/* 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/thread.h>

#include "internal.h"

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

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

// This file implements the wNAF-based interleaving multi-exponentiation method

// at:

//   http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13

//   http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf

void ec_compute_wNAF(const EC_GROUP *group, int8_t *out,

                     const EC_SCALAR *scalar, size_t bits, int w) {

  // 'int8_t' can represent integers with absolute values less than 2^7.

  assert(0 < w && w <= 7);

  assert(bits != 0);

  int bit = 1 << w;         // 2^w, at most 128

  int next_bit = bit << 1;  // 2^(w+1), at most 256

  int mask = next_bit - 1;  // at most 255

  int window_val = scalar->words[0] & mask;

  for (size_t j = 0; j < bits + 1; j++) {

    assert(0 <= window_val && window_val <= next_bit);

    int digit = 0;

    if (window_val & 1) {

      assert(0 < window_val && window_val < next_bit);

      if (window_val & bit) {

        digit = window_val - next_bit;

        // We know -next_bit < digit < 0 and window_val - digit = next_bit.

        // modified wNAF

        if (j + w + 1 >= bits) {

          // special case for generating modified wNAFs:

          // no new bits will be added into window_val,

          // so using a positive digit here will decrease

          // the total length of the representation

          digit = window_val & (mask >> 1);

          // We know 0 < digit < bit and window_val - digit = bit.

        }

      } else {

        digit = window_val;

        // We know 0 < digit < bit and window_val - digit = 0.

      }

      window_val -= digit;

      // Now window_val is 0 or 2^(w+1) in standard wNAF generation.

      // For modified window NAFs, it may also be 2^w.

      //

      // See the comments above for the derivation of each of these bounds.

      assert(window_val == 0 || window_val == next_bit || window_val == bit);

      assert(-bit < digit && digit < bit);

      // window_val was odd, so digit is also odd.

      assert(digit & 1);

    }

    out[j] = digit;

    // Incorporate the next bit. Previously, |window_val| <= |next_bit|, so if

    // we shift and add at most one copy of |bit|, this will continue to hold

    // afterwards.

    window_val >>= 1;

    window_val += bit * bn_is_bit_set_words(scalar->words, group->order.N.width,

                                            j + w + 1);

    assert(window_val <= next_bit);

  }

  // bits + 1 entries should be sufficient to consume all bits.

  assert(window_val == 0);

}

// compute_precomp sets |out[i]| to (2*i+1)*p, for i from 0 to |len|.

static void compute_precomp(const EC_GROUP *group, EC_JACOBIAN *out,

                            const EC_JACOBIAN *p, size_t len) {

  ec_GFp_simple_point_copy(&out[0], p);

  EC_JACOBIAN two_p;

  ec_GFp_mont_dbl(group, &two_p, p);

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

    ec_GFp_mont_add(group, &out[i], &out[i - 1], &two_p);

  }

}

static void lookup_precomp(const EC_GROUP *group, EC_JACOBIAN *out,

                           const EC_JACOBIAN *precomp, int digit) {

  if (digit < 0) {

    digit = -digit;

    ec_GFp_simple_point_copy(out, &precomp[digit >> 1]);

    ec_GFp_simple_invert(group, out);

  } else {

    ec_GFp_simple_point_copy(out, &precomp[digit >> 1]);

  }

}

// EC_WNAF_WINDOW_BITS is the window size to use for |ec_GFp_mont_mul_public|.

#define EC_WNAF_WINDOW_BITS 4

// EC_WNAF_TABLE_SIZE is the table size to use for |ec_GFp_mont_mul_public|.

#define EC_WNAF_TABLE_SIZE (1 << (EC_WNAF_WINDOW_BITS - 1))

// EC_WNAF_STACK is the number of points worth of data to stack-allocate and

// avoid a malloc.

#define EC_WNAF_STACK 3

int ec_GFp_mont_mul_public_batch(const EC_GROUP *group, EC_JACOBIAN *r,

                                 const EC_SCALAR *g_scalar,

                                 const EC_JACOBIAN *points,

                                 const EC_SCALAR *scalars, size_t num) {

  size_t bits = EC_GROUP_order_bits(group);

  size_t wNAF_len = bits + 1;

  int ret = 0;

  int8_t wNAF_stack[EC_WNAF_STACK][EC_MAX_BYTES * 8 + 1];

  int8_t (*wNAF_alloc)[EC_MAX_BYTES * 8 + 1] = NULL;

  int8_t (*wNAF)[EC_MAX_BYTES * 8 + 1];

  EC_JACOBIAN precomp_stack[EC_WNAF_STACK][EC_WNAF_TABLE_SIZE];

  EC_JACOBIAN (*precomp_alloc)[EC_WNAF_TABLE_SIZE] = NULL;

  EC_JACOBIAN (*precomp)[EC_WNAF_TABLE_SIZE];

  if (num <= EC_WNAF_STACK) {

    wNAF = wNAF_stack;

    precomp = precomp_stack;

  } else {

    wNAF_alloc = OPENSSL_calloc(num, sizeof(wNAF_alloc[0]));

    precomp_alloc = OPENSSL_calloc(num, sizeof(precomp_alloc[0]));

    if (wNAF_alloc == NULL || precomp_alloc == NULL) {

      goto err;

    }

    wNAF = wNAF_alloc;

    precomp = precomp_alloc;

  }

  int8_t g_wNAF[EC_MAX_BYTES * 8 + 1];

  EC_JACOBIAN g_precomp[EC_WNAF_TABLE_SIZE];

  assert(wNAF_len <= OPENSSL_ARRAY_SIZE(g_wNAF));

  const EC_JACOBIAN *g = &group->generator.raw;

  if (g_scalar != NULL) {

    ec_compute_wNAF(group, g_wNAF, g_scalar, bits, EC_WNAF_WINDOW_BITS);

    compute_precomp(group, g_precomp, g, EC_WNAF_TABLE_SIZE);

  }

  for (size_t i = 0; i < num; i++) {

    assert(wNAF_len <= OPENSSL_ARRAY_SIZE(wNAF[i]));

    ec_compute_wNAF(group, wNAF[i], &scalars[i], bits, EC_WNAF_WINDOW_BITS);

    compute_precomp(group, precomp[i], &points[i], EC_WNAF_TABLE_SIZE);

  }

  EC_JACOBIAN tmp;

  int r_is_at_infinity = 1;

  for (size_t k = wNAF_len - 1; k < wNAF_len; k--) {

    if (!r_is_at_infinity) {

      ec_GFp_mont_dbl(group, r, r);

    }

    if (g_scalar != NULL && g_wNAF[k] != 0) {

      lookup_precomp(group, &tmp, g_precomp, g_wNAF[k]);

      if (r_is_at_infinity) {

        ec_GFp_simple_point_copy(r, &tmp);

        r_is_at_infinity = 0;

      } else {

        ec_GFp_mont_add(group, r, r, &tmp);

      }

    }

    for (size_t i = 0; i < num; i++) {

      if (wNAF[i][k] != 0) {

        lookup_precomp(group, &tmp, precomp[i], wNAF[i][k]);

        if (r_is_at_infinity) {

          ec_GFp_simple_point_copy(r, &tmp);

          r_is_at_infinity = 0;

        } else {

          ec_GFp_mont_add(group, r, r, &tmp);

        }

      }

    }

  }

  if (r_is_at_infinity) {

    ec_GFp_simple_point_set_to_infinity(group, r);

  }

  ret = 1;

err:

  OPENSSL_free(wNAF_alloc);

  OPENSSL_free(precomp_alloc);

  return ret;

}