boringssl/crypto/fipsmodule/ec/ec.c

/* Originally written by Bodo Moeller for the OpenSSL project.
 * ====================================================================
 * Copyright (c) 1998-2005 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 <openssl/ec.h>

#include <assert.h>
#include <string.h>

#include <openssl/bn.h>
#include <openssl/err.h>
#include <openssl/mem.h>
#include <openssl/nid.h>

#include "internal.h"
#include "../../internal.h"
#include "../delocate.h"


static const uint8_t kP224Params[6 * 28] = {
    // p
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
    0x00, 0x00, 0x00, 0x01,
    // a
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFE,
    // b
    0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, 0x32, 0x56,
    0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, 0x27, 0x0B, 0x39, 0x43,
    0x23, 0x55, 0xFF, 0xB4,
    // x
    0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, 0x90, 0xB9,
    0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xD6,
    0x11, 0x5C, 0x1D, 0x21,
    // y
    0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, 0xdf, 0xe6,
    0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, 0x44, 0xd5, 0x81, 0x99,
    0x85, 0x00, 0x7e, 0x34,
    // order
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0x16, 0xA2, 0xE0, 0xB8, 0xF0, 0x3E, 0x13, 0xDD, 0x29, 0x45,
    0x5C, 0x5C, 0x2A, 0x3D,
};

static const uint8_t kP256Params[6 * 32] = {
    // p
    0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00,
    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    // a
    0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00,
    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC,
    // b
    0x5A, 0xC6, 0x35, 0xD8, 0xAA, 0x3A, 0x93, 0xE7, 0xB3, 0xEB, 0xBD, 0x55,
    0x76, 0x98, 0x86, 0xBC, 0x65, 0x1D, 0x06, 0xB0, 0xCC, 0x53, 0xB0, 0xF6,
    0x3B, 0xCE, 0x3C, 0x3E, 0x27, 0xD2, 0x60, 0x4B,
    // x
    0x6B, 0x17, 0xD1, 0xF2, 0xE1, 0x2C, 0x42, 0x47, 0xF8, 0xBC, 0xE6, 0xE5,
    0x63, 0xA4, 0x40, 0xF2, 0x77, 0x03, 0x7D, 0x81, 0x2D, 0xEB, 0x33, 0xA0,
    0xF4, 0xA1, 0x39, 0x45, 0xD8, 0x98, 0xC2, 0x96,
    // y
    0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, 0x8e, 0xe7, 0xeb, 0x4a,
    0x7c, 0x0f, 0x9e, 0x16, 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce,
    0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5,
    // order
    0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xBC, 0xE6, 0xFA, 0xAD, 0xA7, 0x17, 0x9E, 0x84,
    0xF3, 0xB9, 0xCA, 0xC2, 0xFC, 0x63, 0x25, 0x51,
};

static const uint8_t kP384Params[6 * 48] = {
    // p
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF,
    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF,
    // a
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF,
    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFC,
    // b
    0xB3, 0x31, 0x2F, 0xA7, 0xE2, 0x3E, 0xE7, 0xE4, 0x98, 0x8E, 0x05, 0x6B,
    0xE3, 0xF8, 0x2D, 0x19, 0x18, 0x1D, 0x9C, 0x6E, 0xFE, 0x81, 0x41, 0x12,
    0x03, 0x14, 0x08, 0x8F, 0x50, 0x13, 0x87, 0x5A, 0xC6, 0x56, 0x39, 0x8D,
    0x8A, 0x2E, 0xD1, 0x9D, 0x2A, 0x85, 0xC8, 0xED, 0xD3, 0xEC, 0x2A, 0xEF,
    // x
    0xAA, 0x87, 0xCA, 0x22, 0xBE, 0x8B, 0x05, 0x37, 0x8E, 0xB1, 0xC7, 0x1E,
    0xF3, 0x20, 0xAD, 0x74, 0x6E, 0x1D, 0x3B, 0x62, 0x8B, 0xA7, 0x9B, 0x98,
    0x59, 0xF7, 0x41, 0xE0, 0x82, 0x54, 0x2A, 0x38, 0x55, 0x02, 0xF2, 0x5D,
    0xBF, 0x55, 0x29, 0x6C, 0x3A, 0x54, 0x5E, 0x38, 0x72, 0x76, 0x0A, 0xB7,
    // y
    0x36, 0x17, 0xde, 0x4a, 0x96, 0x26, 0x2c, 0x6f, 0x5d, 0x9e, 0x98, 0xbf,
    0x92, 0x92, 0xdc, 0x29, 0xf8, 0xf4, 0x1d, 0xbd, 0x28, 0x9a, 0x14, 0x7c,
    0xe9, 0xda, 0x31, 0x13, 0xb5, 0xf0, 0xb8, 0xc0, 0x0a, 0x60, 0xb1, 0xce,
    0x1d, 0x7e, 0x81, 0x9d, 0x7a, 0x43, 0x1d, 0x7c, 0x90, 0xea, 0x0e, 0x5f,
    // order
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xC7, 0x63, 0x4D, 0x81, 0xF4, 0x37, 0x2D, 0xDF, 0x58, 0x1A, 0x0D, 0xB2,
    0x48, 0xB0, 0xA7, 0x7A, 0xEC, 0xEC, 0x19, 0x6A, 0xCC, 0xC5, 0x29, 0x73,
};

