2 * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the Apache License 2.0 (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
12 * ECDSA low level APIs are deprecated for public use, but still ok for
15 #include "internal/deprecated.h"
18 #include <openssl/err.h>
20 #include "internal/cryptlib.h"
21 #include "crypto/bn.h"
23 #include "internal/refcount.h"
26 * This file implements the wNAF-based interleaving multi-exponentiation method
28 * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp
29 * You might now find it here:
30 * http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
31 * http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
32 * For multiplication with precomputation, we use wNAF splitting, formerly at:
33 * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp
36 /* structure for precomputed multiples of the generator */
37 struct ec_pre_comp_st
{
38 const EC_GROUP
*group
; /* parent EC_GROUP object */
39 size_t blocksize
; /* block size for wNAF splitting */
40 size_t numblocks
; /* max. number of blocks for which we have
42 size_t w
; /* window size */
43 EC_POINT
**points
; /* array with pre-calculated multiples of
44 * generator: 'num' pointers to EC_POINT
45 * objects followed by a NULL */
46 size_t num
; /* numblocks * 2^(w-1) */
47 CRYPTO_REF_COUNT references
;
51 static EC_PRE_COMP
*ec_pre_comp_new(const EC_GROUP
*group
)
53 EC_PRE_COMP
*ret
= NULL
;
58 ret
= OPENSSL_zalloc(sizeof(*ret
));
60 ECerr(EC_F_EC_PRE_COMP_NEW
, ERR_R_MALLOC_FAILURE
);
65 ret
->blocksize
= 8; /* default */
66 ret
->w
= 4; /* default */
69 ret
->lock
= CRYPTO_THREAD_lock_new();
70 if (ret
->lock
== NULL
) {
71 ECerr(EC_F_EC_PRE_COMP_NEW
, ERR_R_MALLOC_FAILURE
);
78 EC_PRE_COMP
*EC_ec_pre_comp_dup(EC_PRE_COMP
*pre
)
82 CRYPTO_UP_REF(&pre
->references
, &i
, pre
->lock
);
86 void EC_ec_pre_comp_free(EC_PRE_COMP
*pre
)
93 CRYPTO_DOWN_REF(&pre
->references
, &i
, pre
->lock
);
94 REF_PRINT_COUNT("EC_ec", pre
);
97 REF_ASSERT_ISNT(i
< 0);
99 if (pre
->points
!= NULL
) {
102 for (pts
= pre
->points
; *pts
!= NULL
; pts
++)
104 OPENSSL_free(pre
->points
);
106 CRYPTO_THREAD_lock_free(pre
->lock
);
110 #define EC_POINT_BN_set_flags(P, flags) do { \
111 BN_set_flags((P)->X, (flags)); \
112 BN_set_flags((P)->Y, (flags)); \
113 BN_set_flags((P)->Z, (flags)); \
117 * This functions computes a single point multiplication over the EC group,
118 * using, at a high level, a Montgomery ladder with conditional swaps, with
119 * various timing attack defenses.
121 * It performs either a fixed point multiplication
122 * (scalar * generator)
123 * when point is NULL, or a variable point multiplication
125 * when point is not NULL.
127 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all
128 * constant time bets are off (where n is the cardinality of the EC group).
130 * This function expects `group->order` and `group->cardinality` to be well
131 * defined and non-zero: it fails with an error code otherwise.
133 * NB: This says nothing about the constant-timeness of the ladder step
134 * implementation (i.e., the default implementation is based on EC_POINT_add and
135 * EC_POINT_dbl, which of course are not constant time themselves) or the
136 * underlying multiprecision arithmetic.
138 * The product is stored in `r`.
140 * This is an internal function: callers are in charge of ensuring that the
141 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
143 * Returns 1 on success, 0 otherwise.
