/* 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);
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;
ok = 1;
err:
- BN_CTX_end(ctx);
if (!ok)
{
OPENSSL_free(r);
}
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];
projects / openssl.git / blobdiff