/* crypto/ec/ec_mult.c */
+/*
+ * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
+ */
/* ====================================================================
- * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
+ * Copyright (c) 1998-2003 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
* Hudson (tjh@cryptsoft.com).
*
*/
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ * Portions of this software developed by SUN MICROSYSTEMS, INC.,
+ * and contributed to the OpenSSL project.
+ */
+
+#include <string.h>
#include <openssl/err.h>
#include "ec_lcl.h"
-/* TODO: optional precomputation of multiples of the generator */
-
-
-#if 1
/*
- * wNAF-based interleaving multi-exponentation method
- * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>)
+ * This file implements the wNAF-based interleaving multi-exponentation method
+ * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
+ * for multiplication with precomputation, we use wNAF splitting
+ * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
*/
-/* Determine the width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
+
+/* structure for precomputed multiples of the generator */
+typedef struct ec_pre_comp_st {
+ const EC_GROUP *group; /* parent EC_GROUP object */
+ size_t blocksize; /* block size for wNAF splitting */
+ size_t numblocks; /* max. number of blocks for which we have precomputation */
+ size_t w; /* window size */
+ EC_POINT **points; /* array with pre-calculated multiples of generator:
+ * 'num' pointers to EC_POINT objects followed by a NULL */
+ size_t num; /* numblocks * 2^(w-1) */
+ int references;
+} EC_PRE_COMP;
+
+/* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
+static void *ec_pre_comp_dup(void *);
+static void ec_pre_comp_free(void *);
+static void ec_pre_comp_clear_free(void *);
+
+static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
+ {
+ EC_PRE_COMP *ret = NULL;
+
+ if (!group)
+ return NULL;
+
+ ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
+ if (!ret)
+ return ret;
+ ret->group = group;
+ ret->blocksize = 8; /* default */
+ ret->numblocks = 0;
+ ret->w = 4; /* default */
+ ret->points = NULL;
+ ret->num = 0;
+ ret->references = 1;
+ return ret;
+ }
+
+static void *ec_pre_comp_dup(void *src_)
+ {
+ EC_PRE_COMP *src = src_;
+
+ /* no need to actually copy, these objects never change! */
+
+ CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
+
+ return src_;
+ }
+
+static void ec_pre_comp_free(void *pre_)
+ {
+ int i;
+ EC_PRE_COMP *pre = pre_;
+
+ if (!pre)
+ return;
+
+ i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
+ if (i > 0)
+ return;
+
+ if (pre->points)
+ {
+ EC_POINT **p;
+
+ for (p = pre->points; *p != NULL; p++)
+ EC_POINT_free(*p);
+ OPENSSL_free(pre->points);
+ }
+ OPENSSL_free(pre);
+ }
+
+static void ec_pre_comp_clear_free(void *pre_)
+ {
+ int i;
+ EC_PRE_COMP *pre = pre_;
+
+ if (!pre)
+ return;
+
+ i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
+ if (i > 0)
+ return;
+
+ if (pre->points)
+ {
+ EC_POINT **p;
+
+ for (p = pre->points; *p != NULL; p++)
+ EC_POINT_clear_free(*p);
+ OPENSSL_cleanse(pre->points, sizeof pre->points);
+ OPENSSL_free(pre->points);
+ }
+ OPENSSL_cleanse(pre, sizeof pre);
+ OPENSSL_free(pre);
+ }
+
+
+
+
+/* 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 (BN_get_sign(scalar))
{
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
+ * (*ret_len will be set to the actual length, i.e. at most
+ * BN_num_bits(scalar) + 1) */
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);
* scalar*generator
* in the addition if scalar != NULL
*/
-int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+int ec_wNAF_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 blocksize = 0, numblocks = 0; /* for wNAF splitting */
