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ec_mult.c

/* crypto/ec/ec_mult.c */
/*
 * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
 */
/* ====================================================================
 * Copyright (c) 1998-2007 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 this software developed by SUN MICROSYSTEMS, INC.,
 * and contributed to the OpenSSL project.
 */

#include <string.h>

#include <openssl/err.h>

#include "ec_lcl.h"


/*
 * This file implements the wNAF-based interleaving multi-exponentation method
 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
 * for multiplication with precomputation, we use wNAF splitting
 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
 */




/* structure for precomputed multiples of the generator */
00082 typedef struct ec_pre_comp_st {
      const EC_GROUP *group; /* parent EC_GROUP object */
      size_t blocksize;      /* block size for wNAF splitting */
      size_t numblocks;      /* max. number of blocks for which we have precomputation */
      size_t w;              /* window size */
      EC_POINT **points;     /* array with pre-calculated multiples of generator:
                              * 'num' pointers to EC_POINT objects followed by a NULL */
      size_t num;            /* numblocks * 2^(w-1) */
      int references;
} EC_PRE_COMP;
 
/* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
static void *ec_pre_comp_dup(void *);
static void ec_pre_comp_free(void *);
static void ec_pre_comp_clear_free(void *);

static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
      {
      EC_PRE_COMP *ret = NULL;

      if (!group)
            return NULL;

      ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
      if (!ret)
            {
            ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
            return ret;
            }
      ret->group = group;
      ret->blocksize = 8; /* default */
      ret->numblocks = 0;
      ret->w = 4; /* default */
      ret->points = NULL;
      ret->num = 0;
      ret->references = 1;
      return ret;
      }

static void *ec_pre_comp_dup(void *src_)
      {
      EC_PRE_COMP *src = src_;

      /* no need to actually copy, these objects never change! */

      CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);

      return src_;
      }

static void ec_pre_comp_free(void *pre_)
      {
      int i;
      EC_PRE_COMP *pre = pre_;

      if (!pre)
            return;

      i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
      if (i > 0)
            return;

      if (pre->points)
            {
            EC_POINT **p;

            for (p = pre->points; *p != NULL; p++)
                  EC_POINT_free(*p);
            OPENSSL_free(pre->points);
            }
      OPENSSL_free(pre);
      }

static void ec_pre_comp_clear_free(void *pre_)
      {
      int i;
      EC_PRE_COMP *pre = pre_;

      if (!pre)
            return;

      i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
      if (i > 0)
            return;

      if (pre->points)
            {
            EC_POINT **p;

            for (p = pre->points; *p != NULL; p++)
                  {
                  EC_POINT_clear_free(*p);
                  OPENSSL_cleanse(p, sizeof *p);
                  }
            OPENSSL_free(pre->points);
            }
      OPENSSL_cleanse(pre, sizeof *pre);
      OPENSSL_free(pre);
      }




/* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
 * This is an array  r[]  of values that are either zero or odd with an
 * absolute value less than  2^w  satisfying
 *     scalar = \sum_j r[j]*2^j
 * where at most one of any  w+1  consecutive digits is non-zero
 * with the exception that the most significant digit may be only
 * w-1 zeros away from that next non-zero digit.
 */
static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
      {
      int window_val;
      int ok = 0;
      signed char *r = NULL;
      int sign = 1;
      int bit, next_bit, mask;
      size_t len = 0, j;
      
      if (BN_is_zero(scalar))
            {
            r = OPENSSL_malloc(1);
            if (!r)
                  {
                  ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
                  goto err;
                  }
            r[0] = 0;
            *ret_len = 1;
            return r;
            }
            
      if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
            {
            ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
            goto err;
            }
      bit = 1 << w; /* at most 128 */
      next_bit = bit << 1; /* at most 256 */
      mask = next_bit - 1; /* at most 255 */

      if (BN_is_negative(scalar))
            {
            sign = -1;
            }

      if (scalar->d == NULL || scalar->top == 0)
            {
            ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
            goto err;
            }

      len = BN_num_bits(scalar);
      r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
                                    * (*ret_len will be set to the actual length, i.e. at most
                                    * BN_num_bits(scalar) + 1) */
      if (r == NULL)
            {
            ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
            goto err;
            }
      window_val = scalar->d[0] & mask;
      j = 0;
      while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
            {
            int digit = 0;

