text: /*
   * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved.
   *
   * Licensed under the OpenSSL license (the "License").  You may not use
   * this file except in compliance with the License.  You can obtain a copy
   * in the file LICENSE in the source distribution or at
   * https://www.openssl.org/source/license.html
   */
  
  /* ====================================================================
   * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
   *
   * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
   * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
   * to the OpenSSL project.
   *
   * The ECC Code is licensed pursuant to the OpenSSL open source
   * license provided below.
   *
   * The software is originally written by Sheueling Chang Shantz and
   * Douglas Stebila of Sun Microsystems Laboratories.
   *
   */
  
  #include BLIK_OPENSSL_V_openssl__err_h //original-code:<openssl/err.h>
  
  #include BLIK_OPENSSL_U_internal__bn_int_h //original-code:"internal/bn_int.h"
  #include "ec_lcl.h"
  
  #ifndef OPENSSL_NO_EC2M
  
  /*-
   * Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
   * coordinates.
   * Uses algorithm Mdouble in appendix of
   *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
   *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
   * modified to not require precomputation of c=b^{2^{m-1}}.
   */
  static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z,
                          BN_CTX *ctx)
  {
      BIGNUM *t1;
      int ret = 0;
  
      /* Since Mdouble is static we can guarantee that ctx != NULL. */
      BN_CTX_start(ctx);
      t1 = BN_CTX_get(ctx);
      if (t1 == NULL)
          goto err;
  
      if (!group->meth->field_sqr(group, x, x, ctx))
          goto err;
      if (!group->meth->field_sqr(group, t1, z, ctx))
          goto err;
      if (!group->meth->field_mul(group, z, x, t1, ctx))
          goto err;
      if (!group->meth->field_sqr(group, x, x, ctx))
          goto err;
      if (!group->meth->field_sqr(group, t1, t1, ctx))
          goto err;
      if (!group->meth->field_mul(group, t1, group->b, t1, ctx))
          goto err;
      if (!BN_GF2m_add(x, x, t1))
          goto err;
  
      ret = 1;
  
   err:
      BN_CTX_end(ctx);
      return ret;
  }
  
  /*-
   * Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
   * projective coordinates.
   * Uses algorithm Madd in appendix of
   *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
   *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
   */
  static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1,
                       BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2,
                       BN_CTX *ctx)
  {
      BIGNUM *t1, *t2;
      int ret = 0;
  
      /* Since Madd is static we can guarantee that ctx != NULL. */
      BN_CTX_start(ctx);
      t1 = BN_CTX_get(ctx);
      t2 = BN_CTX_get(ctx);
      if (t2 == NULL)
          goto err;
  
      if (!BN_copy(t1, x))
          goto err;
      if (!group->meth->field_mul(group, x1, x1, z2, ctx))
          goto err;
      if (!group->meth->field_mul(group, z1, z1, x2, ctx))
          goto err;
      if (!group->meth->field_mul(group, t2, x1, z1, ctx))
          goto err;
      if (!BN_GF2m_add(z1, z1, x1))
          goto err;
      if (!group->meth->field_sqr(group, z1, z1, ctx))
          goto err;
      if (!group->meth->field_mul(group, x1, z1, t1, ctx))
          goto err;
      if (!BN_GF2m_add(x1, x1, t2))
          goto err;
  
      ret = 1;
  
   err:
      BN_CTX_end(ctx);
      return ret;
  }
  
  /*-
   * Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
   * using Montgomery point multiplication algorithm Mxy() in appendix of
   *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
   *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
   * Returns:
   *     0 on error
   *     1 if return value should be the point at infinity
   *     2 otherwise
   */
  static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y,
                      BIGNUM *x1, BIGNUM *z1, BIGNUM *x2, BIGNUM *z2,
                      BN_CTX *ctx)
  {
      BIGNUM *t3, *t4, *t5;
      int ret = 0;
  
      if (BN_is_zero(z1)) {
          BN_zero(x2);
          BN_zero(z2);
          return 1;
      }
  
      if (BN_is_zero(z2)) {
          if (!BN_copy(x2, x))
              return 0;
          if (!BN_GF2m_add(z2, x, y))
              return 0;
          return 2;
      }
  
