/* $OpenBSD: ec_mult.c,v 1.21 2017/05/02 03:59:44 deraadt Exp $ */
/*
 * 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 = malloc(sizeof(EC_PRE_COMP));
	if (!ret) {
		ECerror(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);
		free(pre->points);
	}
	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);
			explicit_bzero(p, sizeof *p);
		}
		free(pre->points);
	}
	freezero(pre, sizeof *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 = malloc(1);
		if (!r) {
			ECerror(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 */
		ECerror(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) {
		ECerror(ERR_R_INTERNAL_ERROR);
		goto err;
	}
	len = BN_num_bits(scalar);
	r = 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) {
		ECerror(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)) {
				ECerror(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) {
				ECerror(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) {
			ECerror(ERR_R_INTERNAL_ERROR);
			goto err;
		}
	}

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

err:
	if (!ok) {
		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 */
	signed char *tmp_wNAF = NULL;
	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) {
		ECerror(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) {
			ECerror(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) {
			ECerror(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)) {
				ECerror(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;

	/* includes space for pivot */
	wNAF = reallocarray(NULL, (totalnum + 1), sizeof wNAF[0]);
	if (wNAF == NULL) {
		ECerror(ERR_R_MALLOC_FAILURE);
		goto err;
	}

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

	wsize = reallocarray(NULL, totalnum, sizeof wsize[0]);
	wNAF_len = reallocarray(NULL, totalnum, sizeof wNAF_len[0]);
	val_sub = reallocarray(NULL, totalnum, sizeof val_sub[0]);

	if (wsize == NULL || wNAF_len == NULL || val_sub == NULL) {
		ECerror(ERR_R_MALLOC_FAILURE);
		goto err;
	}

	/* 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) {
				ECerror(ERR_R_INTERNAL_ERROR);
				goto err;
			}
			/* we have already generated a wNAF for 'scalar' */
		} else {
			size_t tmp_len = 0;

			if (num_scalar != 0) {
				ECerror(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 == NULL)
				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;
				tmp_wNAF = NULL;
				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) {
						ECerror(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) {
							ECerror(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] = malloc(wNAF_len[i]);
					if (wNAF[i] == NULL) {
						ECerror(ERR_R_MALLOC_FAILURE);
						goto err;
					}
					memcpy(wNAF[i], pp, wNAF_len[i]);
					if (wNAF_len[i] > max_len)
						max_len = wNAF_len[i];

					if (*tmp_points == NULL) {
						ECerror(ERR_R_INTERNAL_ERROR);
						goto err;
					}
					val_sub[i] = tmp_points;
					tmp_points += pre_points_per_block;
					pp += blocksize;
				}
			}
		}
	}
	/*
	 * 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 = reallocarray(NULL, (num_val + 1), sizeof val[0]);
	if (val == NULL) {
		ECerror(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)) {
		ECerror(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 (!EC_POINTs_make_affine(group, num_val, val, ctx))
		goto err;

	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:
	BN_CTX_free(new_ctx);
	EC_POINT_free(tmp);
	free(wsize);
	free(wNAF_len);
	free(tmp_wNAF);
	if (wNAF != NULL) {
		signed char **w;

		for (w = wNAF; *w != NULL; w++)
			free(*w);

		free(wNAF);
	}
	if (val != NULL) {
		for (v = val; *v != NULL; v++)
			EC_POINT_clear_free(*v);
		free(val);
	}
	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) {
		ECerror(EC_R_UNDEFINED_GENERATOR);
		goto err;
	}
	if (ctx == NULL) {
		ctx = new_ctx = BN_CTX_new();
		if (ctx == NULL)
			goto err;
	}
	BN_CTX_start(ctx);
	if ((order = BN_CTX_get(ctx)) == NULL)
		goto err;

	if (!EC_GROUP_get_order(group, order, ctx))
		goto err;
	if (BN_is_zero(order)) {
		ECerror(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 = reallocarray(NULL, (num + 1), sizeof(EC_POINT *));
	if (!points) {
		ECerror(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) {
			ECerror(ERR_R_MALLOC_FAILURE);
			goto err;
		}
	}

	if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) {
		ECerror(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) {
				ECerror(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);
	BN_CTX_free(new_ctx);
	ec_pre_comp_free(pre_comp);
	if (points) {
		EC_POINT **p;

		for (p = points; *p != NULL; p++)
			EC_POINT_free(*p);
		free(points);
	}
	EC_POINT_free(tmp_point);
	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;
}
