2 * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
10 /* ====================================================================
11 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
12 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
13 * and contributed to the OpenSSL project.
17 #include <openssl/err.h>
19 #include "internal/cryptlib.h"
20 #include "internal/bn_int.h"
24 * This file implements the wNAF-based interleaving multi-exponentiation method
25 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
26 * for multiplication with precomputation, we use wNAF splitting
27 * (<URL: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) */
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_atomic_add(&pre
->references
, 1, &i
, pre
->lock
);
80 void EC_ec_pre_comp_free(EC_PRE_COMP
*pre
)
87 CRYPTO_atomic_add(&pre
->references
, -1, &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
);
105 * TODO: table should be optimised for the wNAF-based implementation,
106 * sometimes smaller windows will give better performance (thus the
107 * boundaries should be increased)
109 #define EC_window_bits_for_scalar_size(b) \
120 * \sum scalars[i]*points[i],
123 * in the addition if scalar != NULL
125 int ec_wNAF_mul(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
126 size_t num
, const EC_POINT
*points
[], const BIGNUM
*scalars
[],
129 BN_CTX
*new_ctx
= NULL
;
130 const EC_POINT
*generator
= NULL
;
131 EC_POINT
*tmp
= NULL
;
133 size_t blocksize
= 0, numblocks
= 0; /* for wNAF splitting */
134 size_t pre_points_per_block
= 0;
137 int r_is_inverted
= 0;
138 int r_is_at_infinity
= 1;
139 size_t *wsize
= NULL
; /* individual window sizes */
140 signed char **wNAF
= NULL
; /* individual wNAFs */
141 size_t *wNAF_len
= NULL
;
144 EC_POINT
**val
= NULL
; /* precomputation */
146 EC_POINT
***val_sub
= NULL
; /* pointers to sub-arrays of 'val' or
147 * 'pre_comp->points' */
148 const EC_PRE_COMP
*pre_comp
= NULL
;
149 int num_scalar
= 0; /* flag: will be set to 1 if 'scalar' must be
150 * treated like other scalars, i.e.
151 * precomputation is not available */
154 if (group
->meth
!= r
->meth
) {
155 ECerr(EC_F_EC_WNAF_MUL
, EC_R_INCOMPATIBLE_OBJECTS
);
159 if ((scalar
== NULL
) && (num
== 0)) {
160 return EC_POINT_set_to_infinity(group
, r
);
163 for (i
= 0; i
< num
; i
++) {
164 if (group
->meth
!= points
[i
]->meth
) {
165 ECerr(EC_F_EC_WNAF_MUL
, EC_R_INCOMPATIBLE_OBJECTS
);
171 ctx
= new_ctx
= BN_CTX_new();
176 if (scalar
!= NULL
) {
177 generator
= EC_GROUP_get0_generator(group
);
178 if (generator
== NULL
) {
179 ECerr(EC_F_EC_WNAF_MUL
, EC_R_UNDEFINED_GENERATOR
);
183 /* look if we can use precomputed multiples of generator */
185 pre_comp
= group
->pre_comp
.ec
;
186 if (pre_comp
&& pre_comp
->numblocks
187 && (EC_POINT_cmp(group
, generator
, pre_comp
->points
[0], ctx
) ==
189 blocksize
= pre_comp
->blocksize
;
192 * determine maximum number of blocks that wNAF splitting may
193 * yield (NB: maximum wNAF length is bit length plus one)
195 numblocks
= (BN_num_bits(scalar
) / blocksize
) + 1;
198 * we cannot use more blocks than we have precomputation for
200 if (numblocks
> pre_comp
->numblocks
)
201 numblocks
= pre_comp
->numblocks
;
203 pre_points_per_block
= (size_t)1 << (pre_comp
->w
- 1);
205 /* check that pre_comp looks sane */
206 if (pre_comp
->num
!= (pre_comp
->numblocks
* pre_points_per_block
)) {
207 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
211 /* can't use precomputation */
214 num_scalar
= 1; /* treat 'scalar' like 'num'-th element of
219 totalnum
= num
+ numblocks
;
221 wsize
= OPENSSL_malloc(totalnum
* sizeof wsize
[0]);
222 wNAF_len
= OPENSSL_malloc(totalnum
* sizeof wNAF_len
[0]);
223 wNAF
= OPENSSL_malloc((totalnum
+ 1) * sizeof wNAF
[0]); /* includes space
225 val_sub
= OPENSSL_malloc(totalnum
* sizeof val_sub
[0]);
227 /* Ensure wNAF is initialised in case we end up going to err */
229 wNAF
[0] = NULL
; /* preliminary pivot */
231 if (wsize
== NULL
|| wNAF_len
== NULL
|| wNAF
== NULL
|| val_sub
== NULL
) {
232 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
237 * num_val will be the total number of temporarily precomputed points
241 for (i
= 0; i
< num
+ num_scalar
; i
++) {
244 bits
= i
< num
? BN_num_bits(scalars
[i
]) : BN_num_bits(scalar
);
245 wsize
[i
] = EC_window_bits_for_scalar_size(bits
);
246 num_val
+= (size_t)1 << (wsize
[i
] - 1);
247 wNAF
[i
+ 1] = NULL
; /* make sure we always have a pivot */
249 bn_compute_wNAF((i
< num
? scalars
[i
] : scalar
), wsize
[i
],
253 if (wNAF_len
[i