static const uint8_t kP521Params[6 * 66] = {
    // p
    0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    // a
    0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC,
    // b
    0x00, 0x51, 0x95, 0x3E, 0xB9, 0x61, 0x8E, 0x1C, 0x9A, 0x1F, 0x92, 0x9A,
    0x21, 0xA0, 0xB6, 0x85, 0x40, 0xEE, 0xA2, 0xDA, 0x72, 0x5B, 0x99, 0xB3,
    0x15, 0xF3, 0xB8, 0xB4, 0x89, 0x91, 0x8E, 0xF1, 0x09, 0xE1, 0x56, 0x19,
    0x39, 0x51, 0xEC, 0x7E, 0x93, 0x7B, 0x16, 0x52, 0xC0, 0xBD, 0x3B, 0xB1,
    0xBF, 0x07, 0x35, 0x73, 0xDF, 0x88, 0x3D, 0x2C, 0x34, 0xF1, 0xEF, 0x45,
    0x1F, 0xD4, 0x6B, 0x50, 0x3F, 0x00,
    // x
    0x00, 0xC6, 0x85, 0x8E, 0x06, 0xB7, 0x04, 0x04, 0xE9, 0xCD, 0x9E, 0x3E,
    0xCB, 0x66, 0x23, 0x95, 0xB4, 0x42, 0x9C, 0x64, 0x81, 0x39, 0x05, 0x3F,
    0xB5, 0x21, 0xF8, 0x28, 0xAF, 0x60, 0x6B, 0x4D, 0x3D, 0xBA, 0xA1, 0x4B,
    0x5E, 0x77, 0xEF, 0xE7, 0x59, 0x28, 0xFE, 0x1D, 0xC1, 0x27, 0xA2, 0xFF,
    0xA8, 0xDE, 0x33, 0x48, 0xB3, 0xC1, 0x85, 0x6A, 0x42, 0x9B, 0xF9, 0x7E,
    0x7E, 0x31, 0xC2, 0xE5, 0xBD, 0x66,
    // y
    0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, 0xc0, 0x04, 0x5c, 0x8a,
    0x5f, 0xb4, 0x2c, 0x7d, 0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b,
    0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e, 0x66, 0x2c, 0x97, 0xee,
    0x72, 0x99, 0x5e, 0xf4, 0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad,
    0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe,
    0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50,
    // order
    0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
    0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFA, 0x51, 0x86,
    0x87, 0x83, 0xBF, 0x2F, 0x96, 0x6B, 0x7F, 0xCC, 0x01, 0x48, 0xF7, 0x09,
    0xA5, 0xD0, 0x3B, 0xB5, 0xC9, 0xB8, 0x89, 0x9C, 0x47, 0xAE, 0xBB, 0x6F,
    0xB7, 0x1E, 0x91, 0x38, 0x64, 0x09,
};

// MSan appears to have a bug that causes code to be miscompiled in opt mode.
// While that is being looked at, don't run the uint128_t code under MSan.
#if defined(OPENSSL_64_BIT) && !defined(OPENSSL_WINDOWS) && \
    !defined(MEMORY_SANITIZER)
#define BORINGSSL_USE_INT128_CODE
#endif

