ec_mult.c revision 9dc0df1bac950d6e491f9a7c7e4888f2b301cb15
/*
* Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
*/
/* ====================================================================
* Copyright (c) 1998-2003 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
* 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 "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 {
size_t w; /* window size */
* 'num' pointers to EC_POINT objects followed by a NULL */
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 *);
{
if (!group)
return NULL;
if (!ret)
return ret;
return ret;
}
static void *ec_pre_comp_dup(void *src_)
{
/* no need to actually copy, these objects never change! */
return src_;
}
static void ec_pre_comp_free(void *pre_)
{
int i;
if (!pre)
return;
if (i > 0)
return;
{
EC_POINT **p;
EC_POINT_free(*p);
}
}
static void ec_pre_comp_clear_free(void *pre_)
{
int i;
if (!pre)
return;
if (i > 0)
return;
{
EC_POINT **p;
EC_POINT_clear_free(*p);
}
}
/* 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.
*/
{
int window_val;
int ok = 0;
signed char *r = NULL;
int sign = 1;
if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
{
goto err;
}
if (BN_is_negative(scalar))
{
sign = -1;
}
* (*ret_len will be set to the actual length, i.e. at most
* BN_num_bits(scalar) + 1) */
{
goto err;
}
j = 0;
{
int digit = 0;
/* 0 <= window_val <= 2^(w+1) */
if (window_val & 1)
{
/* 0 < window_val < 2^(w+1) */
if (window_val & bit)
{
#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 */
}
#endif
}
else
{
}
{
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
*/
{
goto err;
}
}
window_val >>= 1;
if (window_val > next_bit)
{
goto err;
}
}
if (j > len + 1)
{
goto err;
}
len = j;
ok = 1;
err:
if (!ok)
{
OPENSSL_free(r);
r = NULL;
}
if (ok)
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
*/
{
size_t i, j;
int k;
int r_is_inverted = 0;
int r_is_at_infinity = 1;
EC_POINT **v;
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;
{
return 0;
}
{
return EC_POINT_set_to_infinity(group, r);
}
for (i = 0; i < num; i++)
{
{
return 0;
}
}
{
goto err;
}
{
{
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))
{
/* determine maximum number of blocks that wNAF splitting may yield
* (NB: maximum wNAF length is bit length plus one) */
/* we cannot use more blocks than we have precomputation for */
/* check that pre_comp looks sane */
{
goto err;
}
}
else
{
/* can't use precomputation */
numblocks = 1;
}
}
goto err;
/* num_val will be the total number of temporarily precomputed points */
num_val = 0;
for (i = 0; i < num + num_scalar; i++)
{
goto err;
}
if (numblocks)
{
/* we go here iff scalar != NULL */
{
if (num_scalar != 1)
{
goto err;
}
/* we have already generated a wNAF for 'scalar' */
}
else
{
if (num_scalar != 0)
{
goto err;
}
/* use the window size for which we have precomputation */
if (!tmp_wNAF)
goto err;
{
/* 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;
/* pre_comp->points starts with the points that we need here: */
}
else
{
/* don't include tmp_wNAF directly into wNAF array
* - use wNAF splitting and include the blocks */
signed char *pp;
{
/* possibly we can do with fewer blocks than estimated */
{
goto err;
}
}
/* split wNAF in 'numblocks' parts */
{
if (i < totalnum - 1)
{
{
goto err;
}
}
else
/* last block gets whatever is left
* (this could be more or less than 'blocksize'!) */
{
goto err;
}
if (*tmp_points == NULL)
{
goto err;
}
val_sub[i] = tmp_points;
}
}
}
}
/* 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. */
/* allocate points for precomputation */
v = val;
for (i = 0; i < num + num_scalar; i++)
{
val_sub[i] = v;
{
*v = EC_POINT_new(group);
v++;
}
}
{
goto err;
}
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)
{
}
else
{
}
if (wsize[i] > 1)
{
{
}
}
}
#if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
goto err;
#endif
r_is_at_infinity = 1;
for (k = max_len - 1; k >= 0; k--)
{
if (!r_is_at_infinity)
{
}
for (i = 0; i < totalnum; i++)
{
{
int is_neg;
if (digit)
{
if (is_neg)
if (is_neg != r_is_inverted)
{
if (!r_is_at_infinity)
{
}
}
/* digit > 0 */
if (r_is_at_infinity)
{
r_is_at_infinity = 0;
}
else
{
}
}
}
}
}
if (r_is_at_infinity)
{
}
else
{
if (r_is_inverted)
}
ret = 1;
err:
{
signed char **w;
OPENSSL_free(*w);
}
{
EC_POINT_clear_free(*v);
}
{
}
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 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);
return 0;
{
goto err;
}
{
goto err;
}
if (BN_is_zero(order))
{
goto err;
}
/* 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 ... */
}
numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
if (!points)
{
goto err;
}
for (i = 0; i < num; i++)
{
{
goto err;
}
}
{
goto err;
}
goto err;
/* do the precomputation */
for (i = 0; i < numblocks; i++)
{
size_t j;
goto err;
goto err;
{
/* calculate odd multiples of the current base point */
goto err;
}
if (i < numblocks - 1)
{
/* get the next base (multiply current one by 2^blocksize) */
size_t k;
if (blocksize <= 2)
{
goto err;
}
goto err;
for (k = 2; k < blocksize; k++)
{
goto err;
}
}
}
goto err;
pre_comp->w = w;
goto err;
ret = 1;
err:
if (pre_comp)
if (points)
{
EC_POINT **p;
EC_POINT_free(*p);
}
if (tmp_point)
if (base)
return ret;
}
{
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;
}