            /* 0 <= window_val <= 2^(w+1) */

            if (window_val & 1)
                  {
                  /* 0 < window_val < 2^(w+1) */

                  if (window_val & bit)
                        {
                        digit = window_val - next_bit; /* -2^w < digit < 0 */

#if 1 /* modified wNAF */
                        if (j + w + 1 >= len)
                              {
                              /* 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); /* 0 < digit < 2^w */
                              }
#endif
                        }
                  else
                        {
                        digit = window_val; /* 0 < digit < 2^w */
                        }
                  
                  if (digit <= -bit || digit >= bit || !(digit & 1))
                        {
                        ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
                        goto err;
                        }

                  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
                   */
                  if (window_val != 0 && window_val != next_bit && window_val != bit)
                        {
                        ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
                        goto err;
                        }
                  }

            r[j++] = sign * digit;

            window_val >>= 1;
            window_val += bit * BN_is_bit_set(scalar, j + w);

            if (window_val > next_bit)
                  {
                  ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
                  goto err;
                  }
            }

      if (j > len + 1)
            {
            ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
            goto err;
            }
      len = j;
      ok = 1;

 err:
      if (!ok)
            {
            OPENSSL_free(r);
            r = NULL;
            }
      if (ok)
            *ret_len = len;
      return r;
      }


/* TODO: table should be optimised for the wNAF-based implementation,
 *       sometimes smaller windows will give better performance
 *       (thus the boundaries should be increased)
 */
#define EC_window_bits_for_scalar_size(b) \
            ((size_t) \
             ((b) >= 2000 ? 6 : \
              (b) >=  800 ? 5 : \
              (b) >=  300 ? 4 : \
              (b) >=   70 ? 3 : \
              (b) >=   20 ? 2 : \
              1))

/* Compute
 *      \sum scalars[i]*points[i],
 * also including
 *      scalar*generator
 * in the addition if scalar != NULL
 */
int ec_wNAF_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;
      const EC_POINT *generator = NULL;
      EC_POINT *tmp = NULL;
      size_t totalnum;
      size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
      size_t pre_points_per_block = 0;
      size_t i, j;
      int k;
      int r_is_inverted = 0;
      int r_is_at_infinity = 1;
      size_t *wsize = NULL; /* individual window sizes */
      signed char **wNAF = NULL; /* individual wNAFs */
      size_t *wNAF_len = NULL;
      size_t max_len = 0;
      size_t num_val;
      EC_POINT **val = NULL; /* precomputation */
      EC_POINT **v;
      EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
      const EC_PRE_COMP *pre_comp = NULL;
      int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
                           * i.e. precomputation is not available */
      int ret = 0;
      
      if (group->meth != r->meth)
            {
            ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
            return 0;
            }

      if ((scalar == NULL) && (num == 0))
            {
            return EC_POINT_set_to_infinity(group, r);
            }

      for (i = 0; i < num; i++)
            {
            if (group->meth != points[i]->meth)
                  {
                  ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
                  return 0;
                  }
            }

      if (ctx == NULL)
            {
            ctx = new_ctx = BN_CTX_new();
            if (ctx == NULL)
                  goto err;
            }

      if (scalar != NULL)
            {
            generator = EC_GROUP_get0_generator(group);
            if (generator == NULL)
                  {
                  ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
                  goto err;
                  }
            
            /* look if we can use precomputed multiples of generator */

            pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);

            if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
                  {
                  blocksize = pre_comp->blocksize;

                  /* determine maximum number of blocks that wNAF splitting may yield
                   * (NB: maximum wNAF length is bit length plus one) */
                  numblocks = (BN_num_bits(scalar) / blocksize) + 1;

                  /* we cannot use more blocks than we have precomputation for */
                  if (numblocks > pre_comp->numblocks)
                        numblocks = pre_comp->numblocks;

                  pre_points_per_block = (size_t)1 << (pre_comp->w - 1);

