oct.c

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/* 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 <openssl/bn.h>
#include <openssl/err.h>
 
#include "internal.h"
 
 
size_t ec_point_to_bytes(const EC_GROUP *group, const EC_AFFINE *point,
                         point_conversion_form_t form, uint8_t *buf,
                         size_t len) {
  if (form != POINT_CONVERSION_COMPRESSED &&
      form != POINT_CONVERSION_UNCOMPRESSED) {
    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FORM);
    return 0;
  }
 
  const size_t field_len = BN_num_bytes(&group->field);
  size_t output_len = 1 /* type byte */ + field_len;
  if (form == POINT_CONVERSION_UNCOMPRESSED) {
    // Uncompressed points have a second coordinate.
    output_len += field_len;
  }
 
  // if 'buf' is NULL, just return required length
  if (buf != NULL) {
    if (len < output_len) {
      OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
      return 0;
    }
 
    size_t field_len_out;
    ec_felem_to_bytes(group, buf + 1, &field_len_out, &point->X);
    assert(field_len_out == field_len);
 
    if (form == POINT_CONVERSION_UNCOMPRESSED) {
      ec_felem_to_bytes(group, buf + 1 + field_len, &field_len_out, &point->Y);
      assert(field_len_out == field_len);
      buf[0] = form;
    } else {
      uint8_t y_buf[EC_MAX_BYTES];
      ec_felem_to_bytes(group, y_buf, &field_len_out, &point->Y);
      buf[0] = form + (y_buf[field_len_out - 1] & 1);
    }
  }
 
  return output_len;
}
 
int ec_point_from_uncompressed(const EC_GROUP *group, EC_AFFINE *out,
                               const uint8_t *in, size_t len) {
  const size_t field_len = BN_num_bytes(&group->field);
  if (len != 1 + 2 * field_len || in[0] != POINT_CONVERSION_UNCOMPRESSED) {
    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
    return 0;
  }
 
  EC_FELEM x, y;
  if (!ec_felem_from_bytes(group, &x, in + 1, field_len) ||
      !ec_felem_from_bytes(group, &y, in + 1 + field_len, field_len) ||
      !ec_point_set_affine_coordinates(group, out, &x, &y)) {
    return 0;
  }
 
  return 1;
}
 
static int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
                                   const uint8_t *buf, size_t len,
                                   BN_CTX *ctx) {
  if (len == 0) {
    OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
    return 0;
  }
 
  point_conversion_form_t form = buf[0];
  if (form == POINT_CONVERSION_UNCOMPRESSED) {
    EC_AFFINE affine;
    if (!ec_point_from_uncompressed(group, &affine, buf, len)) {
      // In the event of an error, defend against the caller not checking the
      // return value by setting a known safe value.
      ec_set_to_safe_point(group, &point->raw);
      return 0;
    }
    ec_affine_to_jacobian(group, &point->raw, &affine);
    return 1;
  }
 
  const int y_bit = form & 1;
  const size_t field_len = BN_num_bytes(&group->field);
  form = form & ~1u;
  if (form != POINT_CONVERSION_COMPRESSED ||
      len != 1 /* type byte */ + field_len) {
    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
    return 0;
  }
 
  // TODO(davidben): Integrate compressed coordinates with the lower-level EC
  // abstractions. This requires a way to compute square roots, which is tricky
  // for primes which are not 3 (mod 4), namely P-224 and custom curves. P-224's
  // prime is particularly inconvenient for compressed coordinates. See
  // https://cr.yp.to/papers/sqroot.pdf
  BN_CTX *new_ctx = NULL;
  if (ctx == NULL) {
    ctx = new_ctx = BN_CTX_new();
    if (ctx == NULL) {
      return 0;
    }
  }
 
  int ret = 0;
  BN_CTX_start(ctx);
  BIGNUM *x = BN_CTX_get(ctx);
  if (x == NULL || !BN_bin2bn(buf + 1, field_len, x)) {
    goto err;
  }
  if (BN_ucmp(x, &group->field) >= 0) {
    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
    goto err;
  }
 