DEFINE_METHOD_FUNCTION(struct built_in_curves, OPENSSL_built_in_curves) {
  // 1.3.132.0.35
  static const uint8_t kOIDP521[] = {0x2b, 0x81, 0x04, 0x00, 0x23};
  out->curves[0].nid = NID_secp521r1;
  out->curves[0].oid = kOIDP521;
  out->curves[0].oid_len = sizeof(kOIDP521);
  out->curves[0].comment = "NIST P-521";
  out->curves[0].param_len = 66;
  out->curves[0].params = kP521Params;
  out->curves[0].method = EC_GFp_mont_method();

  // 1.3.132.0.34
  static const uint8_t kOIDP384[] = {0x2b, 0x81, 0x04, 0x00, 0x22};
  out->curves[1].nid = NID_secp384r1;
  out->curves[1].oid = kOIDP384;
  out->curves[1].oid_len = sizeof(kOIDP384);
  out->curves[1].comment = "NIST P-384";
  out->curves[1].param_len = 48;
  out->curves[1].params = kP384Params;
  out->curves[1].method = EC_GFp_mont_method();

  // 1.2.840.10045.3.1.7
  static const uint8_t kOIDP256[] = {0x2a, 0x86, 0x48, 0xce,
                                     0x3d, 0x03, 0x01, 0x07};
  out->curves[2].nid = NID_X9_62_prime256v1;
  out->curves[2].oid = kOIDP256;
  out->curves[2].oid_len = sizeof(kOIDP256);
  out->curves[2].comment = "NIST P-256";
  out->curves[2].param_len = 32;
  out->curves[2].params = kP256Params;
  out->curves[2].method =
#if defined(BORINGSSL_USE_INT128_CODE)
#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
    !defined(OPENSSL_SMALL)
      EC_GFp_nistz256_method();
#else
      EC_GFp_nistp256_method();
#endif
#else
      EC_GFp_mont_method();
#endif

  // 1.3.132.0.33
  static const uint8_t kOIDP224[] = {0x2b, 0x81, 0x04, 0x00, 0x21};
  out->curves[3].nid = NID_secp224r1;
  out->curves[3].oid = kOIDP224;
  out->curves[3].oid_len = sizeof(kOIDP224);
  out->curves[3].comment = "NIST P-224";
  out->curves[3].param_len = 28;
  out->curves[3].params = kP224Params;
  out->curves[3].method =
#if defined(BORINGSSL_USE_INT128_CODE) && !defined(OPENSSL_SMALL)
      EC_GFp_nistp224_method();
#else
      EC_GFp_mont_method();
#endif
}

// built_in_curve_scalar_field_monts contains Montgomery contexts for
// performing inversions in the scalar fields of each of the built-in
// curves. It's protected by |built_in_curve_scalar_field_monts_once|.
DEFINE_LOCAL_DATA(BN_MONT_CTX **, built_in_curve_scalar_field_monts) {
  const struct built_in_curves *const curves = OPENSSL_built_in_curves();

  BN_MONT_CTX **monts =
      OPENSSL_malloc(sizeof(BN_MONT_CTX *) * OPENSSL_NUM_BUILT_IN_CURVES);
  if (monts == NULL) {
    return;
  }

  OPENSSL_memset(monts, 0, sizeof(BN_MONT_CTX *) * OPENSSL_NUM_BUILT_IN_CURVES);

  BIGNUM *order = BN_new();
  BN_CTX *bn_ctx = BN_CTX_new();
  BN_MONT_CTX *mont_ctx = NULL;

  if (bn_ctx == NULL ||
      order == NULL) {
    goto err;
  }

  for (size_t i = 0; i < OPENSSL_NUM_BUILT_IN_CURVES; i++) {
    const struct built_in_curve *curve = &curves->curves[i];
    const unsigned param_len = curve->param_len;
    const uint8_t *params = curve->params;

    mont_ctx = BN_MONT_CTX_new();
    if (mont_ctx == NULL) {
      goto err;
    }

    if (!BN_bin2bn(params + 5 * param_len, param_len, order) ||
        !BN_MONT_CTX_set(mont_ctx, order, bn_ctx)) {
      goto err;
    }