                  /* check that pre_comp looks sane */
                  if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
                        {
                        ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
                        goto err;
                        }
                  }
            else
                  {
                  /* can't use precomputation */
                  pre_comp = NULL;
                  numblocks = 1;
                  num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
                  }
            }
      
      totalnum = num + numblocks;

      wsize    = OPENSSL_malloc(totalnum * sizeof wsize[0]);
      wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
      wNAF     = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
      val_sub  = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
             
      if (!wsize || !wNAF_len || !wNAF || !val_sub)
            {
            ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
            goto err;
            }

      wNAF[0] = NULL;   /* preliminary pivot */

      /* num_val will be the total number of temporarily precomputed points */
      num_val = 0;

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

            bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
            wsize[i] = EC_window_bits_for_scalar_size(bits);
            num_val += (size_t)1 << (wsize[i] - 1);
            wNAF[i + 1] = NULL; /* make sure we always have a pivot */
            wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
            if (wNAF[i] == NULL)
                  goto err;
            if (wNAF_len[i] > max_len)
                  max_len = wNAF_len[i];
            }

      if (numblocks)
            {
            /* we go here iff scalar != NULL */
            
            if (pre_comp == NULL)
                  {
                  if (num_scalar != 1)
                        {
                        ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
                        goto err;
                        }
                  /* we have already generated a wNAF for 'scalar' */
                  }
            else
                  {
                  signed char *tmp_wNAF = NULL;
                  size_t tmp_len = 0;
                  
                  if (num_scalar != 0)
                        {
                        ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
                        goto err;
                        }

                  /* use the window size for which we have precomputation */
                  wsize[num] = pre_comp->w;
                  tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
                  if (!tmp_wNAF)
                        goto err;

                  if (tmp_len <= max_len)
                        {
                        /* One of the other wNAFs is at least as long
                         * as the wNAF belonging to the generator,
                         * so wNAF splitting will not buy us anything. */

                        numblocks = 1;
                        totalnum = num + 1; /* don't use wNAF splitting */
                        wNAF[num] = tmp_wNAF;
                        wNAF[num + 1] = NULL;
                        wNAF_len[num] = tmp_len;
                        if (tmp_len > max_len)
                              max_len = tmp_len;
                        /* pre_comp->points starts with the points that we need here: */
                        val_sub[num] = pre_comp->points;
                        }
                  else
                        {
                        /* don't include tmp_wNAF directly into wNAF array
                         * - use wNAF splitting and include the blocks */

                        signed char *pp;
                        EC_POINT **tmp_points;
                        
                        if (tmp_len < numblocks * blocksize)
                              {
                              /* possibly we can do with fewer blocks than estimated */
                              numblocks = (tmp_len + blocksize - 1) / blocksize;
                              if (numblocks > pre_comp->numblocks)
                                    {
                                    ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
                                    goto err;
                                    }
                              totalnum = num + numblocks;
                              }
                        
                        /* split wNAF in 'numblocks' parts */
                        pp = tmp_wNAF;
                        tmp_points = pre_comp->points;

                        for (i = num; i < totalnum; i++)
                              {
                              if (i < totalnum - 1)
                                    {
                                    wNAF_len[i] = blocksize;
                                    if (tmp_len < blocksize)
                                          {
                                          ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
                                          goto err;
                                          }
                                    tmp_len -= blocksize;
                                    }
                              else
                                    /* last block gets whatever is left
                                     * (this could be more or less than 'blocksize'!) */
                                    wNAF_len[i] = tmp_len;
                              
                              wNAF[i + 1] = NULL;
                              wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
                              if (wNAF[i] == NULL)
                                    {
                                    ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
                                    OPENSSL_free(tmp_wNAF);
                                    goto err;
                                    }
                              memcpy(wNAF[i], pp, wNAF_len[i]);
                              if (wNAF_len[i] > max_len)
                                    max_len = wNAF_len[i];

                              if (*tmp_points == NULL)
                                    {
                                    ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
                                    OPENSSL_free(tmp_wNAF);
                                    goto err;
                                    }
                              val_sub[i] = tmp_points;
                              tmp_points += pre_points_per_block;
                              pp += blocksize;
                              }
                        OPENSSL_free(tmp_wNAF);
                        }
                  }
            }

