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 #include <openssl/err.h>
14 #include "internal/cryptlib.h"
15 #include "internal/bn_int.h"
17 #include "internal/refcount.h"
20 * This file implements the wNAF-based interleaving multi-exponentiation method
22 * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp
23 * You might now find it here:
24 * http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
25 * http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
26 * For multiplication with precomputation, we use wNAF splitting, formerly at:
27 * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp
30 /* structure for precomputed multiples of the generator */
31 struct ec_pre_comp_st
{
32 const EC_GROUP
*group
; /* parent EC_GROUP object */
33 size_t blocksize
; /* block size for wNAF splitting */
34 size_t numblocks
; /* max. number of blocks for which we have
36 size_t w
; /* window size */
37 EC_POINT
**points
; /* array with pre-calculated multiples of
38 * generator: 'num' pointers to EC_POINT
39 * objects followed by a NULL */
40 size_t num
; /* numblocks * 2^(w-1) */
41 CRYPTO_REF_COUNT references
;
45 static EC_PRE_COMP
*ec_pre_comp_new(const EC_GROUP
*group
)
47 EC_PRE_COMP
*ret
= NULL
;
52 ret
= OPENSSL_zalloc(sizeof(*ret
));
54 ECerr(EC_F_EC_PRE_COMP_NEW
, ERR_R_MALLOC_FAILURE
);
59 ret
->blocksize
= 8; /* default */
60 ret
->w
= 4; /* default */
63 ret
->lock
= CRYPTO_THREAD_lock_new();
64 if (ret
->lock
== NULL
) {
65 ECerr(EC_F_EC_PRE_COMP_NEW
, ERR_R_MALLOC_FAILURE
);
72 EC_PRE_COMP
*EC_ec_pre_comp_dup(EC_PRE_COMP
*pre
)
76 CRYPTO_UP_REF(&pre
->references
, &i
, pre
->lock
);
80 void EC_ec_pre_comp_free(EC_PRE_COMP
*pre
)
87 CRYPTO_DOWN_REF(&pre
->references
, &i
, pre
->lock
);
88 REF_PRINT_COUNT("EC_ec", pre
);
91 REF_ASSERT_ISNT(i
< 0);
93 if (pre
->points
!= NULL
) {
96 for (pts
= pre
->points
; *pts
!= NULL
; pts
++)
98 OPENSSL_free(pre
->points
);
100 CRYPTO_THREAD_lock_free(pre
->lock
);
104 #define EC_POINT_BN_set_flags(P, flags) do { \
105 BN_set_flags((P)->X, (flags)); \
106 BN_set_flags((P)->Y, (flags)); \
107 BN_set_flags((P)->Z, (flags)); \
111 * This functions computes a single point multiplication over the EC group,
112 * using, at a high level, a Montgomery ladder with conditional swaps, with
113 * various timing attack defenses.
115 * It performs either a fixed point multiplication
116 * (scalar * generator)
117 * when point is NULL, or a variable point multiplication
119 * when point is not NULL.
121 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all
122 * constant time bets are off (where n is the cardinality of the EC group).
124 * This function expects `group->order` and `group->cardinality` to be well
125 * defined and non-zero: it fails with an error code otherwise.
127 * NB: This says nothing about the constant-timeness of the ladder step
128 * implementation (i.e., the default implementation is based on EC_POINT_add and
129 * EC_POINT_dbl, which of course are not constant time themselves) or the
130 * underlying multiprecision arithmetic.
132 * The product is stored in `r`.
134 * This is an internal function: callers are in charge of ensuring that the
135 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
137 * Returns 1 on success, 0 otherwise.
