2 * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
4 /* ====================================================================
5 * Copyright (c) 1998-2007 The OpenSSL Project. All rights reserved.
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
11 * 1. Redistributions of source code must retain the above copyright
12 * notice, this list of conditions and the following disclaimer.
14 * 2. Redistributions in binary form must reproduce the above copyright
15 * notice, this list of conditions and the following disclaimer in
16 * the documentation and/or other materials provided with the
19 * 3. All advertising materials mentioning features or use of this
20 * software must display the following acknowledgment:
21 * "This product includes software developed by the OpenSSL Project
22 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
24 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
25 * endorse or promote products derived from this software without
26 * prior written permission. For written permission, please contact
27 * openssl-core@openssl.org.
29 * 5. Products derived from this software may not be called "OpenSSL"
30 * nor may "OpenSSL" appear in their names without prior written
31 * permission of the OpenSSL Project.
33 * 6. Redistributions of any form whatsoever must retain the following
35 * "This product includes software developed by the OpenSSL Project
36 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
39 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
40 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
41 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
42 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
43 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
44 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
45 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
46 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
47 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
48 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
49 * OF THE POSSIBILITY OF SUCH DAMAGE.
50 * ====================================================================
52 * This product includes cryptographic software written by Eric Young
53 * (eay@cryptsoft.com). This product includes software written by Tim
54 * Hudson (tjh@cryptsoft.com).
57 /* ====================================================================
58 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
59 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
60 * and contributed to the OpenSSL project.
64 #include <openssl/err.h>
66 #include "internal/bn_int.h"
70 * This file implements the wNAF-based interleaving multi-exponentation method
71 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
72 * for multiplication with precomputation, we use wNAF splitting
73 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
76 /* structure for precomputed multiples of the generator */
77 struct ec_pre_comp_st
{
78 const EC_GROUP
*group
; /* parent EC_GROUP object */
79 size_t blocksize
; /* block size for wNAF splitting */
80 size_t numblocks
; /* max. number of blocks for which we have
82 size_t w
; /* window size */
83 EC_POINT
**points
; /* array with pre-calculated multiples of
84 * generator: 'num' pointers to EC_POINT
85 * objects followed by a NULL */
86 size_t num
; /* numblocks * 2^(w-1) */
90 static EC_PRE_COMP
*ec_pre_comp_new(const EC_GROUP
*group
)
92 EC_PRE_COMP
*ret
= NULL
;
97 ret
= OPENSSL_zalloc(sizeof(*ret
));
99 ECerr(EC_F_EC_PRE_COMP_NEW
, ERR_R_MALLOC_FAILURE
);
103 ret
->blocksize
= 8; /* default */
104 ret
->w
= 4; /* default */
109 EC_PRE_COMP
*EC_ec_pre_comp_dup(EC_PRE_COMP
*pre
)
112 CRYPTO_add(&pre
->references
, 1, CRYPTO_LOCK_EC_PRE_COMP
);
116 void EC_ec_pre_comp_free(EC_PRE_COMP
*pre
)
119 || CRYPTO_add(&pre
->references
, -1, CRYPTO_LOCK_EC_PRE_COMP
) > 0)
122 if (pre
->points
!= NULL
) {
125 for (pts
= pre
->points
; *pts
!= NULL
; pts
++)
127 OPENSSL_free(pre
->points
);
133 * TODO: table should be optimised for the wNAF-based implementation,
134 * sometimes smaller windows will give better performance (thus the
135 * boundaries should be increased)
137 #define EC_window_bits_for_scalar_size(b) \
148 * \sum scalars[i]*points[i],
151 * in the addition if scalar != NULL
153 int ec_wNAF_mul(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
154 size_t num
, const EC_POINT
*points
[], const BIGNUM
*scalars
[],
157 BN_CTX
*new_ctx
= NULL
;
158 const EC_POINT
*generator
= NULL
;
159 EC_POINT
*tmp
= NULL
;
161 size_t blocksize
= 0, numblocks
= 0; /* for wNAF splitting */
162 size_t pre_points_per_block
= 0;
165 int r_is_inverted
= 0;
166 int r_is_at_infinity
= 1;
167 size_t *wsize
= NULL
; /* individual window sizes */
168 signed char **wNAF
= NULL
; /* individual wNAFs */
169 size_t *wNAF_len
= NULL
;
172 EC_POINT
**val
= NULL
; /* precomputation */
174 EC_POINT
***val_sub
= NULL
; /* pointers to sub-arrays of 'val' or
175 * 'pre_comp->points' */
176 const EC_PRE_COMP
*pre_comp
= NULL
;
177 int num_scalar
= 0; /* flag: will be set to 1 if 'scalar' must be
178 * treated like other scalars, i.e.
