Improve EC efficiency.
diff --git a/CHANGES b/CHANGES
index 26cf061..f51029e 100644
--- a/CHANGES
+++ b/CHANGES
@@ -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 @@
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).
diff --git a/crypto/ec/ec.h b/crypto/ec/ec.h
index 066c384..a52d4ed 100644
--- a/crypto/ec/ec.h
+++ b/crypto/ec/ec.h
@@ -177,6 +177,7 @@
/* 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
diff --git a/crypto/ec/ec_err.c b/crypto/ec/ec_err.c
index 49aff31..394cdc0 100644
--- a/crypto/ec/ec_err.c
+++ b/crypto/ec/ec_err.c
@@ -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"},
diff --git a/crypto/ec/ec_mult.c b/crypto/ec/ec_mult.c
index e075a1e..60429e0 100644
--- a/crypto/ec/ec_mult.c
+++ b/crypto/ec/ec_mult.c
@@ -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 @@
}
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)
