = "string to make the random number generator think it has entropy";
  
  int main(int argc, char *argv[])
  	{	
  	
  	/* enable memory leak checking unless explicitly disabled */
  	if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
  		{
  		CRYPTO_malloc_debug_init();
  		CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
  		}
  	else
  		{
  		/* OPENSSL_DEBUG_MEMORY=off */
  		CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
  		}
  	CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
  	ERR_load_crypto_strings();
  
  	RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
  
  	prime_field_tests();
  	puts("");
  #ifndef OPENSSL_NO_EC2M
  	char2_field_tests();
  #endif
  #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
  	nistp_tests();
  #endif
  	/* test the internal curves */
  	internal_curve_test();
  
  #ifndef OPENSSL_NO_ENGINE
  	ENGINE_cleanup();
  #endif
  	CRYPTO_cleanup_all_ex_data();
  	ERR_free_strings();
  	ERR_remove_thread_state(NULL);
  	CRYPTO_mem_leaks_fp(stderr);
  	
  	return 0;
  	}
  #endif
  