179 * precomputation is not available */
182 if (group
->meth
!= r
->meth
) {
183 ECerr(EC_F_EC_WNAF_MUL
, EC_R_INCOMPATIBLE_OBJECTS
);
187 if ((scalar
== NULL
) && (num
== 0)) {
188 return EC_POINT_set_to_infinity(group
, r
);
191 for (i
= 0; i
< num
; i
++) {
192 if (group
->meth
!= points
[i
]->meth
) {
193 ECerr(EC_F_EC_WNAF_MUL
, EC_R_INCOMPATIBLE_OBJECTS
);
199 ctx
= new_ctx
= BN_CTX_new();
204 if (scalar
!= NULL
) {
205 generator
= EC_GROUP_get0_generator(group
);
206 if (generator
== NULL
) {
207 ECerr(EC_F_EC_WNAF_MUL
, EC_R_UNDEFINED_GENERATOR
);
211 /* look if we can use precomputed multiples of generator */
213 pre_comp
= group
->pre_comp
.ec
;
214 if (pre_comp
&& pre_comp
->numblocks
215 && (EC_POINT_cmp(group
, generator
, pre_comp
->points
[0], ctx
) ==
217 blocksize
= pre_comp
->blocksize
;
220 * determine maximum number of blocks that wNAF splitting may
221 * yield (NB: maximum wNAF length is bit length plus one)
223 numblocks
= (BN_num_bits(scalar
) / blocksize
) + 1;
226 * we cannot use more blocks than we have precomputation for
228 if (numblocks
> pre_comp
->numblocks
)
229 numblocks
= pre_comp
->numblocks
;
231 pre_points_per_block
= (size_t)1 << (pre_comp
->w
- 1);
233 /* check that pre_comp looks sane */
234 if (pre_comp
->num
!= (pre_comp
->numblocks
* pre_points_per_block
)) {
235 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
239 /* can't use precomputation */
242 num_scalar
= 1; /* treat 'scalar' like 'num'-th element of
247 totalnum
= num
+ numblocks
;
249 wsize
= OPENSSL_malloc(totalnum
* sizeof wsize
[0]);
250 wNAF_len
= OPENSSL_malloc(totalnum
* sizeof wNAF_len
[0]);
251 wNAF
= OPENSSL_malloc((totalnum
+ 1) * sizeof wNAF
[0]); /* includes space
253 val_sub
= OPENSSL_malloc(totalnum
* sizeof val_sub
[0]);
255 /* Ensure wNAF is initialised in case we end up going to err */
257 wNAF
[0] = NULL
; /* preliminary pivot */
259 if (wsize
== NULL
|| wNAF_len
== NULL
|| wNAF
== NULL
|| val_sub
== NULL
) {
260 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
265 * num_val will be the total number of temporarily precomputed points
269 for (i
= 0; i
< num
+ num_scalar
; i
++) {
272 bits
= i
< num
? BN_num_bits(scalars
[i
]) : BN_num_bits(scalar
);
273 wsize
[i
] = EC_window_bits_for_scalar_size(bits
);
274 num_val
+= (size_t)1 << (wsize
[i
] - 1);
275 wNAF
[i
+ 1] = NULL
; /* make sure we always have a pivot */
277 bn_compute_wNAF((i
< num
? scalars
[i
] : scalar
), wsize
[i
],
281 if (wNAF_len
[i
] > max_len
)
282 max_len
= wNAF_len
[i
];
286 /* we go here iff scalar != NULL */
288 if (pre_comp
== NULL
) {
289 if (num_scalar
!= 1) {
290 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
293 /* we have already generated a wNAF for 'scalar' */
295 signed char *tmp_wNAF
= NULL
;
298 if (num_scalar
!= 0) {
299 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
304 * use the window size for which we have precomputation
306 wsize
[num
] = pre_comp
->w
;
307 tmp_wNAF
= bn_compute_wNAF(scalar
, wsize
[num
], &tmp_len
);
311 if (tmp_len
<= max_len
) {
313 * One of the other wNAFs is at least as long as the wNAF
314 * belonging to the generator, so wNAF splitting will not buy
319 totalnum
= num
+ 1; /* don't use wNAF splitting */
320 wNAF
[num
] = tmp_wNAF
;
321 wNAF
[num
+ 1] = NULL
;
322 wNAF_len
[num
] = tmp_len
;
323 if (tmp_len
> max_len
)
326 * pre_comp->points starts with the points that we need here:
328 val_sub
[num
] = pre_comp
->points
;
331 * don't include tmp_wNAF directly into wNAF array - use wNAF
332 * splitting and include the blocks
336 EC_POINT
**tmp_points
;
338 if (tmp_len
< numblocks
* blocksize
) {
340 * possibly we can do with fewer blocks than estimated
342 numblocks
= (tmp_len
+ blocksize
- 1) / blocksize
;
343 if (numblocks
> pre_comp
->numblocks
) {
344 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
347 totalnum
= num
+ numblocks
;
350 /* split wNAF in 'numblocks' parts */
352 tmp_points
= pre_comp
->points
;
354 for (i
= num
; i
< totalnum
; i
++) {
355 if (i
< totalnum
- 1) {
356 wNAF_len
[i
] = blocksize
;
357 if (tmp_len
< blocksize
) {
358 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
361 tmp_len
-= blocksize
;
364 * last block gets whatever is left (this could be
365 * more or less than 'blocksize'!)
