improve wNAF generation
authorBodo Möller <bodo@openssl.org>
Sun, 5 May 2002 23:45:09 +0000 (23:45 +0000)
committerBodo Möller <bodo@openssl.org>
Sun, 5 May 2002 23:45:09 +0000 (23:45 +0000)
crypto/ec/ec_mult.c

index 603ba31..74e1a96 100644 (file)
@@ -1,6 +1,6 @@
 /* crypto/ec/ec_mult.c */
 /* ====================================================================
- * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
+ * Copyright (c) 1998-2002 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
  */
 
 
-/* Determine the width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
+/* 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.
+ * 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.
  */
-static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len, BN_CTX *ctx)
+static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
        {
-       BIGNUM *c;
+       int window_val;
        int ok = 0;
        signed char *r = NULL;
        int sign = 1;
        int bit, next_bit, mask;
        size_t len = 0, j;
        
-       BN_CTX_start(ctx);
-       c = BN_CTX_get(ctx);
-       if (c == NULL) goto err;
-       
        if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
                {
                ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
@@ -96,60 +94,84 @@ static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len, B
        next_bit = bit << 1; /* at most 256 */
        mask = next_bit - 1; /* at most 255 */
 
-       if (!BN_copy(c, scalar)) goto err;
-       if (c->neg)
+       if (scalar->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);
+       len = BN_num_bits(scalar);
+       r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation */
        if (r == NULL) goto err;
 
+       if (scalar->d == NULL || scalar->top == 0)
+               {
+               ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
+               goto err;
+               }
+       window_val = scalar->d[0] & mask;
        j = 0;
-       while (!BN_is_zero(c))
+       while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
                {
-               int u = 0;
+               int digit = 0;
 
-               if (BN_is_odd(c)) 
+               /* 0 <= window_val <= 2^(w+1) */
+
+               if (window_val & 1)
                        {
-                       if (c->d == NULL || c->top == 0)
+                       /* 0 < window_val < 2^(w+1) */
+
+                       if (window_val & bit)
                                {
-                               ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
-                               goto err;
+                               digit = window_val - next_bit; /* -2^w < digit < 0 */
+
+#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 */
+                                       
+                                       digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
+                                       }
+#endif
                                }
-                       u = c->d[0] & mask;
-                       if (u & bit)
+                       else
                                {
-                               u -= next_bit;
-                               /* u < 0 */
-                               if (!BN_add_word(c, -u)) goto err;
+                               digit = window_val; /* 0 < digit < 2^w */
                                }
-                       else
+                       
+                       if (digit <= -bit || digit >= bit || !(digit & 1))
                                {
-                               /* u > 0 */
-                               if (!BN_sub_word(c, u)) goto err;
+                               ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
+                               goto err;
                                }
 
-                       if (u <= -bit || u >= bit || !(u & 1) || c->neg)
+                       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
+                        */
+                       if (window_val != 0 && window_val != next_bit && window_val != bit)
                                {
                                ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
                                goto err;
                                }
                        }
 
-               r[j++] = sign * u;
-               
-               if (BN_is_odd(c))
+               r[j++] = sign * digit;
+
+               window_val >>= 1;
+               window_val += bit * BN_is_bit_set(scalar, j + w);
+
+               if (window_val > next_bit)
                        {
                        ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
                        goto err;
                        }
-               if (!BN_rshift1(c, c)) goto err;
                }
 
-       if (j > len)
+       if (j > len + 1)
                {
                ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
                goto err;
@@ -158,7 +180,6 @@ static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len, B
        ok = 1;
 
  err:
-       BN_CTX_end(ctx);
        if (!ok)
                {
                OPENSSL_free(r);
@@ -314,7 +335,7 @@ int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
                        }
 
                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);
+               wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
                if (wNAF[i] == NULL) goto err;
                if (wNAF_len[i] > max_len)
                        max_len = wNAF_len[i];