/* 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 <string.h>

#include <openssl/bn.h>

#include <openssl/err.h>

#include <openssl/mem.h>

#include "internal.h"

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

// Most method functions in this file are designed to work with non-trivial

// representations of field elements if necessary (see ecp_mont.c): while

// standard modular addition and subtraction are used, the field_mul and

// field_sqr methods will be used for multiplication, and field_encode and

// field_decode (if defined) will be used for converting between

// representations.

//

// Functions here specifically assume that if a non-trivial representation is

// used, it is a Montgomery representation (i.e. 'encoding' means multiplying

// by some factor R).

int ec_GFp_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p,

                                  const BIGNUM *a, const BIGNUM *b,

                                  BN_CTX *ctx) {

  // p must be a prime > 3

  if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {

    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FIELD);

    return 0;

  }

  int ret = 0;

  BN_CTX_start(ctx);

  BIGNUM *tmp = BN_CTX_get(ctx);

  if (tmp == NULL) {

    goto err;

  }

  if (!BN_MONT_CTX_set(&group->field, p, ctx) ||

      !ec_bignum_to_felem(group, &group->a, a) ||

      !ec_bignum_to_felem(group, &group->b, b) ||

      // Reuse Z from the generator to cache the value one.

      !ec_bignum_to_felem(group, &group->generator.raw.Z, BN_value_one())) {

    goto err;

  }

  // group->a_is_minus3

  if (!BN_copy(tmp, a) ||

      !BN_add_word(tmp, 3)) {

    goto err;

  }

  group->a_is_minus3 = (0 == BN_cmp(tmp, &group->field.N));

  ret = 1;

err:

  BN_CTX_end(ctx);

  return ret;

}

int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,

                                  BIGNUM *b) {

  if ((p != NULL && !BN_copy(p, &group->field.N)) ||

      (a != NULL && !ec_felem_to_bignum(group, a, &group->a)) ||

      (b != NULL && !ec_felem_to_bignum(group, b, &group->b))) {

    return 0;

  }

  return 1;

}

void ec_GFp_simple_point_init(EC_JACOBIAN *point) {

  OPENSSL_memset(&point->X, 0, sizeof(EC_FELEM));

  OPENSSL_memset(&point->Y, 0, sizeof(EC_FELEM));

  OPENSSL_memset(&point->Z, 0, sizeof(EC_FELEM));

}

void ec_GFp_simple_point_copy(EC_JACOBIAN *dest, const EC_JACOBIAN *src) {

  OPENSSL_memcpy(&dest->X, &src->X, sizeof(EC_FELEM));

  OPENSSL_memcpy(&dest->Y, &src->Y, sizeof(EC_FELEM));

  OPENSSL_memcpy(&dest->Z, &src->Z, sizeof(EC_FELEM));

}

void ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,

                                         EC_JACOBIAN *point) {

  // Although it is strictly only necessary to zero Z, we zero the entire point

  // in case |point| was stack-allocated and yet to be initialized.

  ec_GFp_simple_point_init(point);

}

void ec_GFp_simple_invert(const EC_GROUP *group, EC_JACOBIAN *point) {

  ec_felem_neg(group, &point->Y, &point->Y);

}

int ec_GFp_simple_is_at_infinity(const EC_GROUP *group,

                                 const EC_JACOBIAN *point) {

  return ec_felem_non_zero_mask(group, &point->Z) == 0;

}

int ec_GFp_simple_is_on_curve(const EC_GROUP *group,

                              const EC_JACOBIAN *point) {

  // We have a curve defined by a Weierstrass equation

  //      y^2 = x^3 + a*x + b.

  // The point to consider is given in Jacobian projective coordinates

  // where  (X, Y, Z)  represents  (x, y) = (X/Z^2, Y/Z^3).

  // Substituting this and multiplying by  Z^6  transforms the above equation

  // into

  //      Y^2 = X^3 + a*X*Z^4 + b*Z^6.

  // To test this, we add up the right-hand side in 'rh'.

  //

  // This function may be used when double-checking the secret result of a point

  // multiplication, so we proceed in constant-time.

  void (*const felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a,

                          const EC_FELEM *b) = group->meth->felem_mul;

  void (*const felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a) =

      group->meth->felem_sqr;

  // rh := X^2

  EC_FELEM rh;

  felem_sqr(group, &rh, &point->X);

  EC_FELEM tmp, Z4, Z6;

  felem_sqr(group, &tmp, &point->Z);

  felem_sqr(group, &Z4, &tmp);

  felem_mul(group, &Z6, &Z4, &tmp);

  // rh := rh + a*Z^4

  if (group->a_is_minus3) {

    ec_felem_add(group, &tmp, &Z4, &Z4);

    ec_felem_add(group, &tmp, &tmp, &Z4);

    ec_felem_sub(group, &rh, &rh, &tmp);

  } else {

    felem_mul(group, &tmp, &Z4, &group->a);

    ec_felem_add(group, &rh, &rh, &tmp);

  }

  // rh := (rh + a*Z^4)*X

  felem_mul(group, &rh, &rh, &point->X);

  // rh := rh + b*Z^6

  felem_mul(group, &tmp, &group->b, &Z6);

  ec_felem_add(group, &rh, &rh, &tmp);

  // 'lh' := Y^2

  felem_sqr(group, &tmp, &point->Y);

  ec_felem_sub(group, &tmp, &tmp, &rh);

  BN_ULONG not_equal = ec_felem_non_zero_mask(group, &tmp);

  // If Z = 0, the point is infinity, which is always on the curve.