    monts[i] = mont_ctx;
    mont_ctx = NULL;
  }

  *out = monts;
  goto done;

err:
  BN_MONT_CTX_free(mont_ctx);
  for (size_t i = 0; i < OPENSSL_NUM_BUILT_IN_CURVES; i++) {
    BN_MONT_CTX_free(monts[i]);
  }
  OPENSSL_free((BN_MONT_CTX**) monts);

done:
  BN_free(order);
  BN_CTX_free(bn_ctx);
}

EC_GROUP *ec_group_new(const EC_METHOD *meth) {
  EC_GROUP *ret;

  if (meth == NULL) {
    OPENSSL_PUT_ERROR(EC, EC_R_SLOT_FULL);
    return NULL;
  }

  if (meth->group_init == 0) {
    OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
    return NULL;
  }

  ret = OPENSSL_malloc(sizeof(EC_GROUP));
  if (ret == NULL) {
    OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
    return NULL;
  }
  OPENSSL_memset(ret, 0, sizeof(EC_GROUP));

  ret->references = 1;
  ret->meth = meth;
  BN_init(&ret->order);

  if (!meth->group_init(ret)) {
    OPENSSL_free(ret);
    return NULL;
  }

  return ret;
}

EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a,
                                 const BIGNUM *b, BN_CTX *ctx) {
  EC_GROUP *ret = ec_group_new(EC_GFp_mont_method());
  if (ret == NULL) {
    return NULL;
  }

  if (ret->meth->group_set_curve == 0) {
    OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
    return 0;
  }
  if (!ret->meth->group_set_curve(ret, p, a, b, ctx)) {
    EC_GROUP_free(ret);
    return NULL;
  }
  return ret;
}

int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
                           const BIGNUM *order, const BIGNUM *cofactor) {
  if (group->curve_name != NID_undef || group->generator != NULL) {
    // |EC_GROUP_set_generator| may only be used with |EC_GROUP|s returned by
    // |EC_GROUP_new_curve_GFp| and may only used once on each group.
    return 0;
  }

  // Require a cofactor of one for custom curves, which implies prime order.
  if (!BN_is_one(cofactor)) {
    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COFACTOR);
    return 0;
  }

  group->generator = EC_POINT_new(group);
  return group->generator != NULL &&
         EC_POINT_copy(group->generator, generator) &&
         BN_copy(&group->order, order);
}

static EC_GROUP *ec_group_new_from_data(unsigned built_in_index) {
  const struct built_in_curves *const curves = OPENSSL_built_in_curves();
  const struct built_in_curve *curve = &curves->curves[built_in_index];
  EC_GROUP *group = NULL;
  EC_POINT *P = NULL;
  BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL;
  int ok = 0;

  BN_CTX *ctx = BN_CTX_new();
  if (ctx == NULL) {
    OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
    goto err;
  }

  const unsigned param_len = curve->param_len;
  const uint8_t *params = curve->params;

  if (!(p = BN_bin2bn(params + 0 * param_len, param_len, NULL)) ||
      !(a = BN_bin2bn(params + 1 * param_len, param_len, NULL)) ||
      !(b = BN_bin2bn(params + 2 * param_len, param_len, NULL))) {
    OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
    goto err;
  }

  group = ec_group_new(curve->method);
  if (group == NULL ||
      !group->meth->group_set_curve(group, p, a, b, ctx)) {
    OPENSSL_PUT_ERROR(EC, ERR_R_EC_LIB);
    goto err;
  }

  if ((P = EC_POINT_new(group)) == NULL) {
    OPENSSL_PUT_ERROR(EC, ERR_R_EC_LIB);
    goto err;
  }

  if (!(x = BN_bin2bn(params + 3 * param_len, param_len, NULL)) ||
      !(y = BN_bin2bn(params + 4 * param_len, param_len, NULL))) {
    OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
    goto err;
  }

  if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) {
    OPENSSL_PUT_ERROR(EC, ERR_R_EC_LIB);
    goto err;
  }
  if (!BN_bin2bn(params + 5 * param_len, param_len, &group->order)) {
    OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
    goto err;
  }

  const BN_MONT_CTX **monts = *built_in_curve_scalar_field_monts();
  if (monts != NULL) {
    group->order_mont = monts[built_in_index];
  }

  group->generator = P;
  P = NULL;
  ok = 1;

err:
  if (!ok) {
    EC_GROUP_free(group);
    group = NULL;
  }
  EC_POINT_free(P);
  BN_CTX_free(ctx);
  BN_free(p);
  BN_free(a);
  BN_free(b);
  BN_free(x);
  BN_free(y);
  return group;
}

