/* Originally written by Bodo Moeller and Nils Larsch 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 <openssl/mem.h>

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

#include "../delocate.h"

#include "internal.h"

static void ec_GFp_mont_felem_to_montgomery(const EC_GROUP *group,

                                            EC_FELEM *out, const EC_FELEM *in) {

  bn_to_montgomery_small(out->words, in->words, group->field.N.width,

                         &group->field);

}

static void ec_GFp_mont_felem_from_montgomery(const EC_GROUP *group,

                                              EC_FELEM *out,

                                              const EC_FELEM *in) {

  bn_from_montgomery_small(out->words, group->field.N.width, in->words,

                           group->field.N.width, &group->field);

}

static void ec_GFp_mont_felem_inv0(const EC_GROUP *group, EC_FELEM *out,

                                   const EC_FELEM *a) {

  bn_mod_inverse0_prime_mont_small(out->words, a->words, group->field.N.width,

                                   &group->field);

}

void ec_GFp_mont_felem_mul(const EC_GROUP *group, EC_FELEM *r,

                           const EC_FELEM *a, const EC_FELEM *b) {

  bn_mod_mul_montgomery_small(r->words, a->words, b->words,

                              group->field.N.width, &group->field);

}

void ec_GFp_mont_felem_sqr(const EC_GROUP *group, EC_FELEM *r,

                           const EC_FELEM *a) {

  bn_mod_mul_montgomery_small(r->words, a->words, a->words,

                              group->field.N.width, &group->field);

}

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

                                size_t *out_len, const EC_FELEM *in) {

  EC_FELEM tmp;

  ec_GFp_mont_felem_from_montgomery(group, &tmp, in);

  ec_GFp_simple_felem_to_bytes(group, out, out_len, &tmp);

}

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

                                 const uint8_t *in, size_t len) {

  if (!ec_GFp_simple_felem_from_bytes(group, out, in, len)) {

    return 0;

  }

  ec_GFp_mont_felem_to_montgomery(group, out, out);

  return 1;

}

void ec_GFp_mont_felem_reduce(const EC_GROUP *group, EC_FELEM *out,

                              const BN_ULONG *words, size_t num) {

  // Convert "from" Montgomery form so the value is reduced mod p.

  bn_from_montgomery_small(out->words, group->field.N.width, words, num,

                           &group->field);

  // Convert "to" Montgomery form to remove the R^-1 factor added.

  ec_GFp_mont_felem_to_montgomery(group, out, out);

  // Convert to Montgomery form to match this implementation's representation.

  ec_GFp_mont_felem_to_montgomery(group, out, out);

}

void ec_GFp_mont_felem_exp(const EC_GROUP *group, EC_FELEM *out,

                           const EC_FELEM *a, const BN_ULONG *exp,

                           size_t num_exp) {

  bn_mod_exp_mont_small(out->words, a->words, group->field.N.width, exp,

                        num_exp, &group->field);

}

static int ec_GFp_mont_point_get_affine_coordinates(const EC_GROUP *group,

                                                    const EC_JACOBIAN *point,

                                                    EC_FELEM *x, EC_FELEM *y) {

  if (constant_time_declassify_int(

          ec_GFp_simple_is_at_infinity(group, point))) {

    OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);

    return 0;

  }

  // Transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3). Note the check above

  // ensures |point->Z| is non-zero, so the inverse always exists.

  EC_FELEM z1, z2;

  ec_GFp_mont_felem_inv0(group, &z2, &point->Z);

  ec_GFp_mont_felem_sqr(group, &z1, &z2);

  if (x != NULL) {

    ec_GFp_mont_felem_mul(group, x, &point->X, &z1);

  }

  if (y != NULL) {

    ec_GFp_mont_felem_mul(group, &z1, &z1, &z2);

    ec_GFp_mont_felem_mul(group, y, &point->Y, &z1);

  }

  return 1;

}

static int ec_GFp_mont_jacobian_to_affine_batch(const EC_GROUP *group,

                                                EC_AFFINE *out,

                                                const EC_JACOBIAN *in,

                                                size_t num) {

  if (num == 0) {

    return 1;