145 int ec_scalar_mul_ladder(const EC_GROUP
*group
, EC_POINT
*r
,
146 const BIGNUM
*scalar
, const EC_POINT
*point
,
149 int i
, cardinality_bits
, group_top
, kbit
, pbit
, Z_is_one
;
153 BIGNUM
*lambda
= NULL
;
154 BIGNUM
*cardinality
= NULL
;
157 /* early exit if the input point is the point at infinity */
158 if (point
!= NULL
&& EC_POINT_is_at_infinity(group
, point
))
159 return EC_POINT_set_to_infinity(group
, r
);
161 if (BN_is_zero(group
->order
)) {
162 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_UNKNOWN_ORDER
);
165 if (BN_is_zero(group
->cofactor
)) {
166 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_UNKNOWN_COFACTOR
);
172 if (((p
= EC_POINT_new(group
)) == NULL
)
173 || ((s
= EC_POINT_new(group
)) == NULL
)) {
174 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_MALLOC_FAILURE
);
179 if (!EC_POINT_copy(p
, group
->generator
)) {
180 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_EC_LIB
);
184 if (!EC_POINT_copy(p
, point
)) {
185 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_EC_LIB
);
190 EC_POINT_BN_set_flags(p
, BN_FLG_CONSTTIME
);
191 EC_POINT_BN_set_flags(r
, BN_FLG_CONSTTIME
);
192 EC_POINT_BN_set_flags(s
, BN_FLG_CONSTTIME
);
194 cardinality
= BN_CTX_get(ctx
);
195 lambda
= BN_CTX_get(ctx
);
198 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_MALLOC_FAILURE
);
202 if (!BN_mul(cardinality
, group
->order
, group
->cofactor
, ctx
)) {
203 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
208 * Group cardinalities are often on a word boundary.
209 * So when we pad the scalar, some timing diff might
210 * pop if it needs to be expanded due to carries.
211 * So expand ahead of time.
213 cardinality_bits
= BN_num_bits(cardinality
);
214 group_top
= bn_get_top(cardinality
);
215 if ((bn_wexpand(k
, group_top
+ 2) == NULL
)
216 || (bn_wexpand(lambda
, group_top
+ 2) == NULL
)) {
217 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
221 if (!BN_copy(k
, scalar
)) {
222 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
226 BN_set_flags(k
, BN_FLG_CONSTTIME
);
228 if ((BN_num_bits(k
) > cardinality_bits
) || (BN_is_negative(k
))) {
230 * this is an unusual input, and we don't guarantee
233 if (!BN_nnmod(k
, k
, cardinality
, ctx
)) {
234 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
239 if (!BN_add(lambda
, k
, cardinality
)) {
240 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
243 BN_set_flags(lambda
, BN_FLG_CONSTTIME
);
244 if (!BN_add(k
, lambda
, cardinality
)) {
245 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
249 * lambda := scalar + cardinality
250 * k := scalar + 2*cardinality
252 kbit
= BN_is_bit_set(lambda
, cardinality_bits
);
253 BN_consttime_swap(kbit
, k
, lambda
, group_top
+ 2);
255 group_top
= bn_get_top(group
->field
);
256 if ((bn_wexpand(s
->X
, group_top
) == NULL
)
257 || (bn_wexpand(s
->Y
, group_top
) == NULL
)
258 || (bn_wexpand(s
->Z
, group_top
) == NULL
)
259 || (bn_wexpand(r
->X
, group_top
) == NULL
)
260 || (bn_wexpand(r
->Y
, group_top
) == NULL
)
261 || (bn_wexpand(r
->Z
, group_top
) == NULL
)
262 || (bn_wexpand(p
->X
, group_top
) == NULL
)
263 || (bn_wexpand(p
->Y
, group_top
) == NULL
)
264 || (bn_wexpand(p
->Z
, group_top
) == NULL
)) {
265 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
269 /* ensure input point is in affine coords for ladder step efficiency */
270 if (!p
->Z_is_one
&& !EC_POINT_make_affine(group
, p
, ctx
)) {
271 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_EC_LIB
);
275 /* Initialize the Montgomery ladder */
276 if (!ec_point_ladder_pre(group
, r
, s
, p
, ctx
)) {
277 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_LADDER_PRE_FAILURE
);
281 /* top bit is a 1, in a fixed pos */
284 #define EC_POINT_CSWAP(c, a, b, w, t) do { \
285 BN_consttime_swap(c, (a)->X, (b)->X, w); \
286 BN_consttime_swap(c, (a)->Y, (b)->Y, w); \
287 BN_consttime_swap(c, (a)->Z, (b)->Z, w); \
288 t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
289 (a)->Z_is_one ^= (t); \
290 (b)->Z_is_one ^= (t); \
294 * The ladder step, with branches, is
296 * k[i] == 0: S = add(R, S), R = dbl(R)
297 * k[i] == 1: R = add(S, R), S = dbl(S)
299 * Swapping R, S conditionally on k[i] leaves you with state
301 * k[i] == 0: T, U = R, S
302 * k[i] == 1: T, U = S, R
304 * Then perform the ECC ops.