+ size_t pre_points_per_block = 0;
size_t i, j;
int k;
int r_is_inverted = 0;
size_t num_val;
EC_POINT **val = NULL; /* precomputation */
EC_POINT **v;
- EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */
+ EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
+ const EC_PRE_COMP *pre_comp = NULL;
+ int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
+ * i.e. precomputation is not available */
int ret = 0;
- if (scalar != NULL)
+ if (group->meth != r->meth)
{
- generator = EC_GROUP_get0_generator(group);
- if (generator == NULL)
- {
- ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
- return 0;
- }
+ ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
+ return 0;
}
-
+
+ if ((scalar == NULL) && (num == 0))
+ {
+ return EC_POINT_set_to_infinity(group, r);
+ }
+
for (i = 0; i < num; i++)
{
if (group->meth != points[i]->meth)
{
- ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
+ ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
return 0;
}
}
- totalnum = num + (scalar != NULL);
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ goto err;
+ }
- 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)
+ if (scalar != NULL)
{
- wNAF[0] = NULL; /* preliminary pivot */
+ generator = EC_GROUP_get0_generator(group);
+ if (generator == NULL)
+ {
+ ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
+ goto err;
+ }
+
+ /* look if we can use precomputed multiples of generator */
+
+ pre_comp = EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
+
+ if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
+ {
+ blocksize = pre_comp->blocksize;
+
+ /* determine maximum number of blocks that wNAF splitting may yield
+ * (NB: maximum wNAF length is bit length plus one) */
+ numblocks = (BN_num_bits(scalar) / blocksize) + 1;
+
+ /* we cannot use more blocks than we have precomputation for */
+ if (numblocks > pre_comp->numblocks)
+ numblocks = pre_comp->numblocks;
+
+ pre_points_per_block = 1u << (pre_comp->w - 1);
+
+ /* check that pre_comp looks sane */
+ if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
+ {
+ ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+ }
+ else
+ {
+ /* can't use precomputation */
+ pre_comp = NULL;
+ numblocks = 1;
+ num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
+ }
}
- if (wsize == NULL || wNAF_len == NULL || wNAF == NULL) goto err;
+
+ totalnum = num + numblocks;
+
+ wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
+ wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
+ wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
+ val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
+
+ if (!wsize || !wNAF_len || !wNAF || !val_sub)
+ goto err;
+
+ wNAF[0] = NULL; /* preliminary pivot */
- /* num_val := total number of points to precompute */
+ /* num_val will be the total number of temporarily precomputed points */
num_val = 0;
- for (i = 0; i < totalnum; i++)
+
+ for (i = 0; i < num + num_scalar; 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);
+ 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]);
+ if (wNAF[i] == NULL)
+ goto err;
+ if (wNAF_len[i] > max_len)
+ max_len = wNAF_len[i];
+ }
+
+ if (numblocks)
+ {
+ /* we go here iff scalar != NULL */
+
+ if (pre_comp == NULL)
+ {
+ if (num_scalar != 1)
+ {
+ ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+ /* we have already generated a wNAF for 'scalar' */
+ }
+ else
+ {
+ signed char *tmp_wNAF = NULL;
+ size_t tmp_len = 0;
+
+ if (num_scalar != 0)
+ {
+ ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+
+ /* use the window size for which we have precomputation */
+ wsize[num] = pre_comp->w;
+ tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
+ if (!tmp_wNAF)
+ goto err;
+
+ if (tmp_len <= max_len)
+ {
+ /* One of the other wNAFs is at least as long
