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Revision 63ef0db60f7b9fc0c2bcabdc7e2bd133784ddd60 authored by Adam Langley on 13 December 2014, 20:13:10 UTC, committed by Matt Caswell on 16 December 2014, 14:46:57 UTC
Don't set client_version to the ServerHello version.
The client_version needs to be preserved for the RSA key exchange.

This change also means that renegotiation will, like TLS, repeat the old
client_version rather than advertise only the final version. (Either way,
version change on renego is not allowed.) This is necessary in TLS to work
around an SChannel bug, but it's not strictly necessary in DTLS.

(From BoringSSL)

Reviewed-by: Emilia Käsper <emilia@openssl.org>
(cherry picked from commit ec1af3c4195c1dfecdd9dc7458850ab1b8b951e0)
1 parent f74f5c8
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  • ec
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  • ec_mult.c
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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 */
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]);

	/* Ensure wNAF is initialised in case we end up going to err */
	if (wNAF) wNAF[0] = NULL;	/* preliminary pivot */

	if (!wsize || !wNAF_len || !wNAF || !val_sub)
		{
		ECerr(EC_F_EC_WNAF_MUL, 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)
				{
				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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