139 int ec_scalar_mul_ladder(const EC_GROUP
*group
, EC_POINT
*r
,
140 const BIGNUM
*scalar
, const EC_POINT
*point
,
143 int i
, cardinality_bits
, group_top
, kbit
, pbit
, Z_is_one
;
147 BIGNUM
*lambda
= NULL
;
148 BIGNUM
*cardinality
= NULL
;
151 /* early exit if the input point is the point at infinity */
152 if (point
!= NULL
&& EC_POINT_is_at_infinity(group
, point
))
153 return EC_POINT_set_to_infinity(group
, r
);
155 if (BN_is_zero(group
->order
)) {
156 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_UNKNOWN_ORDER
);
159 if (BN_is_zero(group
->cofactor
)) {
160 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_UNKNOWN_COFACTOR
);
166 if (((p
= EC_POINT_new(group
)) == NULL
)
167 || ((s
= EC_POINT_new(group
)) == NULL
)) {
168 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_MALLOC_FAILURE
);
173 if (!EC_POINT_copy(p
, group
->generator
)) {
174 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_EC_LIB
);
178 if (!EC_POINT_copy(p
, point
)) {
179 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_EC_LIB
);
184 EC_POINT_BN_set_flags(p
, BN_FLG_CONSTTIME
);
185 EC_POINT_BN_set_flags(r
, BN_FLG_CONSTTIME
);
186 EC_POINT_BN_set_flags(s
, BN_FLG_CONSTTIME
);
188 cardinality
= BN_CTX_get(ctx
);
189 lambda
= BN_CTX_get(ctx
);
192 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_MALLOC_FAILURE
);
196 if (!BN_mul(cardinality
, group
->order
, group
->cofactor
, ctx
)) {
197 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
202 * Group cardinalities are often on a word boundary.
203 * So when we pad the scalar, some timing diff might
204 * pop if it needs to be expanded due to carries.
205 * So expand ahead of time.
207 cardinality_bits
= BN_num_bits(cardinality
);
208 group_top
= bn_get_top(cardinality
);
209 if ((bn_wexpand(k
, group_top
+ 2) == NULL
)
210 || (bn_wexpand(lambda
, group_top
+ 2) == NULL
)) {
211 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
215 if (!BN_copy(k
, scalar
)) {
216 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
220 BN_set_flags(k
, BN_FLG_CONSTTIME
);
222 if ((BN_num_bits(k
) > cardinality_bits
) || (BN_is_negative(k
))) {
224 * this is an unusual input, and we don't guarantee
227 if (!BN_nnmod(k
, k
, cardinality
, ctx
)) {
228 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
233 if (!BN_add(lambda
, k
, cardinality
)) {
234 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
237 BN_set_flags(lambda
, BN_FLG_CONSTTIME
);
238 if (!BN_add(k
, lambda
, cardinality
)) {
239 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
243 * lambda := scalar + cardinality
244 * k := scalar + 2*cardinality
246 kbit
= BN_is_bit_set(lambda
, cardinality_bits
);
247 BN_consttime_swap(kbit
, k
, lambda
, group_top
+ 2);
249 group_top
= bn_get_top(group
->field
);
250 if ((bn_wexpand(s
->X
, group_top
) == NULL
)
251 || (bn_wexpand(s
->Y
, group_top
) == NULL
)
252 || (bn_wexpand(s
->Z
, group_top
) == NULL
)
253 || (bn_wexpand(r
->X
, group_top
) == NULL
)
254 || (bn_wexpand(r
->Y
, group_top
) == NULL
)
255 || (bn_wexpand(r
->Z
, group_top
) == NULL
)
256 || (bn_wexpand(p
->X
, group_top
) == NULL
)
257 || (bn_wexpand(p
->Y
, group_top
) == NULL
)
258 || (bn_wexpand(p
->Z
, group_top
) == NULL
)) {
259 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, ERR_R_BN_LIB
);
264 * Apply coordinate blinding for EC_POINT.
266 * The underlying EC_METHOD can optionally implement this function:
267 * ec_point_blind_coordinates() returns 0 in case of errors or 1 on
268 * success or if coordinate blinding is not implemented for this
271 if (!ec_point_blind_coordinates(group
, p
, ctx
)) {
272 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_POINT_COORDINATES_BLIND_FAILURE
);
276 /* Initialize the Montgomery ladder */
277 if (!ec_point_ladder_pre(group
, r
, s
, p
, ctx
)) {
278 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_LADDER_PRE_FAILURE
);
282 /* top bit is a 1, in a fixed pos */
285 #define EC_POINT_CSWAP(c, a, b, w, t) do { \
286 BN_consttime_swap(c, (a)->X, (b)->X, w); \
287 BN_consttime_swap(c, (a)->Y, (b)->Y, w); \
288 BN_consttime_swap(c, (a)->Z, (b)->Z, w); \
289 t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
290 (a)->Z_is_one ^= (t); \
291 (b)->Z_is_one ^= (t); \
295 * The ladder step, with branches, is
297 * k[i] == 0: S = add(R, S), R = dbl(R)
298 * k[i] == 1: R = add(S, R), S = dbl(S)
300 * Swapping R, S conditionally on k[i] leaves you with state
302 * k[i] == 0: T, U = R, S
303 * k[i] == 1: T, U = S, R
305 * Then perform the ECC ops.