      /* All points we precompute now go into a single array 'val'.
       * 'val_sub[i]' is a pointer to the subarray for the i-th point,
       * or to a subarray of 'pre_comp->points' if we already have precomputation. */
      val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
      if (val == NULL)
            {
            ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
            goto err;
            }
      val[num_val] = NULL; /* pivot element */

      /* allocate points for precomputation */
      v = val;
      for (i = 0; i < num + num_scalar; i++)
            {
            val_sub[i] = v;
            for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++)
                  {
                  *v = EC_POINT_new(group);
                  if (*v == NULL) goto err;
                  v++;
                  }
            }
      if (!(v == val + num_val))
            {
            ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
            goto err;
            }

      if (!(tmp = EC_POINT_new(group)))
            goto err;

      /* prepare precomputed values:
       *    val_sub[i][0] :=     points[i]
       *    val_sub[i][1] := 3 * points[i]
       *    val_sub[i][2] := 5 * points[i]
       *    ...
       */
      for (i = 0; i < num + num_scalar; i++)
            {
            if (i < num)
                  {
                  if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
                  }
            else
                  {
                  if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
                  }

            if (wsize[i] > 1)
                  {
                  if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
                  for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++)
                        {
                        if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
                        }
                  }
            }

#if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
      if (!EC_POINTs_make_affine(group, num_val, val, ctx))
            goto err;
#endif

      r_is_at_infinity = 1;

      for (k = max_len - 1; k >= 0; k--)
            {
            if (!r_is_at_infinity)
                  {
                  if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
                  }
            
            for (i = 0; i < totalnum; i++)
                  {
                  if (wNAF_len[i] > (size_t)k)
                        {
                        int digit = wNAF[i][k];
                        int is_neg;

                        if (digit) 
                              {
                              is_neg = digit < 0;

                              if (is_neg)
                                    digit = -digit;

                              if (is_neg != r_is_inverted)
                                    {
                                    if (!r_is_at_infinity)
                                          {
                                          if (!EC_POINT_invert(group, r, ctx)) goto err;
                                          }
                                    r_is_inverted = !r_is_inverted;
                                    }

                              /* digit > 0 */

                              if (r_is_at_infinity)
                                    {
                                    if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
                                    r_is_at_infinity = 0;
                                    }
                              else
                                    {
                                    if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
                                    }
                              }
                        }
                  }
            }

      if (r_is_at_infinity)
            {
            if (!EC_POINT_set_to_infinity(group, r)) goto err;
            }
      else
            {
            if (r_is_inverted)
                  if (!EC_POINT_invert(group, r, ctx)) goto err;
            }
      
      ret = 1;

 err:
      if (new_ctx != NULL)
            BN_CTX_free(new_ctx);
      if (tmp != NULL)
            EC_POINT_free(tmp);
      if (wsize != NULL)
            OPENSSL_free(wsize);
      if (wNAF_len != NULL)
            OPENSSL_free(wNAF_len);
      if (wNAF != NULL)
            {
            signed char **w;
            
            for (w = wNAF; *w != NULL; w++)
                  OPENSSL_free(*w);
            
            OPENSSL_free(wNAF);
            }
      if (val != NULL)
            {
            for (v = val; *v != NULL; v++)
                  EC_POINT_clear_free(*v);

            OPENSSL_free(val);
            }
      if (val_sub != NULL)
            {
            OPENSSL_free(val_sub);
            }
      return ret;
      }


/* ec_wNAF_precompute_mult()
 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
 * for use with wNAF splitting as implemented in ec_wNAF_mul().
 * 
 * 'pre_comp->points' is an array of multiples of the generator
 * of the following form:
 * points[0] =     generator;
 * points[1] = 3 * generator;
 * ...
 * points[2^(w-1)-1] =     (2^(w-1)-1) * generator;
 * points[2^(w-1)]   =     2^blocksize * generator;
 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
 * ...
 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) *  2^(blocksize*(numblocks-2)) * generator
 * points[2^(w-1)*(numblocks-1)]   =              2^(blocksize*(numblocks-1)) * generator
 * ...
 * points[2^(w-1)*numblocks-1]     = (2^(w-1)) *  2^(blocksize*(numblocks-1)) * generator
 * points[2^(w-1)*numblocks]       = NULL
 */
int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
      {
      const EC_POINT *generator;
      EC_POINT *tmp_point = NULL, *base = NULL, **var;
      BN_CTX *new_ctx = NULL;
      BIGNUM *order;
      size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
      EC_POINT **points = NULL;
      EC_PRE_COMP *pre_comp;
      int ret = 0;