309 * Which leaves you with state
311 * k[i] == 0: U = add(R, S), T = dbl(R)
312 * k[i] == 1: U = add(S, R), T = dbl(S)
314 * Swapping T, U conditionally on k[i] leaves you with state
316 * k[i] == 0: R, S = T, U
317 * k[i] == 1: R, S = U, T
319 * Which leaves you with state
321 * k[i] == 0: S = add(R, S), R = dbl(R)
322 * k[i] == 1: R = add(S, R), S = dbl(S)
324 * So we get the same logic, but instead of a branch it's a
325 * conditional swap, followed by ECC ops, then another conditional swap.
327 * Optimization: The end of iteration i and start of i-1 looks like
334 * CSWAP(k[i-1], R, S)
336 * CSWAP(k[i-1], R, S)
339 * So instead of two contiguous swaps, you can merge the condition
340 * bits and do a single swap.
342 * k[i] k[i-1] Outcome
348 * This is XOR. pbit tracks the previous bit of k.
351 for (i
= cardinality_bits
- 1; i
>= 0; i
--) {
352 kbit
= BN_is_bit_set(k
, i
) ^ pbit
;
353 EC_POINT_CSWAP(kbit
, r
, s
, group_top
, Z_is_one
);
355 /* Perform a single step of the Montgomery ladder */
356 if (!ec_point_ladder_step(group
, r
, s
, p
, ctx
)) {
357 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_LADDER_STEP_FAILURE
);
361 * pbit logic merges this cswap with that of the
366 /* one final cswap to move the right value into r */
367 EC_POINT_CSWAP(pbit
, r
, s
, group_top
, Z_is_one
);
368 #undef EC_POINT_CSWAP
370 /* Finalize ladder (and recover full point coordinates) */
371 if (!ec_point_ladder_post(group
, r
, s
, p
, ctx
)) {
372 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_LADDER_POST_FAILURE
);
380 EC_POINT_clear_free(s
);
386 #undef EC_POINT_BN_set_flags
389 * TODO: table should be optimised for the wNAF-based implementation,
390 * sometimes smaller windows will give better performance (thus the
391 * boundaries should be increased)
393 #define EC_window_bits_for_scalar_size(b) \
404 * \sum scalars[i]*points[i],
407 * in the addition if scalar != NULL
409 int ec_wNAF_mul(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
410 size_t num
, const EC_POINT
*points
[], const BIGNUM
*scalars
[],
413 const EC_POINT
*generator
= NULL
;
414 EC_POINT
*tmp
= NULL
;
416 size_t blocksize
= 0, numblocks
= 0; /* for wNAF splitting */
417 size_t pre_points_per_block
= 0;
420 int r_is_inverted
= 0;
421 int r_is_at_infinity
= 1;
422 size_t *wsize
= NULL
; /* individual window sizes */
423 signed char **wNAF
= NULL
; /* individual wNAFs */
424 size_t *wNAF_len
= NULL
;
427 EC_POINT
**val
= NULL
; /* precomputation */
429 EC_POINT
***val_sub
= NULL
; /* pointers to sub-arrays of 'val' or
430 * 'pre_comp->points' */
431 const EC_PRE_COMP
*pre_comp
= NULL
;
432 int num_scalar
= 0; /* flag: will be set to 1 if 'scalar' must be
433 * treated like other scalars, i.e.
434 * precomputation is not available */
437 if (!BN_is_zero(group
->order
) && !BN_is_zero(group
->cofactor
)) {
439 * Handle the common cases where the scalar is secret, enforcing a
440 * scalar multiplication implementation based on a Montgomery ladder,
441 * with various timing attack defenses.
443 if ((scalar
!= group
->order
) && (scalar
!= NULL
) && (num
== 0)) {
445 * In this case we want to compute scalar * GeneratorPoint: this
446 * codepath is reached most prominently by (ephemeral) key
447 * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup,
448 * ECDH keygen/first half), where the scalar is always secret. This
449 * is why we ignore if BN_FLG_CONSTTIME is actually set and we
450 * always call the ladder version.