  BN_ULONG not_infinity = ec_felem_non_zero_mask(group, &point->Z);

  return 1 & ~(not_infinity & not_equal);

}

int ec_GFp_simple_points_equal(const EC_GROUP *group, const EC_JACOBIAN *a,

                               const EC_JACOBIAN *b) {

  // This function is implemented in constant-time for two reasons. First,

  // although EC points are usually public, their Jacobian Z coordinates may be

  // secret, or at least are not obviously public. Second, more complex

  // protocols will sometimes manipulate secret points.

  //

  // This does mean that we pay a 6M+2S Jacobian comparison when comparing two

  // publicly affine points costs no field operations at all. If needed, we can

  // restore this optimization by keeping better track of affine vs. Jacobian

  // forms. See https://crbug.com/boringssl/326.

  // If neither |a| or |b| is infinity, we have to decide whether

  //     (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),

  // or equivalently, whether

  //     (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).

  void (*const felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a,

                          const EC_FELEM *b) = group->meth->felem_mul;

  void (*const felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a) =

      group->meth->felem_sqr;

  EC_FELEM tmp1, tmp2, Za23, Zb23;

  felem_sqr(group, &Zb23, &b->Z);         // Zb23 = Z_b^2

  felem_mul(group, &tmp1, &a->X, &Zb23);  // tmp1 = X_a * Z_b^2

  felem_sqr(group, &Za23, &a->Z);         // Za23 = Z_a^2

  felem_mul(group, &tmp2, &b->X, &Za23);  // tmp2 = X_b * Z_a^2

  ec_felem_sub(group, &tmp1, &tmp1, &tmp2);

  const BN_ULONG x_not_equal = ec_felem_non_zero_mask(group, &tmp1);

  felem_mul(group, &Zb23, &Zb23, &b->Z);  // Zb23 = Z_b^3

  felem_mul(group, &tmp1, &a->Y, &Zb23);  // tmp1 = Y_a * Z_b^3

  felem_mul(group, &Za23, &Za23, &a->Z);  // Za23 = Z_a^3

  felem_mul(group, &tmp2, &b->Y, &Za23);  // tmp2 = Y_b * Z_a^3

  ec_felem_sub(group, &tmp1, &tmp1, &tmp2);

  const BN_ULONG y_not_equal = ec_felem_non_zero_mask(group, &tmp1);

  const BN_ULONG x_and_y_equal = ~(x_not_equal | y_not_equal);

  const BN_ULONG a_not_infinity = ec_felem_non_zero_mask(group, &a->Z);

  const BN_ULONG b_not_infinity = ec_felem_non_zero_mask(group, &b->Z);

  const BN_ULONG a_and_b_infinity = ~(a_not_infinity | b_not_infinity);

  const BN_ULONG equal =

      a_and_b_infinity | (a_not_infinity & b_not_infinity & x_and_y_equal);

  return equal & 1;

}

int ec_affine_jacobian_equal(const EC_GROUP *group, const EC_AFFINE *a,

                             const EC_JACOBIAN *b) {

  // If |b| is not infinity, we have to decide whether

  //     (X_a, Y_a) = (X_b/Z_b^2, Y_b/Z_b^3),

  // or equivalently, whether

  //     (X_a*Z_b^2, Y_a*Z_b^3) = (X_b, Y_b).

  void (*const felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a,

                          const EC_FELEM *b) = group->meth->felem_mul;

  void (*const felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a) =

      group->meth->felem_sqr;

  EC_FELEM tmp, Zb2;

  felem_sqr(group, &Zb2, &b->Z);        // Zb2 = Z_b^2

  felem_mul(group, &tmp, &a->X, &Zb2);  // tmp = X_a * Z_b^2

  ec_felem_sub(group, &tmp, &tmp, &b->X);

  const BN_ULONG x_not_equal = ec_felem_non_zero_mask(group, &tmp);

  felem_mul(group, &tmp, &a->Y, &Zb2);  // tmp = Y_a * Z_b^2

  felem_mul(group, &tmp, &tmp, &b->Z);  // tmp = Y_a * Z_b^3

  ec_felem_sub(group, &tmp, &tmp, &b->Y);

  const BN_ULONG y_not_equal = ec_felem_non_zero_mask(group, &tmp);

  const BN_ULONG x_and_y_equal = ~(x_not_equal | y_not_equal);

  const BN_ULONG b_not_infinity = ec_felem_non_zero_mask(group, &b->Z);

  const BN_ULONG equal = b_not_infinity & x_and_y_equal;

  return equal & 1;

}

int ec_GFp_simple_cmp_x_coordinate(const EC_GROUP *group, const EC_JACOBIAN *p,

                                   const EC_SCALAR *r) {

  if (ec_GFp_simple_is_at_infinity(group, p)) {

    // |ec_get_x_coordinate_as_scalar| will check this internally, but this way

    // we do not push to the error queue.

    return 0;

  }

  EC_SCALAR x;

  return ec_get_x_coordinate_as_scalar(group, &x, p) &&

         ec_scalar_equal_vartime(group, &x, r);

}

void ec_GFp_simple_felem_to_bytes(const EC_GROUP *group, uint8_t *out,

                                  size_t *out_len, const EC_FELEM *in) {

  size_t len = BN_num_bytes(&group->field.N);

  bn_words_to_big_endian(out, len, in->words, group->field.N.width);

  *out_len = len;

}

int ec_GFp_simple_felem_from_bytes(const EC_GROUP *group, EC_FELEM *out,

                                   const uint8_t *in, size_t len) {

  if (len != BN_num_bytes(&group->field.N)) {

    OPENSSL_PUT_ERROR(EC, EC_R_DECODE_ERROR);

    return 0;

  }

  bn_big_endian_to_words(out->words, group->field.N.width, in, len);

  if (!bn_less_than_words(out->words, group->field.N.d, group->field.N.width)) {

    OPENSSL_PUT_ERROR(EC, EC_R_DECODE_ERROR);

    return 0;

  }

  return 1;

}