      /* Since Mxy is static we can guarantee that ctx != NULL. */
      BN_CTX_start(ctx);
      t3 = BN_CTX_get(ctx);
      t4 = BN_CTX_get(ctx);
      t5 = BN_CTX_get(ctx);
      if (t5 == NULL)
          goto err;
  
      if (!BN_one(t5))
          goto err;
  
      if (!group->meth->field_mul(group, t3, z1, z2, ctx))
          goto err;
  
      if (!group->meth->field_mul(group, z1, z1, x, ctx))
          goto err;
      if (!BN_GF2m_add(z1, z1, x1))
          goto err;
      if (!group->meth->field_mul(group, z2, z2, x, ctx))
          goto err;
      if (!group->meth->field_mul(group, x1, z2, x1, ctx))
          goto err;
      if (!BN_GF2m_add(z2, z2, x2))
          goto err;
  
      if (!group->meth->field_mul(group, z2, z2, z1, ctx))
          goto err;
      if (!group->meth->field_sqr(group, t4, x, ctx))
          goto err;
      if (!BN_GF2m_add(t4, t4, y))
          goto err;
      if (!group->meth->field_mul(group, t4, t4, t3, ctx))
          goto err;
      if (!BN_GF2m_add(t4, t4, z2))
          goto err;
  
      if (!group->meth->field_mul(group, t3, t3, x, ctx))
          goto err;
      if (!group->meth->field_div(group, t3, t5, t3, ctx))
          goto err;
      if (!group->meth->field_mul(group, t4, t3, t4, ctx))
          goto err;
      if (!group->meth->field_mul(group, x2, x1, t3, ctx))
          goto err;
      if (!BN_GF2m_add(z2, x2, x))
          goto err;
  
      if (!group->meth->field_mul(group, z2, z2, t4, ctx))
          goto err;
      if (!BN_GF2m_add(z2, z2, y))
          goto err;
  
      ret = 2;
  
   err:
      BN_CTX_end(ctx);
      return ret;
  }
  
  /*-
   * Computes scalar*point and stores the result in r.
   * point can not equal r.
   * Uses a modified algorithm 2P of
   *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
   *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
   *
   * To protect against side-channel attack the function uses constant time swap,
   * avoiding conditional branches.
   */
  static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group,
                                               EC_POINT *r,
                                               const BIGNUM *scalar,
                                               const EC_POINT *point,
                                               BN_CTX *ctx)
  {
      BIGNUM *x1, *x2, *z1, *z2;
      int ret = 0, i;
      BN_ULONG mask, word;
  
      if (r == point) {
          ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
          return 0;
      }
  
      /* if result should be point at infinity */
      if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
          EC_POINT_is_at_infinity(group, point)) {
          return EC_POINT_set_to_infinity(group, r);
      }
  
      /* only support affine coordinates */
      if (!point->Z_is_one)
          return 0;
  
      /*
       * Since point_multiply is static we can guarantee that ctx != NULL.
       */
      BN_CTX_start(ctx);
      x1 = BN_CTX_get(ctx);
      z1 = BN_CTX_get(ctx);
      if (z1 == NULL)
          goto err;
  
      x2 = r->X;
      z2 = r->Y;
  
      bn_wexpand(x1, bn_get_top(group->field));
      bn_wexpand(z1, bn_get_top(group->field));
      bn_wexpand(x2, bn_get_top(group->field));
      bn_wexpand(z2, bn_get_top(group->field));
  
      if (!BN_GF2m_mod_arr(x1, point->X, group->poly))
          goto err;               /* x1 = x */
      if (!BN_one(z1))
          goto err;               /* z1 = 1 */
      if (!group->meth->field_sqr(group, z2, x1, ctx))
          goto err;               /* z2 = x1^2 = x^2 */
      if (!group->meth->field_sqr(group, x2, z2, ctx))
          goto err;
      if (!BN_GF2m_add(x2, x2, group->b))
          goto err;               /* x2 = x^4 + b */
  