452 return ec_scalar_mul_ladder(group
, r
, scalar
, NULL
, ctx
);
454 if ((scalar
== NULL
) && (num
== 1) && (scalars
[0] != group
->order
)) {
456 * In this case we want to compute scalar * VariablePoint: this
457 * codepath is reached most prominently by the second half of ECDH,
458 * where the secret scalar is multiplied by the peer's public point.
459 * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is
460 * actually set and we always call the ladder version.
462 return ec_scalar_mul_ladder(group
, r
, scalars
[0], points
[0], ctx
);
466 if (scalar
!= NULL
) {
467 generator
= EC_GROUP_get0_generator(group
);
468 if (generator
== NULL
) {
469 ECerr(EC_F_EC_WNAF_MUL
, EC_R_UNDEFINED_GENERATOR
);
473 /* look if we can use precomputed multiples of generator */
475 pre_comp
= group
->pre_comp
.ec
;
476 if (pre_comp
&& pre_comp
->numblocks
477 && (EC_POINT_cmp(group
, generator
, pre_comp
->points
[0], ctx
) ==
479 blocksize
= pre_comp
->blocksize
;
482 * determine maximum number of blocks that wNAF splitting may
483 * yield (NB: maximum wNAF length is bit length plus one)
485 numblocks
= (BN_num_bits(scalar
) / blocksize
) + 1;
488 * we cannot use more blocks than we have precomputation for
490 if (numblocks
> pre_comp
->numblocks
)
491 numblocks
= pre_comp
->numblocks
;
493 pre_points_per_block
= (size_t)1 << (pre_comp
->w
- 1);
495 /* check that pre_comp looks sane */
496 if (pre_comp
->num
!= (pre_comp
->numblocks
* pre_points_per_block
)) {
497 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
501 /* can't use precomputation */
504 num_scalar
= 1; /* treat 'scalar' like 'num'-th element of
509 totalnum
= num
+ numblocks
;
511 wsize
= OPENSSL_malloc(totalnum
* sizeof(wsize
[0]));
512 wNAF_len
= OPENSSL_malloc(totalnum
* sizeof(wNAF_len
[0]));
513 /* include space for pivot */
514 wNAF
= OPENSSL_malloc((totalnum
+ 1) * sizeof(wNAF
[0]));
515 val_sub
= OPENSSL_malloc(totalnum
* sizeof(val_sub
[0]));
517 /* Ensure wNAF is initialised in case we end up going to err */
519 wNAF
[0] = NULL
; /* preliminary pivot */
521 if (wsize
== NULL
|| wNAF_len
== NULL
|| wNAF
== NULL
|| val_sub
== NULL
) {
522 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
527 * num_val will be the total number of temporarily precomputed points
531 for (i
= 0; i
< num
+ num_scalar
; i
++) {
534 bits
= i
< num
? BN_num_bits(scalars
[i
]) : BN_num_bits(scalar
);
535 wsize
[i
] = EC_window_bits_for_scalar_size(bits
);
536 num_val
+= (size_t)1 << (wsize
[i
] - 1);
537 wNAF
[i
+ 1] = NULL
; /* make sure we always have a pivot */
539 bn_compute_wNAF((i
< num
? scalars
[i
] : scalar
), wsize
[i
],
543 if (wNAF_len
[i
] > max_len
)
544 max_len
= wNAF_len
[i
];
548 /* we go here iff scalar != NULL */
550 if (pre_comp
== NULL
) {
551 if (num_scalar
!= 1) {
552 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
555 /* we have already generated a wNAF for 'scalar' */
557 signed char *tmp_wNAF
= NULL
;
560 if (num_scalar
!= 0) {
561 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
566 * use the window size for which we have precomputation
568 wsize
[num
] = pre_comp
->w
;
569 tmp_wNAF
= bn_compute_wNAF(scalar
, wsize
[num
], &tmp_len
);
573 if (tmp_len
<= max_len
) {
575 * One of the other wNAFs is at least as long as the wNAF
576 * belonging to the generator, so wNAF splitting will not buy
581 totalnum
= num
+ 1; /* don't use wNAF splitting */
582 wNAF
[num
] = tmp_wNAF
;
583 wNAF
[num
+ 1] = NULL
;
584 wNAF_len
[num
] = tmp_len
;
586 * pre_comp->points starts with the points that we need here:
588 val_sub
[num
] = pre_comp
->points
;
591 * don't include tmp_wNAF directly into wNAF array - use wNAF
592 * splitting and include the blocks
596 EC_POINT
**tmp_points
;
598 if (tmp_len
< numblocks
* blocksize
) {
600 * possibly we can do with fewer blocks than estimated
602 numblocks
= (tmp_len
+ blocksize
- 1) / blocksize
;
603 if (numblocks
> pre_comp
->numblocks
) {
604 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
605 OPENSSL_free(tmp_wNAF
);
608 totalnum
= num
+ numblocks
;
611 /* split wNAF in 'numblocks' parts */
613 tmp_points
= pre_comp
->points
;
615 for (i
= num
; i
< totalnum
; i
++) {
616 if (i
< totalnum
- 1) {
617 wNAF_len
[i
] = blocksize
;
618 if (tmp_len
< blocksize
) {
619 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
620 OPENSSL_free(tmp_wNAF
);
623 tmp_len
-= blocksize
;
626 * last block gets whatever is left (this could be
627 * more or less than 'blocksize'!)