  }

  // Compute prefix products of all Zs. Use |out[i].X| as scratch space

  // to store these values.

  out[0].X = in[0].Z;

  for (size_t i = 1; i < num; i++) {

    ec_GFp_mont_felem_mul(group, &out[i].X, &out[i - 1].X, &in[i].Z);

  }

  // Some input was infinity iff the product of all Zs is zero.

  if (ec_felem_non_zero_mask(group, &out[num - 1].X) == 0) {

    OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);

    return 0;

  }

  // Invert the product of all Zs.

  EC_FELEM zinvprod;

  ec_GFp_mont_felem_inv0(group, &zinvprod, &out[num - 1].X);

  for (size_t i = num - 1; i < num; i--) {

    // Our loop invariant is that |zinvprod| is Z0^-1 * Z1^-1 * ... * Zi^-1.

    // Recover Zi^-1 by multiplying by the previous product.

    EC_FELEM zinv, zinv2;

    if (i == 0) {

      zinv = zinvprod;

    } else {

      ec_GFp_mont_felem_mul(group, &zinv, &zinvprod, &out[i - 1].X);

      // Maintain the loop invariant for the next iteration.

      ec_GFp_mont_felem_mul(group, &zinvprod, &zinvprod, &in[i].Z);

    }

    // Compute affine coordinates: x = X * Z^-2 and y = Y * Z^-3.

    ec_GFp_mont_felem_sqr(group, &zinv2, &zinv);

    ec_GFp_mont_felem_mul(group, &out[i].X, &in[i].X, &zinv2);

    ec_GFp_mont_felem_mul(group, &out[i].Y, &in[i].Y, &zinv2);

    ec_GFp_mont_felem_mul(group, &out[i].Y, &out[i].Y, &zinv);

  }

  return 1;

}

void ec_GFp_mont_add(const EC_GROUP *group, EC_JACOBIAN *out,

                     const EC_JACOBIAN *a, const EC_JACOBIAN *b) {

  if (a == b) {

    ec_GFp_mont_dbl(group, out, a);

    return;

  }

  // The method is taken from:

  //   http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#addition-add-2007-bl

  //

  // Coq transcription and correctness proof:

  // <https://github.com/davidben/fiat-crypto/blob/c7b95f62b2a54b559522573310e9b487327d219a/src/Curves/Weierstrass/Jacobian.v#L467>

  // <https://github.com/davidben/fiat-crypto/blob/c7b95f62b2a54b559522573310e9b487327d219a/src/Curves/Weierstrass/Jacobian.v#L544>

  EC_FELEM x_out, y_out, z_out;

  BN_ULONG z1nz = ec_felem_non_zero_mask(group, &a->Z);

  BN_ULONG z2nz = ec_felem_non_zero_mask(group, &b->Z);

  // z1z1 = z1z1 = z1**2

  EC_FELEM z1z1;

  ec_GFp_mont_felem_sqr(group, &z1z1, &a->Z);

  // z2z2 = z2**2

  EC_FELEM z2z2;

  ec_GFp_mont_felem_sqr(group, &z2z2, &b->Z);

  // u1 = x1*z2z2

  EC_FELEM u1;

  ec_GFp_mont_felem_mul(group, &u1, &a->X, &z2z2);

  // two_z1z2 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2

  EC_FELEM two_z1z2;

  ec_felem_add(group, &two_z1z2, &a->Z, &b->Z);

  ec_GFp_mont_felem_sqr(group, &two_z1z2, &two_z1z2);

  ec_felem_sub(group, &two_z1z2, &two_z1z2, &z1z1);

  ec_felem_sub(group, &two_z1z2, &two_z1z2, &z2z2);

  // s1 = y1 * z2**3

  EC_FELEM s1;

  ec_GFp_mont_felem_mul(group, &s1, &b->Z, &z2z2);

  ec_GFp_mont_felem_mul(group, &s1, &s1, &a->Y);