310 * Which leaves you with state
312 * k[i] == 0: U = add(R, S), T = dbl(R)
313 * k[i] == 1: U = add(S, R), T = dbl(S)
315 * Swapping T, U conditionally on k[i] leaves you with state
317 * k[i] == 0: R, S = T, U
318 * k[i] == 1: R, S = U, T
320 * Which leaves you with state
322 * k[i] == 0: S = add(R, S), R = dbl(R)
323 * k[i] == 1: R = add(S, R), S = dbl(S)
325 * So we get the same logic, but instead of a branch it's a
326 * conditional swap, followed by ECC ops, then another conditional swap.
328 * Optimization: The end of iteration i and start of i-1 looks like
335 * CSWAP(k[i-1], R, S)
337 * CSWAP(k[i-1], R, S)
340 * So instead of two contiguous swaps, you can merge the condition
341 * bits and do a single swap.
343 * k[i] k[i-1] Outcome
349 * This is XOR. pbit tracks the previous bit of k.
352 for (i
= cardinality_bits
- 1; i
>= 0; i
--) {
353 kbit
= BN_is_bit_set(k
, i
) ^ pbit
;
354 EC_POINT_CSWAP(kbit
, r
, s
, group_top
, Z_is_one
);
356 /* Perform a single step of the Montgomery ladder */
357 if (!ec_point_ladder_step(group
, r
, s
, p
, ctx
)) {
358 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_LADDER_STEP_FAILURE
);
362 * pbit logic merges this cswap with that of the
367 /* one final cswap to move the right value into r */
368 EC_POINT_CSWAP(pbit
, r
, s
, group_top
, Z_is_one
);
369 #undef EC_POINT_CSWAP
371 /* Finalize ladder (and recover full point coordinates) */
372 if (!ec_point_ladder_post(group
, r
, s
, p
, ctx
)) {
373 ECerr(EC_F_EC_SCALAR_MUL_LADDER
, EC_R_LADDER_POST_FAILURE
);
387 #undef EC_POINT_BN_set_flags
390 * TODO: table should be optimised for the wNAF-based implementation,
391 * sometimes smaller windows will give better performance (thus the
392 * boundaries should be increased)
394 #define EC_window_bits_for_scalar_size(b) \
405 * \sum scalars[i]*points[i],
408 * in the addition if scalar != NULL
410 int ec_wNAF_mul(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
411 size_t num
, const EC_POINT
*points
[], const BIGNUM
*scalars
[],
414 const EC_POINT
*generator
= NULL
;
415 EC_POINT
*tmp
= NULL
;
417 size_t blocksize
= 0, numblocks
= 0; /* for wNAF splitting */
418 size_t pre_points_per_block
= 0;
421 int r_is_inverted
= 0;
422 int r_is_at_infinity
= 1;
423 size_t *wsize
= NULL
; /* individual window sizes */
424 signed char **wNAF
= NULL
; /* individual wNAFs */
425 size_t *wNAF_len
= NULL
;
428 EC_POINT
**val
= NULL
; /* precomputation */
430 EC_POINT
***val_sub
= NULL
; /* pointers to sub-arrays of 'val' or
431 * 'pre_comp->points' */
432 const EC_PRE_COMP
*pre_comp
= NULL
;
433 int num_scalar
= 0; /* flag: will be set to 1 if 'scalar' must be
434 * treated like other scalars, i.e.
435 * precomputation is not available */
438 if (!BN_is_zero(group
->order
) && !BN_is_zero(group
->cofactor
)) {
440 * Handle the common cases where the scalar is secret, enforcing a
441 * scalar multiplication implementation based on a Montgomery ladder,
442 * with various timing attack defenses.
444 if ((scalar
!= NULL
) && (num
== 0)) {
446 * In this case we want to compute scalar * GeneratorPoint: this
447 * codepath is reached most prominently by (ephemeral) key
448 * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup,
449 * ECDH keygen/first half), where the scalar is always secret. This
450 * is why we ignore if BN_FLG_CONSTTIME is actually set and we
451 * always call the ladder version.