629 wNAF_len
[i
] = tmp_len
;
632 wNAF
[i
] = OPENSSL_malloc(wNAF_len
[i
]);
633 if (wNAF
[i
] == NULL
) {
634 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
635 OPENSSL_free(tmp_wNAF
);
638 memcpy(wNAF
[i
], pp
, wNAF_len
[i
]);
639 if (wNAF_len
[i
] > max_len
)
640 max_len
= wNAF_len
[i
];
642 if (*tmp_points
== NULL
) {
643 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
644 OPENSSL_free(tmp_wNAF
);
647 val_sub
[i
] = tmp_points
;
648 tmp_points
+= pre_points_per_block
;
651 OPENSSL_free(tmp_wNAF
);
657 * All points we precompute now go into a single array 'val'.
658 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
659 * subarray of 'pre_comp->points' if we already have precomputation.
661 val
= OPENSSL_malloc((num_val
+ 1) * sizeof(val
[0]));
663 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
666 val
[num_val
] = NULL
; /* pivot element */
668 /* allocate points for precomputation */
670 for (i
= 0; i
< num
+ num_scalar
; i
++) {
672 for (j
= 0; j
< ((size_t)1 << (wsize
[i
] - 1)); j
++) {
673 *v
= EC_POINT_new(group
);
679 if (!(v
== val
+ num_val
)) {
680 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
684 if ((tmp
= EC_POINT_new(group
)) == NULL
)
688 * prepare precomputed values:
689 * val_sub[i][0] := points[i]
690 * val_sub[i][1] := 3 * points[i]
691 * val_sub[i][2] := 5 * points[i]
694 for (i
= 0; i
< num
+ num_scalar
; i
++) {
696 if (!EC_POINT_copy(val_sub
[i
][0], points
[i
]))
699 if (!EC_POINT_copy(val_sub
[i
][0], generator
))
704 if (!EC_POINT_dbl(group
, tmp
, val_sub
[i
][0], ctx
))
706 for (j
= 1; j
< ((size_t)1 << (wsize
[i
] - 1)); j
++) {
708 (group
, val_sub
[i
][j
], val_sub
[i
][j
- 1], tmp
, ctx
))
714 if (!EC_POINTs_make_affine(group
, num_val
, val
, ctx
))
717 r_is_at_infinity
= 1;
719 for (k
= max_len
- 1; k
>= 0; k
--) {
720 if (!r_is_at_infinity
) {
721 if (!EC_POINT_dbl(group
, r
, r
, ctx
))
725 for (i
= 0; i
< totalnum
; i
++) {
726 if (wNAF_len
[i
] > (size_t)k
) {
727 int digit
= wNAF
[i
][k
];
736 if (is_neg
!= r_is_inverted
) {
737 if (!r_is_at_infinity
) {
738 if (!EC_POINT_invert(group
, r
, ctx
))
741 r_is_inverted
= !r_is_inverted
;
746 if (r_is_at_infinity
) {
747 if (!EC_POINT_copy(r
, val_sub
[i
][digit
>> 1]))
749 r_is_at_infinity
= 0;
752 (group
, r
, r
, val_sub
[i
][digit
>> 1], ctx
))
760 if (r_is_at_infinity
) {
761 if (!EC_POINT_set_to_infinity(group
, r
))
765 if (!EC_POINT_invert(group
, r
, ctx
))
774 OPENSSL_free(wNAF_len
);
778 for (w
= wNAF
; *w
!= NULL
; w
++)
784 for (v
= val
; *v
!= NULL
; v
++)
785 EC_POINT_clear_free(*v
);
789 OPENSSL_free(val_sub
);
794 * ec_wNAF_precompute_mult()
795 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
796 * for use with wNAF splitting as implemented in ec_wNAF_mul().