  // u2 = x2*z1z1

  EC_FELEM u2;

  ec_GFp_mont_felem_mul(group, &u2, &b->X, &z1z1);

  // h = u2 - u1

  EC_FELEM h;

  ec_felem_sub(group, &h, &u2, &u1);

  BN_ULONG xneq = ec_felem_non_zero_mask(group, &h);

  // z_out = two_z1z2 * h

  ec_GFp_mont_felem_mul(group, &z_out, &h, &two_z1z2);

  // z1z1z1 = z1 * z1z1

  EC_FELEM z1z1z1;

  ec_GFp_mont_felem_mul(group, &z1z1z1, &a->Z, &z1z1);

  // s2 = y2 * z1**3

  EC_FELEM s2;

  ec_GFp_mont_felem_mul(group, &s2, &b->Y, &z1z1z1);

  // r = (s2 - s1)*2

  EC_FELEM r;

  ec_felem_sub(group, &r, &s2, &s1);

  ec_felem_add(group, &r, &r, &r);

  BN_ULONG yneq = ec_felem_non_zero_mask(group, &r);

  // This case will never occur in the constant-time |ec_GFp_mont_mul|.

  BN_ULONG is_nontrivial_double = ~xneq & ~yneq & z1nz & z2nz;

  if (constant_time_declassify_w(is_nontrivial_double)) {

    ec_GFp_mont_dbl(group, out, a);

    return;

  }

  // I = (2h)**2

  EC_FELEM i;

  ec_felem_add(group, &i, &h, &h);

  ec_GFp_mont_felem_sqr(group, &i, &i);

  // J = h * I

  EC_FELEM j;

  ec_GFp_mont_felem_mul(group, &j, &h, &i);

  // V = U1 * I

  EC_FELEM v;

  ec_GFp_mont_felem_mul(group, &v, &u1, &i);

  // x_out = r**2 - J - 2V

  ec_GFp_mont_felem_sqr(group, &x_out, &r);

  ec_felem_sub(group, &x_out, &x_out, &j);

  ec_felem_sub(group, &x_out, &x_out, &v);

  ec_felem_sub(group, &x_out, &x_out, &v);

  // y_out = r(V-x_out) - 2 * s1 * J

  ec_felem_sub(group, &y_out, &v, &x_out);

  ec_GFp_mont_felem_mul(group, &y_out, &y_out, &r);

  EC_FELEM s1j;

  ec_GFp_mont_felem_mul(group, &s1j, &s1, &j);

  ec_felem_sub(group, &y_out, &y_out, &s1j);

  ec_felem_sub(group, &y_out, &y_out, &s1j);

  ec_felem_select(group, &x_out, z1nz, &x_out, &b->X);

  ec_felem_select(group, &out->X, z2nz, &x_out, &a->X);

  ec_felem_select(group, &y_out, z1nz, &y_out, &b->Y);

  ec_felem_select(group, &out->Y, z2nz, &y_out, &a->Y);

  ec_felem_select(group, &z_out, z1nz, &z_out, &b->Z);

  ec_felem_select(group, &out->Z, z2nz, &z_out, &a->Z);

}

void ec_GFp_mont_dbl(const EC_GROUP *group, EC_JACOBIAN *r,

                     const EC_JACOBIAN *a) {

  if (group->a_is_minus3) {

    // The method is taken from:

    //   http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b

    //

    // Coq transcription and correctness proof:

    // <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/Jacobian.v#L93>

    // <https://github.com/mit-plv/fiat-crypto/blob/79f8b5f39ed609339f0233098dee1a3c4e6b3080/src/Curves/Weierstrass/Jacobian.v#L201>

    EC_FELEM delta, gamma, beta, ftmp, ftmp2, tmptmp, alpha, fourbeta;

    // delta = z^2

    ec_GFp_mont_felem_sqr(group, &delta, &a->Z);

    // gamma = y^2

    ec_GFp_mont_felem_sqr(group, &gamma, &a->Y);

    // beta = x*gamma

    ec_GFp_mont_felem_mul(group, &beta, &a->X, &gamma);