      /* find top most bit and go one past it */
      i = bn_get_top(scalar) - 1;
      mask = BN_TBIT;
      word = bn_get_words(scalar)[i];
      while (!(word & mask))
          mask >>= 1;
      mask >>= 1;
      /* if top most bit was at word break, go to next word */
      if (!mask) {
          i--;
          mask = BN_TBIT;
      }
  
      for (; i >= 0; i--) {
          word = bn_get_words(scalar)[i];
          while (mask) {
              BN_consttime_swap(word & mask, x1, x2, bn_get_top(group->field));
              BN_consttime_swap(word & mask, z1, z2, bn_get_top(group->field));
              if (!gf2m_Madd(group, point->X, x2, z2, x1, z1, ctx))
                  goto err;
              if (!gf2m_Mdouble(group, x1, z1, ctx))
                  goto err;
              BN_consttime_swap(word & mask, x1, x2, bn_get_top(group->field));
              BN_consttime_swap(word & mask, z1, z2, bn_get_top(group->field));
              mask >>= 1;
          }
          mask = BN_TBIT;
      }
  
      /* convert out of "projective" coordinates */
      i = gf2m_Mxy(group, point->X, point->Y, x1, z1, x2, z2, ctx);
      if (i == 0)
          goto err;
      else if (i == 1) {
          if (!EC_POINT_set_to_infinity(group, r))
              goto err;
      } else {
          if (!BN_one(r->Z))
              goto err;
          r->Z_is_one = 1;
      }
  
      /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
      BN_set_negative(r->X, 0);
      BN_set_negative(r->Y, 0);
  
      ret = 1;
  
   err:
      BN_CTX_end(ctx);
      return ret;
  }
  
  /*-
   * Computes the sum
   *     scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
   * gracefully ignoring NULL scalar values.
   */
  int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
                         const BIGNUM *scalar, size_t num,
                         const EC_POINT *points[], const BIGNUM *scalars[],
                         BN_CTX *ctx)
  {
      BN_CTX *new_ctx = NULL;
      int ret = 0;
      size_t i;
      EC_POINT *p = NULL;
      EC_POINT *acc = NULL;
  
      if (ctx == NULL) {
          ctx = new_ctx = BN_CTX_new();
          if (ctx == NULL)
              return 0;
      }
  
      /*
       * This implementation is more efficient than the wNAF implementation for
       * 2 or fewer points.  Use the ec_wNAF_mul implementation for 3 or more
       * points, or if we can perform a fast multiplication based on
       * precomputation.
       */
      if ((scalar && (num > 1)) || (num > 2)
          || (num == 0 && EC_GROUP_have_precompute_mult(group))) {
          ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
          goto err;
      }
  
      if ((p = EC_POINT_new(group)) == NULL)
          goto err;
      if ((acc = EC_POINT_new(group)) == NULL)
          goto err;
  
      if (!EC_POINT_set_to_infinity(group, acc))
          goto err;
  
      if (scalar) {
          if (!ec_GF2m_montgomery_point_multiply
              (group, p, scalar, group->generator, ctx))
              goto err;
          if (BN_is_negative(scalar))
              if (!group->meth->invert(group, p, ctx))
                  goto err;
          if (!group->meth->add(group, acc, acc, p, ctx))
              goto err;
      }
  
      for (i = 0; i < num; i++) {
          if (!ec_GF2m_montgomery_point_multiply
              (group, p, scalars[i], points[i], ctx))
              goto err;
          if (BN_is_negative(scalars[i]))
              if (!group->meth->invert(group, p, ctx))
                  goto err;
          if (!group->meth->add(group, acc, acc, p, ctx))
              goto err;
      }
  
      if (!EC_POINT_copy(r, acc))
          goto err;
  
      ret = 1;
  
   err:
      EC_POINT_free(p);
      EC_POINT_free(acc);
      BN_CTX_free(new_ctx);
      return ret;
  }
  
  /*
   * Precomputation for point multiplication: fall back to wNAF methods because
   * ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate
   */
  
  int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
  {
      return ec_wNAF_precompute_mult(group, ctx);
  }
  
  int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
  {
      return ec_wNAF_have_precompute_mult(group);
  }
  
  #endif
  