  if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) {
    goto err;
  }
 
  ret = 1;
 
err:
  BN_CTX_end(ctx);
  BN_CTX_free(new_ctx);
  return ret;
}
 
int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point,
                       const uint8_t *buf, size_t len, BN_CTX *ctx) {
  if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  return ec_GFp_simple_oct2point(group, point, buf, len, ctx);
}
 
size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point,
                          point_conversion_form_t form, uint8_t *buf,
                          size_t len, BN_CTX *ctx) {
  if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  EC_AFFINE affine;
  if (!ec_jacobian_to_affine(group, &affine, &point->raw)) {
    return 0;
  }
  return ec_point_to_bytes(group, &affine, form, buf, len);
}
 
int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group,
                                            EC_POINT *point, const BIGNUM *x,
                                            int y_bit, BN_CTX *ctx) {
  if (EC_GROUP_cmp(group, point->group, NULL) != 0) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
 
  if (BN_is_negative(x) || BN_cmp(x, &group->field) >= 0) {
    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSED_POINT);
    return 0;
  }
 
  BN_CTX *new_ctx = NULL;
  int ret = 0;
 
  ERR_clear_error();
 
  if (ctx == NULL) {
    ctx = new_ctx = BN_CTX_new();
    if (ctx == NULL) {
      return 0;
    }
  }
 
  y_bit = (y_bit != 0);
 
  BN_CTX_start(ctx);
  BIGNUM *tmp1 = BN_CTX_get(ctx);
  BIGNUM *tmp2 = BN_CTX_get(ctx);
  BIGNUM *a = BN_CTX_get(ctx);
  BIGNUM *b = BN_CTX_get(ctx);
  BIGNUM *y = BN_CTX_get(ctx);
  if (y == NULL ||
      !EC_GROUP_get_curve_GFp(group, NULL, a, b, ctx)) {
    goto err;
  }
 
  // Recover y.  We have a Weierstrass equation
  //     y^2 = x^3 + a*x + b,
  // so  y  is one of the square roots of  x^3 + a*x + b.
 
  // tmp1 := x^3
  if (!BN_mod_sqr(tmp2, x, &group->field, ctx) ||
      !BN_mod_mul(tmp1, tmp2, x, &group->field, ctx)) {
    goto err;
  }
 
  // tmp1 := tmp1 + a*x
  if (group->a_is_minus3) {
    if (!bn_mod_lshift1_consttime(tmp2, x, &group->field, ctx) ||
        !bn_mod_add_consttime(tmp2, tmp2, x, &group->field, ctx) ||
        !bn_mod_sub_consttime(tmp1, tmp1, tmp2, &group->field, ctx)) {
      goto err;
    }
  } else {
    if (!BN_mod_mul(tmp2, a, x, &group->field, ctx) ||
        !bn_mod_add_consttime(tmp1, tmp1, tmp2, &group->field, ctx)) {
      goto err;
    }
  }
 
  // tmp1 := tmp1 + b
  if (!bn_mod_add_consttime(tmp1, tmp1, b, &group->field, ctx)) {
    goto err;
  }
 
  if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) {
    unsigned long err = ERR_peek_last_error();
 
    if (ERR_GET_LIB(err) == ERR_LIB_BN &&
        ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) {
      ERR_clear_error();
      OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSED_POINT);
    } else {
      OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
    }
    goto err;
  }
 
  if (y_bit != BN_is_odd(y)) {
    if (BN_is_zero(y)) {
      OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COMPRESSION_BIT);
      goto err;
    }
    if (!BN_usub(y, &group->field, y)) {
      goto err;
    }
  }
  if (y_bit != BN_is_odd(y)) {
    OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
    goto err;
  }
 
  if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
    goto err;
  }
 
  ret = 1;
 
err:
  BN_CTX_end(ctx);
  BN_CTX_free(new_ctx);
  return ret;
}