] > max_len
)
254 max_len
= wNAF_len
[i
];
258 /* we go here iff scalar != NULL */
260 if (pre_comp
== NULL
) {
261 if (num_scalar
!= 1) {
262 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
265 /* we have already generated a wNAF for 'scalar' */
267 signed char *tmp_wNAF
= NULL
;
270 if (num_scalar
!= 0) {
271 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
276 * use the window size for which we have precomputation
278 wsize
[num
] = pre_comp
->w
;
279 tmp_wNAF
= bn_compute_wNAF(scalar
, wsize
[num
], &tmp_len
);
283 if (tmp_len
<= max_len
) {
285 * One of the other wNAFs is at least as long as the wNAF
286 * belonging to the generator, so wNAF splitting will not buy
291 totalnum
= num
+ 1; /* don't use wNAF splitting */
292 wNAF
[num
] = tmp_wNAF
;
293 wNAF
[num
+ 1] = NULL
;
294 wNAF_len
[num
] = tmp_len
;
296 * pre_comp->points starts with the points that we need here:
298 val_sub
[num
] = pre_comp
->points
;
301 * don't include tmp_wNAF directly into wNAF array - use wNAF
302 * splitting and include the blocks
306 EC_POINT
**tmp_points
;
308 if (tmp_len
< numblocks
* blocksize
) {
310 * possibly we can do with fewer blocks than estimated
312 numblocks
= (tmp_len
+ blocksize
- 1) / blocksize
;
313 if (numblocks
> pre_comp
->numblocks
) {
314 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
317 totalnum
= num
+ numblocks
;
320 /* split wNAF in 'numblocks' parts */
322 tmp_points
= pre_comp
->points
;
324 for (i
= num
; i
< totalnum
; i
++) {
325 if (i
< totalnum
- 1) {
326 wNAF_len
[i
] = blocksize
;
327 if (tmp_len
< blocksize
) {
328 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
331 tmp_len
-= blocksize
;
334 * last block gets whatever is left (this could be
335 * more or less than 'blocksize'!)
337 wNAF_len
[i
] = tmp_len
;
340 wNAF
[i
] = OPENSSL_malloc(wNAF_len
[i
]);
341 if (wNAF
[i
] == NULL
) {
342 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
343 OPENSSL_free(tmp_wNAF
);
346 memcpy(wNAF
[i
], pp
, wNAF_len
[i
]);
347 if (wNAF_len
[i
] > max_len
)
348 max_len
= wNAF_len
[i
];
350 if (*tmp_points
== NULL
) {
351 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
352 OPENSSL_free(tmp_wNAF
);
355 val_sub
[i
] = tmp_points
;
356 tmp_points
+= pre_points_per_block
;
359 OPENSSL_free(tmp_wNAF
);
365 * All points we precompute now go into a single array 'val'.
366 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
367 * subarray of 'pre_comp->points' if we already have precomputation.
369 val
= OPENSSL_malloc((num_val
+ 1) * sizeof val
[0]);
371 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
374 val
[num_val
] = NULL
; /* pivot element */
376 /* allocate points for precomputation */
378 for (i
= 0; i
< num
+ num_scalar
; i
++) {
380 for (j
= 0; j
< ((size_t)1 << (wsize
[i
] - 1)); j
++) {
381 *v
= EC_POINT_new(group
);
387 if (!(v
== val
+ num_val
)) {
388 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
392 if ((tmp
= EC_POINT_new(group
)) == NULL
)
396 * prepare precomputed values:
397 * val_sub[i][0] := points[i]
398 * val_sub[i][1] := 3 * points[i]
399 * val_sub[i][2] := 5 * points[i]
402 for (i
= 0; i
< num
+ num_scalar
; i
++) {
404 if (!EC_POINT_copy(val_sub
[i
][0], points
[i
]))
407 if (!EC_POINT_copy(val_sub
[i
][0], generator
))
412 if (!EC_POINT_dbl(group
, tmp
, val_sub
[i
][0], ctx
))
414 for (j
= 1; j
< ((size_t)1 << (wsize
[i
] - 1)); j
++) {
416 (group
, val_sub
[i
][j
], val_sub
[i
][j
- 1], tmp
, ctx
))
422 if (!EC_POINTs_make_affine(group
, num_val
, val
, ctx
))
425 r_is_at_infinity
= 1;
427 for (k
= max_len
- 1; k
>= 0; k
--) {
428 if (!r_is_at_infinity
) {
429 if (!EC_POINT_dbl(group
, r
, r
, ctx
))
433 for (i
= 0; i
< totalnum
; i
++) {
434 if (wNAF_len
[i
] > (size_t)k
) {
435 int digit
= wNAF
[i
][k
];
444 if (is_neg
!= r_is_inverted
) {
445 if (!r_is_at_infinity
) {
446 if (!EC_POINT_invert(group
, r
, ctx
))
449 r_is_inverted
= !r_is_inverted
;
454 if (r_is_at_infinity
) {
455 if (!EC_POINT_copy(r
, val_sub
[i
][digit
>> 1]))
457 r_is_at_infinity
= 0;
460 (group
, r
, r
, val_sub
[i
][digit
>> 1], ctx
))
468 if (r_is_at_infinity
) {
469 if (!EC_POINT_set_to_infinity(group
, r
))
473 if (!EC_POINT_invert(group
, r
, ctx
))
480 BN_CTX_free(new_ctx
);
483 OPENSSL_free(wNAF_len
);
487 for (w
= wNAF
; *w
!= NULL
; w
++)
493 for (v
= val
; *v
!= NULL
; v
++)
494 EC_POINT_clear_free(*v
);
498 OPENSSL_free(val_sub
);
503 * ec_wNAF_precompute_mult()
504 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
505 * for use with wNAF splitting as implemented in ec_wNAF_mul().