798 * 'pre_comp->points' is an array of multiples of the generator
799 * of the following form:
800 * points[0] = generator;
801 * points[1] = 3 * generator;
803 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
804 * points[2^(w-1)] = 2^blocksize * generator;
805 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
807 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
808 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
810 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
811 * points[2^(w-1)*numblocks] = NULL
813 int ec_wNAF_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
)
815 const EC_POINT
*generator
;
816 EC_POINT
*tmp_point
= NULL
, *base
= NULL
, **var
;
818 size_t i
, bits
, w
, pre_points_per_block
, blocksize
, numblocks
, num
;
819 EC_POINT
**points
= NULL
;
820 EC_PRE_COMP
*pre_comp
;
823 BN_CTX
*new_ctx
= NULL
;
826 /* if there is an old EC_PRE_COMP object, throw it away */
827 EC_pre_comp_free(group
);
828 if ((pre_comp
= ec_pre_comp_new(group
)) == NULL
)
831 generator
= EC_GROUP_get0_generator(group
);
832 if (generator
== NULL
) {
833 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, EC_R_UNDEFINED_GENERATOR
);
839 ctx
= new_ctx
= BN_CTX_new();
846 order
= EC_GROUP_get0_order(group
);
849 if (BN_is_zero(order
)) {
850 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, EC_R_UNKNOWN_ORDER
);
854 bits
= BN_num_bits(order
);
856 * The following parameters mean we precompute (approximately) one point
857 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
858 * bit lengths, other parameter combinations might provide better
863 if (EC_window_bits_for_scalar_size(bits
) > w
) {
864 /* let's not make the window too small ... */
865 w
= EC_window_bits_for_scalar_size(bits
);
868 numblocks
= (bits
+ blocksize
- 1) / blocksize
; /* max. number of blocks
872 pre_points_per_block
= (size_t)1 << (w
- 1);
873 num
= pre_points_per_block
* numblocks
; /* number of points to compute
876 points
= OPENSSL_malloc(sizeof(*points
) * (num
+ 1));
877 if (points
== NULL
) {
878 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
883 var
[num
] = NULL
; /* pivot */
884 for (i
= 0; i
< num
; i
++) {
885 if ((var
[i
] = EC_POINT_new(group
)) == NULL
) {
886 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
891 if ((tmp_point
= EC_POINT_new(group
)) == NULL
892 || (base
= EC_POINT_new(group
)) == NULL
) {
893 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
897 if (!EC_POINT_copy(base
, generator
))
900 /* do the precomputation */
901 for (i
= 0; i
< numblocks
; i
++) {
904 if (!EC_POINT_dbl(group
, tmp_point
, base
, ctx
))
907 if (!EC_POINT_copy(*var
++, base
))
910 for (j
= 1; j
< pre_points_per_block
; j
++, var
++) {
912 * calculate odd multiples of the current base point
914 if (!EC_POINT_add(group
, *var
, tmp_point
, *(var
- 1), ctx
))
918 if (i
< numblocks
- 1) {
920 * get the next base (multiply current one by 2^blocksize)
924 if (blocksize
<= 2) {
925 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_INTERNAL_ERROR
);
929 if (!EC_POINT_dbl(group
, base
, tmp_point
, ctx
))
931 for (k
= 2; k
< blocksize
; k
++) {
932 if (!EC_POINT_dbl(group
, base
, base
, ctx
))
938 if (!EC_POINTs_make_affine(group
, num
, points
, ctx
))
941 pre_comp
->group
= group
;
942 pre_comp
->blocksize
= blocksize
;
943 pre_comp
->numblocks
= numblocks
;
945 pre_comp
->points
= points
;
948 SETPRECOMP(group
, ec
, pre_comp
);
955 BN_CTX_free(new_ctx
);
957 EC_ec_pre_comp_free(pre_comp
);
961 for (p
= points
; *p
!= NULL
; p
++)
963 OPENSSL_free(points
);
965 EC_POINT_free(tmp_point
);
970 int ec_wNAF_have_precompute_mult(const EC_GROUP
*group
)
972 return HAVEPRECOMP(group
, ec
);