    // alpha = 3*(x-delta)*(x+delta)

    ec_felem_sub(group, &ftmp, &a->X, &delta);

    ec_felem_add(group, &ftmp2, &a->X, &delta);

    ec_felem_add(group, &tmptmp, &ftmp2, &ftmp2);

    ec_felem_add(group, &ftmp2, &ftmp2, &tmptmp);

    ec_GFp_mont_felem_mul(group, &alpha, &ftmp, &ftmp2);

    // x' = alpha^2 - 8*beta

    ec_GFp_mont_felem_sqr(group, &r->X, &alpha);

    ec_felem_add(group, &fourbeta, &beta, &beta);

    ec_felem_add(group, &fourbeta, &fourbeta, &fourbeta);

    ec_felem_add(group, &tmptmp, &fourbeta, &fourbeta);

    ec_felem_sub(group, &r->X, &r->X, &tmptmp);

    // z' = (y + z)^2 - gamma - delta

    ec_felem_add(group, &delta, &gamma, &delta);

    ec_felem_add(group, &ftmp, &a->Y, &a->Z);

    ec_GFp_mont_felem_sqr(group, &r->Z, &ftmp);

    ec_felem_sub(group, &r->Z, &r->Z, &delta);

    // y' = alpha*(4*beta - x') - 8*gamma^2

    ec_felem_sub(group, &r->Y, &fourbeta, &r->X);

    ec_felem_add(group, &gamma, &gamma, &gamma);

    ec_GFp_mont_felem_sqr(group, &gamma, &gamma);

    ec_GFp_mont_felem_mul(group, &r->Y, &alpha, &r->Y);

    ec_felem_add(group, &gamma, &gamma, &gamma);

    ec_felem_sub(group, &r->Y, &r->Y, &gamma);

  } else {

    // The method is taken from:

    //   http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-2007-bl

    //

    // Coq transcription and correctness proof:

    // <https://github.com/davidben/fiat-crypto/blob/c7b95f62b2a54b559522573310e9b487327d219a/src/Curves/Weierstrass/Jacobian.v#L102>

    // <https://github.com/davidben/fiat-crypto/blob/c7b95f62b2a54b559522573310e9b487327d219a/src/Curves/Weierstrass/Jacobian.v#L534>

    EC_FELEM xx, yy, yyyy, zz;

    ec_GFp_mont_felem_sqr(group, &xx, &a->X);

    ec_GFp_mont_felem_sqr(group, &yy, &a->Y);

    ec_GFp_mont_felem_sqr(group, &yyyy, &yy);

    ec_GFp_mont_felem_sqr(group, &zz, &a->Z);

    // s = 2*((x_in + yy)^2 - xx - yyyy)

    EC_FELEM s;

    ec_felem_add(group, &s, &a->X, &yy);

    ec_GFp_mont_felem_sqr(group, &s, &s);

    ec_felem_sub(group, &s, &s, &xx);

    ec_felem_sub(group, &s, &s, &yyyy);

    ec_felem_add(group, &s, &s, &s);

    // m = 3*xx + a*zz^2

    EC_FELEM m;

    ec_GFp_mont_felem_sqr(group, &m, &zz);

    ec_GFp_mont_felem_mul(group, &m, &group->a, &m);

    ec_felem_add(group, &m, &m, &xx);

    ec_felem_add(group, &m, &m, &xx);

    ec_felem_add(group, &m, &m, &xx);

    // x_out = m^2 - 2*s

    ec_GFp_mont_felem_sqr(group, &r->X, &m);

    ec_felem_sub(group, &r->X, &r->X, &s);

    ec_felem_sub(group, &r->X, &r->X, &s);

    // z_out = (y_in + z_in)^2 - yy - zz

    ec_felem_add(group, &r->Z, &a->Y, &a->Z);

    ec_GFp_mont_felem_sqr(group, &r->Z, &r->Z);

    ec_felem_sub(group, &r->Z, &r->Z, &yy);

    ec_felem_sub(group, &r->Z, &r->Z, &zz);