+ * as the wNAF belonging to the generator,
+ * so wNAF splitting will not buy us anything. */
+
+ numblocks = 1;
+ totalnum = num + 1; /* don't use wNAF splitting */
+ wNAF[num] = tmp_wNAF;
+ wNAF[num + 1] = NULL;
+ wNAF_len[num] = tmp_len;
+ if (tmp_len > max_len)
+ max_len = tmp_len;
+ /* pre_comp->points starts with the points that we need here: */
+ val_sub[num] = pre_comp->points;
+ }
+ else
+ {
+ /* don't include tmp_wNAF directly into wNAF array
+ * - use wNAF splitting and include the blocks */
+
+ signed char *pp;
+ EC_POINT **tmp_points;
+
+ if (tmp_len < numblocks * blocksize)
+ {
+ /* possibly we can do with fewer blocks than estimated */
+ numblocks = (tmp_len + blocksize - 1) / blocksize;
+ if (numblocks > pre_comp->numblocks)
+ {
+ ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+ totalnum = num + numblocks;
+ }
+
+ /* split wNAF in 'numblocks' parts */
+ pp = tmp_wNAF;
+ tmp_points = pre_comp->points;
+
+ for (i = num; i < totalnum; i++)
+ {
+ if (i < totalnum - 1)
+ {
+ wNAF_len[i] = blocksize;
+ if (tmp_len < blocksize)
+ {
+ ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+ tmp_len -= blocksize;
+ }
+ else
+ /* last block gets whatever is left
+ * (this could be more or less than 'blocksize'!) */
+ wNAF_len[i] = tmp_len;
+
+ wNAF[i + 1] = NULL;
+ wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
+ if (wNAF[i] == NULL)
+ {
+ OPENSSL_free(tmp_wNAF);
+ goto err;
+ }
+ memcpy(wNAF[i], pp, wNAF_len[i]);
+ if (wNAF_len[i] > max_len)
+ max_len = wNAF_len[i];
+
+ if (*tmp_points == NULL)
+ {
+ ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
+ OPENSSL_free(tmp_wNAF);
+ goto err;
+ }
+ val_sub[i] = tmp_points;
+ tmp_points += pre_points_per_block;
+ pp += blocksize;
+ }
+ OPENSSL_free(tmp_wNAF);
+ }
+ }
}
- /* all precomputed points go into a single array 'val',
- * 'val_sub[i]' is a pointer to the subarray for the i-th point */
+ /* All points we precompute now go into a single array 'val'.
+ * 'val_sub[i]' is a pointer to the subarray for the i-th point,
+ * or to a subarray of 'pre_comp->points' if we already have precomputation. */
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++)
+ for (i = 0; i < num + num_scalar; i++)
{
val_sub[i] = v;
for (j = 0; j < (1u << (wsize[i] - 1)); j++)
}
if (!(v == val + num_val))
{
- ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR);
+ ECerr(EC_F_EC_WNAF_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;
+ if (!(tmp = EC_POINT_new(group)))
+ goto err;
/* prepare precomputed values:
* val_sub[i][0] := points[i]
* val_sub[i][2] := 5 * points[i]
* ...
*/
- for (i = 0; i < totalnum; i++)
+ for (i = 0; i < num + num_scalar; i++)
{
if (i < num)
{
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;
+ if (!EC_POINTs_make_affine(group, num_val, val, ctx))
+ goto err;
#endif
r_is_at_infinity = 1;
return ret;
}
-#else
-/*
- * Basic interleaving multi-exponentation method
- */
-
-
-
-#define EC_window_bits_for_scalar_size(b) \
- ((b) >= 2000 ? 6 : \
- (b) >= 800 ? 5 : \
- (b) >= 300 ? 4 : \
- (b) >= 70 ? 3 : \
- (b) >= 20 ? 2 : \
- 1)
-/* For window size 'w' (w >= 2), we compute the odd multiples
- * 1*P .. (2^w-1)*P.
- * This accounts for 2^(w-1) point additions (neglecting constants),
- * each of which requires 16 field multiplications (4 squarings
- * and 12 general multiplications) in the case of curves defined
- * over GF(p), which are the only curves we have so far.
- *
- * Converting these precomputed points into affine form takes
- * three field multiplications for inverting Z and one squaring
- * and three multiplications for adjusting X and Y, i.e.
- * 7 multiplications in total (1 squaring and 6 general multiplications),
- * again except for constants.
- *
- * The average number of windows for a 'b' bit scalar is roughly
- * b/(w+1).