453 return ec_scalar_mul_ladder(group
, r
, scalar
, NULL
, ctx
);
455 if ((scalar
== NULL
) && (num
== 1)) {
457 * In this case we want to compute scalar * VariablePoint: this
458 * codepath is reached most prominently by the second half of ECDH,
459 * where the secret scalar is multiplied by the peer's public point.
460 * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is
461 * actually set and we always call the ladder version.
463 return ec_scalar_mul_ladder(group
, r
, scalars
[0], points
[0], ctx
);
467 if (scalar
!= NULL
) {
468 generator
= EC_GROUP_get0_generator(group
);
469 if (generator
== NULL
) {
470 ECerr(EC_F_EC_WNAF_MUL
, EC_R_UNDEFINED_GENERATOR
);
474 /* look if we can use precomputed multiples of generator */
476 pre_comp
= group
->pre_comp
.ec
;
477 if (pre_comp
&& pre_comp
->numblocks
478 && (EC_POINT_cmp(group
, generator
, pre_comp
->points
[0], ctx
) ==
480 blocksize
= pre_comp
->blocksize
;
483 * determine maximum number of blocks that wNAF splitting may
484 * yield (NB: maximum wNAF length is bit length plus one)
486 numblocks
= (BN_num_bits(scalar
) / blocksize
) + 1;
489 * we cannot use more blocks than we have precomputation for
491 if (numblocks
> pre_comp
->numblocks
)
492 numblocks
= pre_comp
->numblocks
;
494 pre_points_per_block
= (size_t)1 << (pre_comp
->w
- 1);
496 /* check that pre_comp looks sane */
497 if (pre_comp
->num
!= (pre_comp
->numblocks
* pre_points_per_block
)) {
498 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
502 /* can't use precomputation */
505 num_scalar
= 1; /* treat 'scalar' like 'num'-th element of
510 totalnum
= num
+ numblocks
;
512 wsize
= OPENSSL_malloc(totalnum
* sizeof(wsize
[0]));
513 wNAF_len
= OPENSSL_malloc(totalnum
* sizeof(wNAF_len
[0]));
514 /* include space for pivot */
515 wNAF
= OPENSSL_malloc((totalnum
+ 1) * sizeof(wNAF
[0]));
516 val_sub
= OPENSSL_malloc(totalnum
* sizeof(val_sub
[0]));
518 /* Ensure wNAF is initialised in case we end up going to err */
520 wNAF
[0] = NULL
; /* preliminary pivot */
522 if (wsize
== NULL
|| wNAF_len
== NULL
|| wNAF
== NULL
|| val_sub
== NULL
) {
523 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
528 * num_val will be the total number of temporarily precomputed points
532 for (i
= 0; i
< num
+ num_scalar
; i
++) {
535 bits
= i
< num
? BN_num_bits(scalars
[i
]) : BN_num_bits(scalar
);
536 wsize
[i
] = EC_window_bits_for_scalar_size(bits
);
537 num_val
+= (size_t)1 << (wsize
[i
] - 1);
538 wNAF
[i
+ 1] = NULL
; /* make sure we always have a pivot */
540 bn_compute_wNAF((i
< num
? scalars
[i
] : scalar
), wsize
[i
],
544 if (wNAF_len
[i
] > max_len
)
545 max_len
= wNAF_len
[i
];
549 /* we go here iff scalar != NULL */
551 if (pre_comp
== NULL
) {
552 if (num_scalar
!= 1) {
553 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
556 /* we have already generated a wNAF for 'scalar' */
558 signed char *tmp_wNAF
= NULL
;
561 if (num_scalar
!= 0) {
562 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
567 * use the window size for which we have precomputation
569 wsize
[num
] = pre_comp
->w
;
570 tmp_wNAF
= bn_compute_wNAF(scalar
, wsize
[num
], &tmp_len
);
574 if (tmp_len
<= max_len
) {
576 * One of the other wNAFs is at least as long as the wNAF
577 * belonging to the generator, so wNAF splitting will not buy
582 totalnum
= num
+ 1; /* don't use wNAF splitting */
583 wNAF
[num
] = tmp_wNAF
;
584 wNAF
[num
+ 1] = NULL
;
585 wNAF_len
[num
] = tmp_len
;
587 * pre_comp->points starts with the points that we need here:
589 val_sub
[num
] = pre_comp
->points
;
592 * don't include tmp_wNAF directly into wNAF array - use wNAF
593 * splitting and include the blocks
597 EC_POINT
**tmp_points
;
599 if (tmp_len
< numblocks
* blocksize
) {
601 * possibly we can do with fewer blocks than estimated
603 numblocks
= (tmp_len
+ blocksize
- 1) / blocksize
;
604 if (numblocks
> pre_comp
->numblocks
) {
605 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
606 OPENSSL_free(tmp_wNAF
);
609 totalnum
= num
+ numblocks
;
612 /* split wNAF in 'numblocks' parts */
614 tmp_points
= pre_comp
->points
;
616 for (i
= num
; i
< totalnum
; i
++) {
617 if (i
< totalnum
- 1) {
618 wNAF_len
[i
] = blocksize
;
619 if (tmp_len
< blocksize
) {
620 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
621 OPENSSL_free(tmp_wNAF
);
624 tmp_len
-= blocksize
;
627 * last block gets whatever is left (this could be
628 * more or less than 'blocksize'!)
