427 lines
12 KiB
C
427 lines
12 KiB
C
/* crypto/ec/ec_mult.c */
|
|
/* ====================================================================
|
|
* Copyright (c) 1998-2001 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).
|
|
*
|
|
*/
|
|
|
|
#include <openssl/err.h>
|
|
|
|
#include "ec_lcl.h"
|
|
|
|
|
|
/* TODO: width-m NAFs */
|
|
|
|
/* TODO: optional precomputation of multiples of the generator */
|
|
|
|
|
|
#define EC_window_bits_for_scalar_size(b) \
|
|
((b) >= 2000 ? 6 : \
|
|
(b) >= 800 ? 5 : \
|
|
(b) >= 300 ? 4 : \
|
|
(b) >= 70 ? 3 : \
|
|
(b) >= 20 ? 2 : \
|
|
1)
|
|
/* For window size 'w' (w >= 2), we compute the odd multiples
|
|
* 1*P .. (2^w-1)*P.
|
|
* This accounts for 2^(w-1) point additions (neglecting constants),
|
|
* each of which requires 16 field multiplications (4 squarings
|
|
* and 12 general multiplications) in the case of curves defined
|
|
* over GF(p), which are the only curves we have so far.
|
|
*
|
|
* Converting these precomputed points into affine form takes
|
|
* three field multiplications for inverting Z and one squaring
|
|
* and three multiplications for adjusting X and Y, i.e.
|
|
* 7 multiplications in total (1 squaring and 6 general multiplications),
|
|
* again except for constants.
|
|
*
|
|
* The average number of windows for a 'b' bit scalar is roughly
|
|
* b/(w+1).
|
|
* Each of these windows (except possibly for the first one, but
|
|
* we are ignoring constants anyway) requires one point addition.
|
|
* As the precomputed table stores points in affine form, these
|
|
* additions take only 11 field multiplications each (3 squarings
|
|
* and 8 general multiplications).
|
|
*
|
|
* So the total workload, except for constants, is
|
|
*
|
|
* 2^(w-1)*[5 squarings + 18 multiplications]
|
|
* + (b/(w+1))*[3 squarings + 8 multiplications]
|
|
*
|
|
* If we assume that 10 squarings are as costly as 9 multiplications,
|
|
* our task is to find the 'w' that, given 'b', minimizes
|
|
*
|
|
* 2^(w-1)*(5*9 + 18*10) + (b/(w+1))*(3*9 + 8*10)
|
|
* = 2^(w-1)*225 + (b/(w+1))*107.
|
|
*
|
|
* Thus optimal window sizes should be roughly as follows:
|
|
*
|
|
* w >= 6 if b >= 1414
|
|
* w = 5 if 1413 >= b >= 505
|
|
* w = 4 if 504 >= b >= 169
|
|
* w = 3 if 168 >= b >= 51
|
|
* w = 2 if 50 >= b >= 13
|
|
* w = 1 if 12 >= b
|
|
*
|
|
* If we assume instead that squarings are exactly as costly as
|
|
* multiplications, we have to minimize
|
|
* 2^(w-1)*23 + (b/(w+1))*11.
|
|
*
|
|
* This gives us the following (nearly unchanged) table of optimal
|
|
* windows sizes:
|
|
*
|
|
* w >= 6 if b >= 1406
|
|
* w = 5 if 1405 >= b >= 502
|
|
* w = 4 if 501 >= b >= 168
|
|
* w = 3 if 167 >= b >= 51
|
|
* w = 2 if 50 >= b >= 13
|
|
* w = 1 if 12 >= b
|
|
*
|
|
* Note that neither table tries to take into account memory usage
|
|
* (allocation overhead, code locality etc.). Actual timings with
|
|
* NIST curves P-192, P-224, and P-256 with scalars of 192, 224,
|
|
* and 256 bits, respectively, show that w = 3 (instead of 4) is
|
|
* preferrable; timings with NIST curve P-384 and 384-bit scalars
|
|
* confirm that w = 4 is optimal for this case; and timings with
|
|
* NIST curve P-521 and 521-bit scalars show that w = 4 (instead
|
|
* of 5) is preferrable. So we generously round up all the
|
|
* boundaries and use the following table:
|
|
*
|
|
* w >= 6 if b >= 2000
|
|
* w = 5 if 1999 >= b >= 800
|
|
* w = 4 if 799 >= b >= 300
|
|
* w = 3 if 299 >= b >= 70
|
|
* w = 2 if 69 >= b >= 20
|
|
* w = 1 if 19 >= b
|
|
*/
|
|
|
|
|
|
|
|
/* Compute
|
|
* \sum scalars[i]*points[i],
|
|
* also including
|
|
* scalar*generator
|
|
* in the addition if scalar != NULL
|
|
*/
|
|
int EC_POINTs_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;
|
|
EC_POINT *generator = NULL;
|
|
EC_POINT *tmp = NULL;
|
|
size_t totalnum;
|
|
size_t i, j;
|
|
int k, t;
|
|
int r_is_at_infinity = 1;
|
|
size_t max_bits = 0;
|
|
size_t *wsize = NULL; /* individual window sizes */
|
|
unsigned long *wbits = NULL; /* individual window contents */
|
|
int *wpos = NULL; /* position of bottom bit of current individual windows
|
|
* (wpos[i] is valid if wbits[i] != 0) */
|
|
size_t num_val;
|
|
EC_POINT **val = NULL; /* precomputation */
|
|
EC_POINT **v;
|
|
EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */
|
|
int ret = 0;
|
|
|
|
if (scalar != NULL)
|
|
{
|
|