- * Each of these windows (except possibly for the first one, but
- * we are ignoring constants anyway) requires one point addition.
- * As the precomputed table stores points in affine form, these
- * additions take only 11 field multiplications each (3 squarings
- * and 8 general multiplications).
- *
- * So the total workload, except for constants, is
- *
- * 2^(w-1)*[5 squarings + 18 multiplications]
- * + (b/(w+1))*[3 squarings + 8 multiplications]
- *
- * If we assume that 10 squarings are as costly as 9 multiplications,
- * our task is to find the 'w' that, given 'b', minimizes
- *
- * 2^(w-1)*(5*9 + 18*10) + (b/(w+1))*(3*9 + 8*10)
- * = 2^(w-1)*225 + (b/(w+1))*107.
- *
- * Thus optimal window sizes should be roughly as follows:
- *
- * w >= 6 if b >= 1414
- * w = 5 if 1413 >= b >= 505
- * w = 4 if 504 >= b >= 169
- * w = 3 if 168 >= b >= 51
- * w = 2 if 50 >= b >= 13
- * w = 1 if 12 >= b
- *
- * If we assume instead that squarings are exactly as costly as
- * multiplications, we have to minimize
- * 2^(w-1)*23 + (b/(w+1))*11.
- *
- * This gives us the following (nearly unchanged) table of optimal
- * windows sizes:
- *
- * w >= 6 if b >= 1406
- * w = 5 if 1405 >= b >= 502
- * w = 4 if 501 >= b >= 168
- * w = 3 if 167 >= b >= 51
- * w = 2 if 50 >= b >= 13
- * w = 1 if 12 >= b
- *
- * Note that neither table tries to take into account memory usage
- * (allocation overhead, code locality etc.). Actual timings with
- * NIST curves P-192, P-224, and P-256 with scalars of 192, 224,
- * and 256 bits, respectively, show that w = 3 (instead of 4) is
- * preferrable; timings with NIST curve P-384 and 384-bit scalars
- * confirm that w = 4 is optimal for this case; and timings with
- * NIST curve P-521 and 521-bit scalars show that w = 4 (instead
- * of 5) is preferrable. So we generously round up all the
- * boundaries and use the following table:
- *
- * w >= 6 if b >= 2000
- * w = 5 if 1999 >= b >= 800
- * w = 4 if 799 >= b >= 300
- * w = 3 if 299 >= b >= 70
- * w = 2 if 69 >= b >= 20
- * w = 1 if 19 >= b
+/* ec_wNAF_precompute_mult()
+ * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
+ * for use with wNAF splitting as implemented in ec_wNAF_mul().
+ *
+ * 'pre_comp->points' is an array of multiples of the generator
+ * of the following form:
+ * points[0] = generator;
+ * points[1] = 3 * generator;
+ * ...
+ * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
+ * points[2^(w-1)] = 2^blocksize * generator;
+ * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
+ * ...
+ * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
+ * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
+ * ...
+ * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
+ * points[2^(w-1)*numblocks] = 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)
+int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
{
+ const EC_POINT *generator;
+ EC_POINT *tmp_point = NULL, *base = NULL, **var;
BN_CTX *new_ctx = NULL;
- EC_POINT *generator = NULL;
- EC_POINT *tmp = NULL;
- size_t totalnum;
- size_t i, j;
- int k, t;
- int r_is_at_infinity = 1;
- size_t max_bits = 0;
- size_t *wsize = NULL; /* individual window sizes */
- unsigned long *wbits = NULL; /* individual window contents */
- int *wpos = NULL; /* position of bottom bit of current individual windows
- * (wpos[i] is valid if wbits[i] != 0) */
- size_t num_val;
- EC_POINT **val = NULL; /* precomputation */
- EC_POINT **v;
- EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */
+ BIGNUM *order;
+ size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
+ EC_POINT **points = NULL;
+ EC_PRE_COMP *pre_comp;
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]);
- wbits = OPENSSL_malloc(totalnum * sizeof wbits[0]);
- wpos = OPENSSL_malloc(totalnum * sizeof wpos[0]);
- if (wsize == NULL || wbits == NULL || wpos == 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);
- if (bits > max_bits)
- max_bits = bits;
- wbits[i] = 0;
- wpos[i] = 0;
- }
- /* 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 */
+ /* if there is an old EC_PRE_COMP object, throw it away */
+ EC_GROUP_free_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
- val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
- if (val_sub == NULL) goto err;
+ if ((pre_comp = ec_pre_comp_new(group)) == NULL)
+ return 0;
- /* 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))
+ generator = EC_GROUP_get0_generator(group);
+ if (generator == NULL)
{
- ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR);
+ ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
goto err;
}
goto err;
}
- tmp = EC_POINT_new(group);
- if (tmp == NULL) goto err;
+ BN_CTX_start(ctx);
+ order = BN_CTX_get(ctx);
+ if (order == NULL) goto err;
+
+ if (!EC_GROUP_get_order(group, order, ctx)) goto err;
+ if (BN_is_zero(order))
+ {
+ ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
+ 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]
- * ...
+ bits = BN_num_bits(order);
+ /* The following parameters mean we precompute (approximately)
+ * one point per bit.
+ *
+ * TBD: The combination 8, 4 is perfect for 160 bits; for other
+ * bit lengths, other parameter combinations might provide better
+ * efficiency.
*/
- for (i = 0; i < totalnum; i++)
+ blocksize = 8;
+ w = 4;
+ if (EC_window_bits_for_scalar_size(bits) > w)
{
- if (i < num)
- {
- if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
- if (scalars[i]->neg)
- {
- if (!EC_POINT_invert(group, val_sub[i][0], ctx)) goto err;
- }
- }
- else
- {
- if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
- if (scalar->neg)
- {
- if (!EC_POINT_invert(group, val_sub[i][0], ctx)) goto err;
- }
- }
+ /* let's not make the window too small ... */
+ w = EC_window_bits_for_scalar_size(bits);
+ }
- if (wsize[i] > 1)
+ numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
+
+ pre_points_per_block = 1u << (w - 1);
+ num = pre_points_per_block * numblocks; /* number of points to compute and store */
+
+ points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
+ if (!points)
+ {
+ ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
+ goto err;
+ }
+
+ var = points;
+ var[num] = NULL; /* pivot */
+ for (i = 0; i < num; i++)
+ {
+ if ((var[i] = EC_POINT_new(group)) == NULL)
{
- 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;
- }
+ ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
+ goto err;
}
}
-#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
+ if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
+ {
+ ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
+ goto err;
+ }
+
+ if (!EC_POINT_copy(base, generator))
+ goto err;
+