630 wNAF_len
[i
] = tmp_len
;
633 wNAF
[i
] = OPENSSL_malloc(wNAF_len
[i
]);
634 if (wNAF
[i
] == NULL
) {
635 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
636 OPENSSL_free(tmp_wNAF
);
639 memcpy(wNAF
[i
], pp
, wNAF_len
[i
]);
640 if (wNAF_len
[i
] > max_len
)
641 max_len
= wNAF_len
[i
];
643 if (*tmp_points
== NULL
) {
644 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
645 OPENSSL_free(tmp_wNAF
);
648 val_sub
[i
] = tmp_points
;
649 tmp_points
+= pre_points_per_block
;
652 OPENSSL_free(tmp_wNAF
);
658 * All points we precompute now go into a single array 'val'.
659 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
660 * subarray of 'pre_comp->points' if we already have precomputation.
662 val
= OPENSSL_malloc((num_val
+ 1) * sizeof(val
[0]));
664 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
667 val
[num_val
] = NULL
; /* pivot element */
669 /* allocate points for precomputation */
671 for (i
= 0; i
< num
+ num_scalar
; i
++) {
673 for (j
= 0; j
< ((size_t)1 << (wsize
[i
] - 1)); j
++) {
674 *v
= EC_POINT_new(group
);
680 if (!(v
== val
+ num_val
)) {
681 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
685 if ((tmp
= EC_POINT_new(group
)) == NULL
)
689 * prepare precomputed values:
690 * val_sub[i][0] := points[i]
691 * val_sub[i][1] := 3 * points[i]
692 * val_sub[i][2] := 5 * points[i]
695 for (i
= 0; i
< num
+ num_scalar
; i
++) {
697 if (!EC_POINT_copy(val_sub
[i
][0], points
[i
]))
700 if (!EC_POINT_copy(val_sub
[i
][0], generator
))
705 if (!EC_POINT_dbl(group
, tmp
, val_sub
[i
][0], ctx
))
707 for (j
= 1; j
< ((size_t)1 << (wsize
[i
] - 1)); j
++) {
709 (group
, val_sub
[i
][j
], val_sub
[i
][j
- 1], tmp
, ctx
))
715 if (!EC_POINTs_make_affine(group
, num_val
, val
, ctx
))
718 r_is_at_infinity
= 1;
720 for (k
= max_len
- 1; k
>= 0; k
--) {
721 if (!r_is_at_infinity
) {
722 if (!EC_POINT_dbl(group
, r
, r
, ctx
))
726 for (i
= 0; i
< totalnum
; i
++) {
727 if (wNAF_len
[i
] > (size_t)k
) {
728 int digit
= wNAF
[i
][k
];
737 if (is_neg
!= r_is_inverted
) {
738 if (!r_is_at_infinity
) {
739 if (!EC_POINT_invert(group
, r
, ctx
))
742 r_is_inverted
= !r_is_inverted
;
747 if (r_is_at_infinity
) {
748 if (!EC_POINT_copy(r
, val_sub
[i
][digit
>> 1]))
750 r_is_at_infinity
= 0;
753 (group
, r
, r
, val_sub
[i
][digit
>> 1], ctx
))
761 if (r_is_at_infinity
) {
762 if (!EC_POINT_set_to_infinity(group
, r
))
766 if (!EC_POINT_invert(group
, r
, ctx
))
775 OPENSSL_free(wNAF_len
);
779 for (w
= wNAF
; *w
!= NULL
; w
++)
785 for (v
= val
; *v
!= NULL
; v
++)
786 EC_POINT_clear_free(*v
);
790 OPENSSL_free(val_sub
);
795 * ec_wNAF_precompute_mult()
796 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
797 * for use with wNAF splitting as implemented in ec_wNAF_mul().
