Improve EC efficiency.
authorBodo Möller <bodo@openssl.org>
Thu, 15 Nov 2001 22:32:11 +0000 (22:32 +0000)
committerBodo Möller <bodo@openssl.org>
Thu, 15 Nov 2001 22:32:11 +0000 (22:32 +0000)
CHANGES
crypto/ec/ec.h
crypto/ec/ec_err.c
crypto/ec/ec_mult.c

diff --git a/CHANGES b/CHANGES
index 26cf061..f51029e 100644 (file)
--- a/CHANGES
+++ b/CHANGES
          *) 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).
index 066c384..a52d4ed 100644 (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
index 49aff31..394cdc0 100644 (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"},
index e075a1e..60429e0 100644 (file)
 #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 : \
  *     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)