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ectest.c

/* 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>

#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)

void prime_field_tests(void);
void char2_field_tests(void);
void internal_curve_test(void);

#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

void prime_field_tests()
      {     
      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 octect 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 octect 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 octect 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");
      
      fprintf(stdout, "verify group order ...");
      fflush(stdout);
      if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
      if (!EC_POINT_mul(group, Q, z, 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, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, " ok\n");

      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");
      
      fprintf(stdout, "verify group order ...");
      fflush(stdout);
      if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
      if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, ".");
      fflush(stdout);
#if 0
      if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
      if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, " ok\n");

      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");
      
      fprintf(stdout, "verify group order ...");
      fflush(stdout);
      if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
      if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, ".");
      fflush(stdout);
#if 0
      if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
      if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, " ok\n");

      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");
      
      fprintf(stdout, "verify group order ...");
      fflush(stdout);
      if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
      if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, ".");
      fflush(stdout);
#if 0
      if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
      if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, " ok\n");

      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");
      
      fprintf(stdout, "verify group order ...");
      fflush(stdout);
      if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
      if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, ".");
      fflush(stdout);
#if 0
      if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
      if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, " ok\n");

      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");
      
      fprintf(stdout, "verify group order ...");
      fflush(stdout);
      if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
      if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, ".");
      fflush(stdout);
#if 0
      if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
      if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
      fprintf(stdout, " ok\n");

      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 (!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"); \
      fprintf(stdout, "verify group order ..."); \
      fflush(stdout); \
      if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \
      if (!EC_POINT_mul(group, Q, z, 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, z, NULL, NULL, ctx)) ABORT; \
      if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \
      fprintf(stdout, " ok\n"); \
      if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
      if (!EC_GROUP_copy(_variable, group)) ABORT;

void char2_field_tests()
      {     
      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);

      }

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");
      else
            fprintf(stdout, " failed\n");
      OPENSSL_free(curves);
      return;
      }

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("");
      char2_field_tests();
      /* test the internal curves */
      internal_curve_test();

#ifndef OPENSSL_NO_ENGINE
      ENGINE_cleanup();
#endif
      CRYPTO_cleanup_all_ex_data();
      ERR_free_strings();
      ERR_remove_state(0);
      CRYPTO_mem_leaks_fp(stderr);
      
      return 0;
      }
#endif

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