wnaf.c

Go to the documentation of this file.

/* 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.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_RAW_POINT *out,
                            const EC_RAW_POINT *p, size_t len) {
  ec_GFp_simple_point_copy(&out[0], p);
  EC_RAW_POINT 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_RAW_POINT *out,
                           const EC_RAW_POINT *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_RAW_POINT *r,
                                 const EC_SCALAR *g_scalar,
                                 const EC_RAW_POINT *points,
                                 const EC_SCALAR *scalars, size_t num) {
  size_t bits = BN_num_bits(&group->order);
  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_RAW_POINT precomp_stack[EC_WNAF_STACK][EC_WNAF_TABLE_SIZE];
  EC_RAW_POINT (*precomp_alloc)[EC_WNAF_TABLE_SIZE] = NULL;
  EC_RAW_POINT (*precomp)[EC_WNAF_TABLE_SIZE];
  if (num <= EC_WNAF_STACK) {
    wNAF = wNAF_stack;
    precomp = precomp_stack;
  } else {
    if (num >= ((size_t)-1) / sizeof(wNAF_alloc[0]) ||
        num >= ((size_t)-1) / sizeof(precomp_alloc[0])) {
      OPENSSL_PUT_ERROR(EC, ERR_R_OVERFLOW);
      goto err;
    }
    wNAF_alloc = OPENSSL_malloc(num * sizeof(wNAF_alloc[0]));
    precomp_alloc = OPENSSL_malloc(num * sizeof(precomp_alloc[0]));
    if (wNAF_alloc == NULL || precomp_alloc == NULL) {
      OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
      goto err;
    }
    wNAF = wNAF_alloc;
    precomp = precomp_alloc;
  }
 
  int8_t g_wNAF[EC_MAX_BYTES * 8 + 1];
  EC_RAW_POINT g_precomp[EC_WNAF_TABLE_SIZE];
  assert(wNAF_len <= OPENSSL_ARRAY_SIZE(g_wNAF));
  const EC_RAW_POINT *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_RAW_POINT 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;
}