      /* if there is an old EC_PRE_COMP object, throw it away */
      EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);

      if ((pre_comp = ec_pre_comp_new(group)) == NULL)
            return 0;

      generator = EC_GROUP_get0_generator(group);
      if (generator == NULL)
            {
            ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
            goto err;
            }

      if (ctx == NULL)
            {
            ctx = new_ctx = BN_CTX_new();
            if (ctx == NULL)
                  goto err;
            }
      
      BN_CTX_start(ctx);
      order = BN_CTX_get(ctx);
      if (order == NULL) goto err;
      
      if (!EC_GROUP_get_order(group, order, ctx)) goto err;       
      if (BN_is_zero(order))
            {
            ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
            goto err;
            }

      bits = BN_num_bits(order);
      /* The following parameters mean we precompute (approximately)
       * one point per bit.
       *
       * TBD: The combination  8, 4  is perfect for 160 bits; for other
       * bit lengths, other parameter combinations might provide better
       * efficiency.
       */
      blocksize = 8;
      w = 4;
      if (EC_window_bits_for_scalar_size(bits) > w)
            {
            /* let's not make the window too small ... */
            w = EC_window_bits_for_scalar_size(bits);
            }

      numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
      
      pre_points_per_block = (size_t)1 << (w - 1);
      num = pre_points_per_block * numblocks; /* number of points to compute and store */

      points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
      if (!points)
            {
            ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
            goto err;
            }

      var = points;
      var[num] = NULL; /* pivot */
      for (i = 0; i < num; i++)
            {
            if ((var[i] = EC_POINT_new(group)) == NULL)
                  {
                  ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
                  goto err;
                  }
            }

      if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
            {
            ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
            goto err;
            }     
      
      if (!EC_POINT_copy(base, generator))
            goto err;
      
      /* do the precomputation */
      for (i = 0; i < numblocks; i++)
            {
            size_t j;

            if (!EC_POINT_dbl(group, tmp_point, base, ctx))
                  goto err;

            if (!EC_POINT_copy(*var++, base))
                  goto err;

            for (j = 1; j < pre_points_per_block; j++, var++)
                  {
                  /* calculate odd multiples of the current base point */
                  if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
                        goto err;
                  }

            if (i < numblocks - 1)
                  {
                  /* get the next base (multiply current one by 2^blocksize) */
                  size_t k;

                  if (blocksize <= 2)
                        {
                        ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
                        goto err;
                        }                       

                  if (!EC_POINT_dbl(group, base, tmp_point, ctx))
                        goto err;
                  for (k = 2; k < blocksize; k++)
                        {
                        if (!EC_POINT_dbl(group,base,base,ctx))
                              goto err;
                        }
                  }
            }

      if (!EC_POINTs_make_affine(group, num, points, ctx))
            goto err;
      
      pre_comp->group = group;
      pre_comp->blocksize = blocksize;
      pre_comp->numblocks = numblocks;
      pre_comp->w = w;
      pre_comp->points = points;
      points = NULL;
      pre_comp->num = num;

      if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
            ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
            goto err;
      pre_comp = NULL;

      ret = 1;
 err:
      if (ctx != NULL)
            BN_CTX_end(ctx);
      if (new_ctx != NULL)
            BN_CTX_free(new_ctx);
      if (pre_comp)
            ec_pre_comp_free(pre_comp);
      if (points)
            {
            EC_POINT **p;

            for (p = points; *p != NULL; p++)
                  EC_POINT_free(*p);
            OPENSSL_free(points);
            }
      if (tmp_point)
            EC_POINT_free(tmp_point);
      if (base)
            EC_POINT_free(base);
      return ret;
      }


int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
      {
      if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
            return 1;
      else
            return 0;
      }

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