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Improve EC efficiency.

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This commit is contained in:
Bodo Möller 2001-11-15 22:32:11 +00:00
parent bbc206fdf7
commit 3ba1f11147
4 changed files with 373 additions and 13 deletions
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13
CHANGES
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@ -12,6 +12,10 @@
*) applies to 0.9.6a/0.9.6b/0.9.6c and 0.9.7
+) applies to 0.9.7 only
+) Use wNAFs in EC_POINTs_mul() for improved efficiency (about 10%
better than before for single multiplications over P-192 or P-224).
[Bodo Moeller]
-) [In 0.9.6c-engine release:]
Add support for Broadcom crypto accelerator cards, backported
from 0.9.7.
@ -943,9 +947,12 @@ des-cbc 3624.96k 5258.21k 5530.91k 5624.30k 5628.26k
don't write to the wrong index in ERR_set_error_data.
[Bodo Moeller]
+) Function EC_POINTs_mul for simultaneous scalar multiplication
of an arbitrary number of elliptic curve points, optionally
including the generator defined for the EC_GROUP.
+) Function EC_POINTs_mul for multiple scalar multiplication
of an arbitrary number of elliptic curve points
\sum scalars[i]*points[i],
optionally including the generator defined for the EC_GROUP:
scalar*generator + \sum scalars[i]*points[i].
EC_POINT_mul is a simple wrapper function for the typical case
that the point list has just one item (besides the optional
generator).

1
crypto/ec/ec.h
View File

@ -177,6 +177,7 @@ void ERR_load_EC_strings(void);
/* Error codes for the EC functions. */
/* Function codes. */
#define EC_F_COMPUTE_WNAF 143
#define EC_F_EC_GFP_MONT_FIELD_DECODE 133
#define EC_F_EC_GFP_MONT_FIELD_ENCODE 134
#define EC_F_EC_GFP_MONT_FIELD_MUL 131

1
crypto/ec/ec_err.c
View File

@ -66,6 +66,7 @@
#ifndef OPENSSL_NO_ERR
static ERR_STRING_DATA EC_str_functs[]=
{
{ERR_PACK(0,EC_F_COMPUTE_WNAF,0), "COMPUTE_WNAF"},
{ERR_PACK(0,EC_F_EC_GFP_MONT_FIELD_DECODE,0), "ec_GFp_mont_field_decode"},
{ERR_PACK(0,EC_F_EC_GFP_MONT_FIELD_ENCODE,0), "ec_GFp_mont_field_encode"},
{ERR_PACK(0,EC_F_EC_GFP_MONT_FIELD_MUL,0), "ec_GFp_mont_field_mul"},

371
crypto/ec/ec_mult.c
View File

@ -58,11 +58,369 @@
#include "ec_lcl.h"
/* TODO: width-m NAFs */
/* TODO: optional precomputation of multiples of the generator */
#if 1
/*
* wNAF-based interleaving multi-exponentation method
*/
/* Determine the width-(w+1) Non-Adjacent Form 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.
*/
static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len, BN_CTX *ctx)
{
BIGNUM *c;
int ok = 0;
signed char *r = NULL;
int sign = 1;
int bit, next_bit, mask;
size_t len, j;
BN_CTX_start(ctx);
c = BN_CTX_get(ctx);
if (c == NULL) goto err;
if (w <= 0 || w > 7) /* 'unsigned 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_copy(c, scalar)) goto err;
if (c->neg)
{
sign = -1;
c->neg = 0;
}
len = BN_num_bits(c) + 1; /* wNAF may be one digit longer than binary representation */
r = OPENSSL_malloc(len);
if (r == NULL) goto err;
j = 0;
while (!BN_is_zero(c))
{
int u = 0;
if (BN_is_odd(c))
{
if (c->d == NULL || c->top == 0)
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
u = c->d[0] & mask;
if (u & bit)
{
u -= next_bit;
/* u < 0 */
if (!BN_add_word(c, -u)) goto err;
}
else
{
/* u > 0 */
if (!BN_sub_word(c, u)) goto err;
}
if (u <= -bit || u >= bit || !(u & 1) || c->neg)
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
}
r[j++] = sign * u;
if (BN_is_odd(c))
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
if (!BN_rshift1(c, c)) goto err;
}
if (j > len)
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
len = j;
ok = 1;
err:
BN_CTX_end(ctx);
if (!ok)
{
OPENSSL_free(r);
r = NULL;
}
if (ok)
*ret_len = len;
return r;
}
/* TODO: table should be optimised for the wNAF-based implementation */
#define EC_window_bits_for_scalar_size(b) \
((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_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;
int r_is_inverted = 0;
int r_is_at_infinity = 1;
size_t *wsize = NULL; /* individual window sizes */
size_t *wNAF_len = NULL;
size_t max_len = 0;
signed char **wNAF = NULL; /* individual wNAFs */
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]);
wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
wNAF = OPENSSL_malloc(totalnum * sizeof wNAF[0] + 1);
if (wNAF != NULL)
{
wNAF[0] = NULL; /* preliminary pivot */
}
if (wsize == NULL || wNAF_len == NULL || wNAF == 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);
}
/* 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;
}
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;
}
}
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], ctx);
if (wNAF[i] == NULL) goto err;
if (wNAF_len[i] > max_len)
max_len = wNAF_len[i];
}
#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] > 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;
}
#else
/*
* Basic interleaving multi-exponentation method
*/
#define EC_window_bits_for_scalar_size(b) \
((b) >= 2000 ? 6 : \
(b) >= 800 ? 5 : \
@ -143,14 +501,6 @@
* 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)
{
@ -369,6 +719,7 @@ int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
}
return ret;
}
#endif
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)