507 * 'pre_comp->points' is an array of multiples of the generator
508 * of the following form:
509 * points[0] = generator;
510 * points[1] = 3 * generator;
512 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
513 * points[2^(w-1)] = 2^blocksize * generator;
514 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
516 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
517 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
519 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
520 * points[2^(w-1)*numblocks] = NULL
522 int ec_wNAF_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
)
524 const EC_POINT
*generator
;
525 EC_POINT
*tmp_point
= NULL
, *base
= NULL
, **var
;
526 BN_CTX
*new_ctx
= NULL
;
528 size_t i
, bits
, w
, pre_points_per_block
, blocksize
, numblocks
, num
;
529 EC_POINT
**points
= NULL
;
530 EC_PRE_COMP
*pre_comp
;
533 /* if there is an old EC_PRE_COMP object, throw it away */
534 EC_pre_comp_free(group
);
535 if ((pre_comp
= ec_pre_comp_new(group
)) == NULL
)
538 generator
= EC_GROUP_get0_generator(group
);
539 if (generator
== NULL
) {
540 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, EC_R_UNDEFINED_GENERATOR
);
545 ctx
= new_ctx
= BN_CTX_new();
552 order
= EC_GROUP_get0_order(group
);
555 if (BN_is_zero(order
)) {
556 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, EC_R_UNKNOWN_ORDER
);
560 bits
= BN_num_bits(order
);
562 * The following parameters mean we precompute (approximately) one point
563 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
564 * bit lengths, other parameter combinations might provide better
569 if (EC_window_bits_for_scalar_size(bits
) > w
) {
570 /* let's not make the window too small ... */
571 w
= EC_window_bits_for_scalar_size(bits
);
574 numblocks
= (bits
+ blocksize
- 1) / blocksize
; /* max. number of blocks
578 pre_points_per_block
= (size_t)1 << (w
- 1);
579 num
= pre_points_per_block
* numblocks
; /* number of points to compute
582 points
= OPENSSL_malloc(sizeof(*points
) * (num
+ 1));
583 if (points
== NULL
) {
584 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
589 var
[num
] = NULL
; /* pivot */
590 for (i
= 0; i
< num
; i
++) {
591 if ((var
[i
] = EC_POINT_new(group
)) == NULL
) {
592 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
597 if ((tmp_point
= EC_POINT_new(group
)) == NULL
598 || (base
= EC_POINT_new(group
)) == NULL
) {
599 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
603 if (!EC_POINT_copy(base
, generator
))
606 /* do the precomputation */
607 for (i
= 0; i
< numblocks
; i
++) {
610 if (!EC_POINT_dbl(group
, tmp_point
, base
, ctx
))
613 if (!EC_POINT_copy(*var
++, base
))
616 for (j
= 1; j
< pre_points_per_block
; j
++, var
++) {
618 * calculate odd multiples of the current base point
620 if (!EC_POINT_add(group
, *var
, tmp_point
, *(var
- 1), ctx
))
624 if (i
< numblocks
- 1) {
626 * get the next base (multiply current one by 2^blocksize)
630 if (blocksize
<= 2) {
631 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_INTERNAL_ERROR
);
635 if (!EC_POINT_dbl(group
, base
, tmp_point
, ctx
))
637 for (k
= 2; k
< blocksize
; k
++) {
638 if (!EC_POINT_dbl(group
, base
, base
, ctx
))
644 if (!EC_POINTs_make_affine(group
, num
, points
, ctx
))
647 pre_comp
->group
= group
;
648 pre_comp
->blocksize
= blocksize
;
649 pre_comp
->numblocks
= numblocks
;
651 pre_comp
->points
= points
;
654 SETPRECOMP(group
, ec
, pre_comp
);
661 BN_CTX_free(new_ctx
);
662 EC_ec_pre_comp_free(pre_comp
);
666 for (p
= points
; *p
!= NULL
; p
++)
668 OPENSSL_free(points
);
670 EC_POINT_free(tmp_point
);
675 int ec_wNAF_have_precompute_mult(const EC_GROUP
*group
)
677 return HAVEPRECOMP(group
, ec
);