    // y_out = m*(s-x_out) - 8*yyyy

    ec_felem_add(group, &yyyy, &yyyy, &yyyy);

    ec_felem_add(group, &yyyy, &yyyy, &yyyy);

    ec_felem_add(group, &yyyy, &yyyy, &yyyy);

    ec_felem_sub(group, &r->Y, &s, &r->X);

    ec_GFp_mont_felem_mul(group, &r->Y, &r->Y, &m);

    ec_felem_sub(group, &r->Y, &r->Y, &yyyy);

  }

}

static int ec_GFp_mont_cmp_x_coordinate(const EC_GROUP *group,

                                        const EC_JACOBIAN *p,

                                        const EC_SCALAR *r) {

  if (!group->field_greater_than_order ||

      group->field.N.width != group->order.N.width) {

    // Do not bother optimizing this case. p > order in all commonly-used

    // curves.

    return ec_GFp_simple_cmp_x_coordinate(group, p, r);

  }

  if (ec_GFp_simple_is_at_infinity(group, p)) {

    return 0;

  }

  // We wish to compare X/Z^2 with r. This is equivalent to comparing X with

  // r*Z^2. Note that X and Z are represented in Montgomery form, while r is

  // not.

  EC_FELEM r_Z2, Z2_mont, X;

  ec_GFp_mont_felem_mul(group, &Z2_mont, &p->Z, &p->Z);

  // r < order < p, so this is valid.

  OPENSSL_memcpy(r_Z2.words, r->words, group->field.N.width * sizeof(BN_ULONG));

  ec_GFp_mont_felem_mul(group, &r_Z2, &r_Z2, &Z2_mont);

  ec_GFp_mont_felem_from_montgomery(group, &X, &p->X);

  if (ec_felem_equal(group, &r_Z2, &X)) {

    return 1;

  }

  // During signing the x coefficient is reduced modulo the group order.

  // Therefore there is a small possibility, less than 1/2^128, that group_order

  // < p.x < P. in that case we need not only to compare against |r| but also to

  // compare against r+group_order.

  BN_ULONG carry = bn_add_words(r_Z2.words, r->words, group->order.N.d,

                                group->field.N.width);

  if (carry == 0 &&

      bn_less_than_words(r_Z2.words, group->field.N.d, group->field.N.width)) {

    // r + group_order < p, so compare (r + group_order) * Z^2 against X.

    ec_GFp_mont_felem_mul(group, &r_Z2, &r_Z2, &Z2_mont);

    if (ec_felem_equal(group, &r_Z2, &X)) {

      return 1;

    }

  }

  return 0;

}

DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_mont_method) {

  out->point_get_affine_coordinates = ec_GFp_mont_point_get_affine_coordinates;

  out->jacobian_to_affine_batch = ec_GFp_mont_jacobian_to_affine_batch;

  out->add = ec_GFp_mont_add;

  out->dbl = ec_GFp_mont_dbl;

  out->mul = ec_GFp_mont_mul;

  out->mul_base = ec_GFp_mont_mul_base;

  out->mul_batch = ec_GFp_mont_mul_batch;

  out->mul_public_batch = ec_GFp_mont_mul_public_batch;

  out->init_precomp = ec_GFp_mont_init_precomp;

  out->mul_precomp = ec_GFp_mont_mul_precomp;

  out->felem_mul = ec_GFp_mont_felem_mul;

  out->felem_sqr = ec_GFp_mont_felem_sqr;

  out->felem_to_bytes = ec_GFp_mont_felem_to_bytes;

  out->felem_from_bytes = ec_GFp_mont_felem_from_bytes;

  out->felem_reduce = ec_GFp_mont_felem_reduce;

  out->felem_exp = ec_GFp_mont_felem_exp;

  out->scalar_inv0_montgomery = ec_simple_scalar_inv0_montgomery;

  out->scalar_to_montgomery_inv_vartime =

      ec_simple_scalar_to_montgomery_inv_vartime;

  out->cmp_x_coordinate = ec_GFp_mont_cmp_x_coordinate;

}