EC_GROUP *EC_GROUP_new_by_curve_name(int nid) {
  const struct built_in_curves *const curves = OPENSSL_built_in_curves();
  EC_GROUP *ret = NULL;

  for (size_t i = 0; i < OPENSSL_NUM_BUILT_IN_CURVES; i++) {
    const struct built_in_curve *curve = &curves->curves[i];
    if (curve->nid == nid) {
      ret = ec_group_new_from_data(i);
      break;
    }
  }

  if (ret == NULL) {
    OPENSSL_PUT_ERROR(EC, EC_R_UNKNOWN_GROUP);
    return NULL;
  }

  ret->curve_name = nid;
  return ret;
}

void EC_GROUP_free(EC_GROUP *group) {
  if (!group ||
      !CRYPTO_refcount_dec_and_test_zero(&group->references)) {
    return;
  }

  if (group->meth->group_finish != NULL) {
    group->meth->group_finish(group);
  }

  EC_POINT_free(group->generator);
  BN_free(&group->order);

  OPENSSL_free(group);
}

const BN_MONT_CTX *ec_group_get_order_mont(const EC_GROUP *group) {
  return group->order_mont;
}

EC_GROUP *EC_GROUP_dup(const EC_GROUP *a) {
  if (a == NULL) {
    return NULL;
  }

  // Groups are logically immutable (but for |EC_GROUP_set_generator| which must
  // be called early on), so we simply take a reference.
  EC_GROUP *group = (EC_GROUP *)a;
  CRYPTO_refcount_inc(&group->references);
  return group;
}

int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ignored) {
  return a->curve_name == NID_undef ||
         b->curve_name == NID_undef ||
         a->curve_name != b->curve_name;
}

const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group) {
  return group->generator;
}

const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group) {
  assert(!BN_is_zero(&group->order));
  return &group->order;
}

int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx) {
  if (BN_copy(order, EC_GROUP_get0_order(group)) == NULL) {
    return 0;
  }
  return 1;
}

int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor,
                          BN_CTX *ctx) {
  // All |EC_GROUP|s have cofactor 1.
  return BN_set_word(cofactor, 1);
}

int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *out_p, BIGNUM *out_a,
                           BIGNUM *out_b, BN_CTX *ctx) {
  return ec_GFp_simple_group_get_curve(group, out_p, out_a, out_b, ctx);
}

int EC_GROUP_get_curve_name(const EC_GROUP *group) { return group->curve_name; }

unsigned EC_GROUP_get_degree(const EC_GROUP *group) {
  return ec_GFp_simple_group_get_degree(group);
}

EC_POINT *EC_POINT_new(const EC_GROUP *group) {
  EC_POINT *ret;

  if (group == NULL) {
    OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER);
    return NULL;
  }

  ret = OPENSSL_malloc(sizeof *ret);
  if (ret == NULL) {
    OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
    return NULL;
  }

  ret->meth = group->meth;

  if (!ec_GFp_simple_point_init(ret)) {
    OPENSSL_free(ret);
    return NULL;
  }

  return ret;
}

void EC_POINT_free(EC_POINT *point) {
  if (!point) {
    return;
  }

  ec_GFp_simple_point_finish(point);

  OPENSSL_free(point);
}

void EC_POINT_clear_free(EC_POINT *point) { EC_POINT_free(point); }

int EC_POINT_copy(EC_POINT *dest, const EC_POINT *src) {
  if (dest->meth != src->meth) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  if (dest == src) {
    return 1;
  }
  return ec_GFp_simple_point_copy(dest, src);
}

EC_POINT *EC_POINT_dup(const EC_POINT *a, const EC_GROUP *group) {
  if (a == NULL) {
    return NULL;
  }

