ec_mult.c   [plain text]

/* 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 */
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(pre->points, sizeof pre->points);
		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;
		}

	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;
		}

	if (scalar->d == NULL || scalar->top == 0)
		{
		ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
		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 = 1u << (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 += 1u << (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 < (1u << (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 < (1u << (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 = 1u << (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;
	}