799 * 'pre_comp->points' is an array of multiples of the generator
800 * of the following form:
801 * points[0] = generator;
802 * points[1] = 3 * generator;
804 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
805 * points[2^(w-1)] = 2^blocksize * generator;
806 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
808 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
809 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
811 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
812 * points[2^(w-1)*numblocks] = NULL
814 int ec_wNAF_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
)
816 const EC_POINT
*generator
;
817 EC_POINT
*tmp_point
= NULL
, *base
= NULL
, **var
;
818 BN_CTX
*new_ctx
= NULL
;
820 size_t i
, bits
, w
, pre_points_per_block
, blocksize
, numblocks
, num
;
821 EC_POINT
**points
= NULL
;
822 EC_PRE_COMP
*pre_comp
;
825 /* if there is an old EC_PRE_COMP object, throw it away */
826 EC_pre_comp_free(group
);
827 if ((pre_comp
= ec_pre_comp_new(group
)) == NULL
)
830 generator
= EC_GROUP_get0_generator(group
);
831 if (generator
== NULL
) {
832 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, EC_R_UNDEFINED_GENERATOR
);
837 ctx
= new_ctx
= BN_CTX_new();
844 order
= EC_GROUP_get0_order(group
);
847 if (BN_is_zero(order
)) {
848 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, EC_R_UNKNOWN_ORDER
);
852 bits
= BN_num_bits(order
);
854 * The following parameters mean we precompute (approximately) one point
855 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
856 * bit lengths, other parameter combinations might provide better
861 if (EC_window_bits_for_scalar_size(bits
) > w
) {
862 /* let's not make the window too small ... */
863 w
= EC_window_bits_for_scalar_size(bits
);
866 numblocks
= (bits
+ blocksize
- 1) / blocksize
; /* max. number of blocks
870 pre_points_per_block
= (size_t)1 << (w
- 1);
871 num
= pre_points_per_block
* numblocks
; /* number of points to compute
874 points
= OPENSSL_malloc(sizeof(*points
) * (num
+ 1));
875 if (points
== NULL
) {
876 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
881 var
[num
] = NULL
; /* pivot */
882 for (i
= 0; i
< num
; i
++) {
883 if ((var
[i
] = EC_POINT_new(group
)) == NULL
) {
884 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
889 if ((tmp_point
= EC_POINT_new(group
)) == NULL
890 || (base
= EC_POINT_new(group
)) == NULL
) {
891 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
895 if (!EC_POINT_copy(base
, generator
))
898 /* do the precomputation */
899 for (i
= 0; i
< numblocks
; i
++) {
902 if (!EC_POINT_dbl(group
, tmp_point
, base
, ctx
))
905 if (!EC_POINT_copy(*var
++, base
))
908 for (j
= 1; j
< pre_points_per_block
; j
++, var
++) {
910 * calculate odd multiples of the current base point
912 if (!EC_POINT_add(group
, *var
, tmp_point
, *(var
- 1), ctx
))
916 if (i
< numblocks
- 1) {
918 * get the next base (multiply current one by 2^blocksize)
922 if (blocksize
<= 2) {
923 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_INTERNAL_ERROR
);
927 if (!EC_POINT_dbl(group
, base
, tmp_point
, ctx
))
929 for (k
= 2; k
< blocksize
; k
++) {
930 if (!EC_POINT_dbl(group
, base
, base
, ctx
))
936 if (!EC_POINTs_make_affine(group
, num
, points
, ctx
))
939 pre_comp
->group
= group
;
940 pre_comp
->blocksize
= blocksize
;
941 pre_comp
->numblocks
= numblocks
;
943 pre_comp
->points
= points
;
946 SETPRECOMP(group
, ec
, pre_comp
);
953 BN_CTX_free(new_ctx
);
954 EC_ec_pre_comp_free(pre_comp
);
958 for (p
= points
; *p
!= NULL
; p
++)
960 OPENSSL_free(points
);
962 EC_POINT_free(tmp_point
);
967 int ec_wNAF_have_precompute_mult(const EC_GROUP
*group
)
969 return HAVEPRECOMP(group
, ec
);