  EC_POINT *ret = EC_POINT_new(group);
  if (ret == NULL ||
      !EC_POINT_copy(ret, a)) {
    EC_POINT_free(ret);
    return NULL;
  }

  return ret;
}

int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point) {
  if (group->meth != point->meth) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  return ec_GFp_simple_point_set_to_infinity(group, point);
}

int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) {
  if (group->meth != point->meth) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  return ec_GFp_simple_is_at_infinity(group, point);
}

int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
                         BN_CTX *ctx) {
  if (group->meth != point->meth) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  return ec_GFp_simple_is_on_curve(group, point, ctx);
}

int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b,
                 BN_CTX *ctx) {
  if ((group->meth != a->meth) || (a->meth != b->meth)) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return -1;
  }
  return ec_GFp_simple_cmp(group, a, b, ctx);
}

int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) {
  if (group->meth != point->meth) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  return ec_GFp_simple_make_affine(group, point, ctx);
}

int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[],
                          BN_CTX *ctx) {
  for (size_t i = 0; i < num; i++) {
    if (group->meth != points[i]->meth) {
      OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
      return 0;
    }
  }
  return ec_GFp_simple_points_make_affine(group, num, points, ctx);
}

int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
                                        const EC_POINT *point, BIGNUM *x,
                                        BIGNUM *y, BN_CTX *ctx) {
  if (group->meth->point_get_affine_coordinates == 0) {
    OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
    return 0;
  }
  if (group->meth != point->meth) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  return group->meth->point_get_affine_coordinates(group, point, x, y, ctx);
}

int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
                                        const BIGNUM *x, const BIGNUM *y,
                                        BN_CTX *ctx) {
  if (group->meth != point->meth) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  if (!ec_GFp_simple_point_set_affine_coordinates(group, point, x, y, ctx)) {
    return 0;
  }

  if (!EC_POINT_is_on_curve(group, point, ctx)) {
    OPENSSL_PUT_ERROR(EC, EC_R_POINT_IS_NOT_ON_CURVE);
    return 0;
  }

  return 1;
}

int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
                 const EC_POINT *b, BN_CTX *ctx) {
  if ((group->meth != r->meth) || (r->meth != a->meth) ||
      (a->meth != b->meth)) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  return ec_GFp_simple_add(group, r, a, b, ctx);
}


int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
                 BN_CTX *ctx) {
  if ((group->meth != r->meth) || (r->meth != a->meth)) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  return ec_GFp_simple_dbl(group, r, a, ctx);
}


int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx) {
  if (group->meth != a->meth) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  return ec_GFp_simple_invert(group, a, ctx);
}

int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
                 const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx) {
  // Previously, this function set |r| to the point at infinity if there was
  // nothing to multiply. But, nobody should be calling this function with
  // nothing to multiply in the first place.
  if ((g_scalar == NULL && p_scalar == NULL) ||
      ((p == NULL) != (p_scalar == NULL)))  {
    OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER);
    return 0;
  }

  if (group->meth != r->meth ||
      (p != NULL && group->meth != p->meth)) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }

  return group->meth->mul(group, r, g_scalar, p, p_scalar, ctx);
}

int ec_point_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
                                             EC_POINT *point, const BIGNUM *x,
                                             const BIGNUM *y, const BIGNUM *z,
                                             BN_CTX *ctx) {
  if (group->meth != point->meth) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  return ec_GFp_simple_set_Jprojective_coordinates_GFp(group, point, x, y, z,
                                                       ctx);
}

void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag) {}

const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group) {
  return NULL;
}

int EC_METHOD_get_field_type(const EC_METHOD *meth) {
  return NID_X9_62_prime_field;
}

void EC_GROUP_set_point_conversion_form(EC_GROUP *group,
                                        point_conversion_form_t form) {
  if (form != POINT_CONVERSION_UNCOMPRESSED) {
    abort();
  }
}

size_t EC_get_builtin_curves(EC_builtin_curve *out_curves,
                             size_t max_num_curves) {
  const struct built_in_curves *const curves = OPENSSL_built_in_curves();

  for (size_t i = 0; i < max_num_curves && i < OPENSSL_NUM_BUILT_IN_CURVES;
       i++) {
    out_curves[i].comment = curves->curves[i].comment;
    out_curves[i].nid = curves->curves[i].nid;
  }

  return OPENSSL_NUM_BUILT_IN_CURVES;
}