generator = EC_GROUP_get0_generator(group);
|
|
if (generator == NULL)
|
|
{
|
|
ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
for (i = 0; i < num; i++)
|
|
{
|
|
if (group->meth != points[i]->meth)
|
|
{
|
|
ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
totalnum = num + (scalar != NULL);
|
|
|
|
wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
|
|
wbits = OPENSSL_malloc(totalnum * sizeof wbits[0]);
|
|
wpos = OPENSSL_malloc(totalnum * sizeof wpos[0]);
|
|
if (wsize == NULL || wbits == NULL || wpos == NULL) goto err;
|
|
|
|
/* num_val := total number of points to precompute */
|
|
num_val = 0;
|
|
for (i = 0; i < totalnum; 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);
|
|
if (bits > max_bits)
|
|
max_bits = bits;
|
|
wbits[i] = 0;
|
|
wpos[i] = 0;
|
|
}
|
|
|
|
/* all precomputed points go into a single array 'val',
|
|
* 'val_sub[i]' is a pointer to the subarray for the i-th point */
|
|
val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
|
|
if (val == NULL) goto err;
|
|
val[num_val] = NULL; /* pivot element */
|
|
|
|
val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
|
|
if (val_sub == NULL) goto err;
|
|
|
|
/* allocate points for precomputation */
|
|
v = val;
|
|
for (i = 0; i < totalnum; 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_POINTS_MUL, ERR_R_INTERNAL_ERROR);
|
|
goto err;
|
|
}
|
|
|
|
if (ctx == NULL)
|
|
{
|
|
ctx = new_ctx = BN_CTX_new();
|
|
if (ctx == NULL)
|
|
goto err;
|
|
}
|
|
|
|
tmp = EC_POINT_new(group);
|
|
if (tmp == NULL) 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 < totalnum; i++)
|
|
{
|
|
if (i < num)
|
|
{
|
|
if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
|
|
if (scalars[i]->neg)
|
|
{
|
|
if (!EC_POINT_invert(group, val_sub[i][0], ctx)) goto err;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
|
|
if (scalar->neg)
|
|
{
|
|
if (!EC_POINT_invert(group, val_sub[i][0], ctx)) 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_bits - 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 (wbits[i] == 0)
|
|
{
|
|
const BIGNUM *s;
|
|
|
|
s = i < num ? scalars[i] : scalar;
|
|
|
|
if (BN_is_bit_set(s, k))
|
|
{
|
|
/* look at bits k - wsize[i] + 1 .. k for this window */
|
|
t = k - wsize[i] + 1;
|
|
while (!BN_is_bit_set(s, t)) /* BN_is_bit_set is false for t < 0 */
|
|
t++;
|
|
wpos[i] = t;
|
|
wbits[i] = 1;
|
|
for (t = k - 1; t >= wpos[i]; t--)
|
|
{
|
|
wbits[i] <<= 1;
|
|
if (BN_is_bit_set(s, t))
|
|
wbits[i]++;
|
|
}
|
|
/* now wbits[i] is the odd bit pattern at bits wpos[i] .. k */
|
|
}
|
|
}
|
|
|
|
if ((wbits[i] != 0) && (wpos[i] == k))
|
|
{
|
|
if (r_is_at_infinity)
|
|
{
|
|
if (!EC_POINT_copy(r, val_sub[i][wbits[i] >> 1])) goto err;
|
|
r_is_at_infinity = 0;
|
|
}
|
|
else
|
|
{
|
|
if (!EC_POINT_add(group, r, r, val_sub[i][wbits[i] >> 1], ctx)) goto err;
|
|
}
|
|
wbits[i] = 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (r_is_at_infinity)
|
|
if (!EC_POINT_set_to_infinity(group, r)) 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 (wbits != NULL)
|
|
OPENSSL_free(wbits);
|
|
if (wpos != NULL)
|
|
OPENSSL_free(wpos);
|
|
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;
|
|
}
|
|
|
|
|
|
int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx)
|
|
{
|
|
const EC_POINT *points[1];
|
|
const BIGNUM *scalars[1];
|
|
|
|
points[0] = point;
|
|
scalars[0] = p_scalar;
|
|
|
|
return EC_POINTs_mul(group, r, g_scalar, (point != NULL && p_scalar != NULL), points, scalars, ctx);
|
|
}
|
|
|
|
|
|
int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
|
|
{
|
|
const EC_POINT *generator;
|
|
BN_CTX *new_ctx = NULL;
|
|
BIGNUM *order;
|
|
int ret = 0;
|
|
|
|
generator = EC_GROUP_get0_generator(group);
|
|
if (generator == NULL)
|
|
{
|
|
ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
|
|
return 0;
|
|
}
|
|
|
|
if (ctx == NULL)
|
|
{
|
|
ctx = new_ctx = BN_CTX_new();
|
|
if (ctx == NULL)
|
|
return 0;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
order = BN_CTX_get(ctx);
|
|
if (order == NULL) goto err;
|
|
|
|
if (!EC_GROUP_get_order(group, order, ctx)) return 0;
|
|
if (BN_is_zero(order))
|
|
{
|
|
ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
|
|
goto err;
|
|
}
|
|
|
|
/* TODO */
|
|
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
if (new_ctx != NULL)
|
|
BN_CTX_free(new_ctx);
|
|
return ret;
|
|
}
|