+ /* do the precomputation */
+ for (i = 0; i < numblocks; i++)
+ {
+ size_t j;
- r_is_at_infinity = 1;
+ if (!EC_POINT_dbl(group, tmp_point, base, ctx))
+ goto err;
- for (k = max_bits - 1; k >= 0; k--)
- {
- if (!r_is_at_infinity)
+ if (!EC_POINT_copy(*var++, base))
+ goto err;
+
+ for (j = 1; j < pre_points_per_block; j++, var++)
{
- if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
+ /* calculate odd multiples of the current base point */
+ if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
+ goto err;
}
-
- for (i = 0; i < totalnum; i++)
+
+ if (i < numblocks - 1)
{
- if (wbits[i] == 0)
- {
- const BIGNUM *s;
+ /* get the next base (multiply current one by 2^blocksize) */
+ size_t k;
- s = i < num ? scalars[i] : scalar;
+ if (blocksize <= 2)
+ {
+ ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
- if (BN_is_bit_set(s, k))
- {
- /* look at bits k - wsize[i] + 1 .. k for this window */
- t = k - wsize[i] + 1;
- while (!BN_is_bit_set(s, t)) /* BN_is_bit_set is false for t < 0 */
- t++;
- wpos[i] = t;
- wbits[i] = 1;
- for (t = k - 1; t >= wpos[i]; t--)
- {
- wbits[i] <<= 1;
- if (BN_is_bit_set(s, t))
- wbits[i]++;
- }
- /* now wbits[i] is the odd bit pattern at bits wpos[i] .. k */
- }
- }
-
- if ((wbits[i] != 0) && (wpos[i] == k))
+ if (!EC_POINT_dbl(group, base, tmp_point, ctx))
+ goto err;
+ for (k = 2; k < blocksize; k++)
{
- if (r_is_at_infinity)
- {
- if (!EC_POINT_copy(r, val_sub[i][wbits[i] >> 1])) goto err;
- r_is_at_infinity = 0;
- }
- else
- {
- if (!EC_POINT_add(group, r, r, val_sub[i][wbits[i] >> 1], ctx)) goto err;
- }
- wbits[i] = 0;
+ if (!EC_POINT_dbl(group,base,base,ctx))
+ goto err;
}
}
- }
+ }
- if (r_is_at_infinity)
- if (!EC_POINT_set_to_infinity(group, r)) goto err;
+ if (!EC_POINTs_make_affine(group, num, points, ctx))
+ goto err;
- ret = 1;
+ pre_comp->group = group;
+ pre_comp->blocksize = blocksize;
+ pre_comp->numblocks = numblocks;
+ pre_comp->w = w;
+ pre_comp->points = points;
+ points = NULL;
+ pre_comp->num = num;
+
+ if (!EC_GROUP_set_extra_data(group, pre_comp,
+ ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
+ goto err;
+ pre_comp = NULL;
+ ret = 1;
err:
+ BN_CTX_end(ctx);
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
- if (tmp != NULL)
- EC_POINT_free(tmp);
- if (wsize != NULL)
- OPENSSL_free(wsize);
- if (wbits != NULL)
- OPENSSL_free(wbits);
- if (wpos != NULL)
- OPENSSL_free(wpos);
- if (val != NULL)
+ if (pre_comp)
+ ec_pre_comp_free(pre_comp);
+ if (points)
{
- for (v = val; *v != NULL; v++)
- EC_POINT_clear_free(*v);
+ EC_POINT **p;
- OPENSSL_free(val);
- }
- if (val_sub != NULL)
- {
- OPENSSL_free(val_sub);
+ for (p = points; *p != NULL; p++)
+ EC_POINT_free(*p);
+ OPENSSL_free(points);
}
+ if (tmp_point)
+ EC_POINT_free(tmp_point);
+ if (base)
+ EC_POINT_free(base);
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)
- {
- const EC_POINT *points[1];
- const BIGNUM *scalars[1];
-
- points[0] = point;
- scalars[0] = p_scalar;
-
- return EC_POINTs_mul(group, r, g_scalar, (point != NULL && p_scalar != NULL), points, scalars, ctx);
- }
-int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
+int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
{
- const EC_POINT *generator;
- BN_CTX *new_ctx = NULL;
- BIGNUM *order;
- int ret = 0;
-
- generator = EC_GROUP_get0_generator(group);
- if (generator == NULL)
- {
- ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
+ if (EC_GROUP_get_extra_data(group, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
+ return 1;
+ else
return 0;
- }
-
- if (ctx == NULL)
- {
- ctx = new_ctx = BN_CTX_new();
- if (ctx == NULL)
- return 0;
- }
-
- BN_CTX_start(ctx);
- order = BN_CTX_get(ctx);
- if (order == NULL) goto err;
-
- if (!EC_GROUP_get_order(group, order, ctx)) return 0;
- if (BN_is_zero(order))
- {
- ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
- goto err;
- }
-
- /* TODO */
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return ret;
}
projects / openssl.git / blobdiff