367 wNAF_len
[i
] = tmp_len
;
370 wNAF
[i
] = OPENSSL_malloc(wNAF_len
[i
]);
371 if (wNAF
[i
] == NULL
) {
372 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
373 OPENSSL_free(tmp_wNAF
);
376 memcpy(wNAF
[i
], pp
, wNAF_len
[i
]);
377 if (wNAF_len
[i
] > max_len
)
378 max_len
= wNAF_len
[i
];
380 if (*tmp_points
== NULL
) {
381 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
382 OPENSSL_free(tmp_wNAF
);
385 val_sub
[i
] = tmp_points
;
386 tmp_points
+= pre_points_per_block
;
389 OPENSSL_free(tmp_wNAF
);
395 * All points we precompute now go into a single array 'val'.
396 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
397 * subarray of 'pre_comp->points' if we already have precomputation.
399 val
= OPENSSL_malloc((num_val
+ 1) * sizeof val
[0]);
401 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
404 val
[num_val
] = NULL
; /* pivot element */
406 /* allocate points for precomputation */
408 for (i
= 0; i
< num
+ num_scalar
; i
++) {
410 for (j
= 0; j
< ((size_t)1 << (wsize
[i
] - 1)); j
++) {
411 *v
= EC_POINT_new(group
);
417 if (!(v
== val
+ num_val
)) {
418 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
422 if ((tmp
= EC_POINT_new(group
)) == NULL
)
426 * prepare precomputed values:
427 * val_sub[i][0] := points[i]
428 * val_sub[i][1] := 3 * points[i]
429 * val_sub[i][2] := 5 * points[i]
432 for (i
= 0; i
< num
+ num_scalar
; i
++) {
434 if (!EC_POINT_copy(val_sub
[i
][0], points
[i
]))
437 if (!EC_POINT_copy(val_sub
[i
][0], generator
))
442 if (!EC_POINT_dbl(group
, tmp
, val_sub
[i
][0], ctx
))
444 for (j
= 1; j
< ((size_t)1 << (wsize
[i
] - 1)); j
++) {
446 (group
, val_sub
[i
][j
], val_sub
[i
][j
- 1], tmp
, ctx
))
452 if (!EC_POINTs_make_affine(group
, num_val
, val
, ctx
))
455 r_is_at_infinity
= 1;
457 for (k
= max_len
- 1; k
>= 0; k
--) {
458 if (!r_is_at_infinity
) {
459 if (!EC_POINT_dbl(group
, r
, r
, ctx
))
463 for (i
= 0; i
< totalnum
; i
++) {
464 if (wNAF_len
[i
] > (size_t)k
) {
465 int digit
= wNAF
[i
][k
];
474 if (is_neg
!= r_is_inverted
) {
475 if (!r_is_at_infinity
) {
476 if (!EC_POINT_invert(group
, r
, ctx
))
479 r_is_inverted
= !r_is_inverted
;
484 if (r_is_at_infinity
) {
485 if (!EC_POINT_copy(r
, val_sub
[i
][digit
>> 1]))
487 r_is_at_infinity
= 0;
490 (group
, r
, r
, val_sub
[i
][digit
>> 1], ctx
))
498 if (r_is_at_infinity
) {
499 if (!EC_POINT_set_to_infinity(group
, r
))
503 if (!EC_POINT_invert(group
, r
, ctx
))
510 BN_CTX_free(new_ctx
);
513 OPENSSL_free(wNAF_len
);
517 for (w
= wNAF
; *w
!= NULL
; w
++)
523 for (v
= val
; *v
!= NULL
; v
++)
524 EC_POINT_clear_free(*v
);
528 OPENSSL_free(val_sub
);
533 * ec_wNAF_precompute_mult()
534 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
535 * for use with wNAF splitting as implemented in ec_wNAF_mul().
537 * 'pre_comp->points' is an array of multiples of the generator
538 * of the following form:
539 * points[0] = generator;
540 * points[1] = 3 * generator;
542 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
543 * points[2^(w-1)] = 2^blocksize * generator;
544 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
546 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
547 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
549 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
550 * points[2^(w-1)*numblocks] = NULL
552 int ec_wNAF_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
)
554 const EC_POINT
*generator
;
555 EC_POINT
*tmp_point
= NULL
, *base
= NULL
, **var
;
556 BN_CTX
*new_ctx
= NULL
;
558 size_t i
, bits
, w
, pre_points_per_block
, blocksize
, numblocks
, num
;
559 EC_POINT
**points
= NULL
;
560 EC_PRE_COMP
*pre_comp
;
563 /* if there is an old EC_PRE_COMP object, throw it away */
564 EC_pre_comp_free(group
);
565 if ((pre_comp
= ec_pre_comp_new(group
)) == NULL
)
568 generator
= EC_GROUP_get0_generator(group
);
569 if (generator
== NULL
) {
570 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, EC_R_UNDEFINED_GENERATOR
);
575 ctx
= new_ctx
= BN_CTX_new();
581 order
= BN_CTX_get(ctx
);
585 if (!EC_GROUP_get_order(group
, order
, ctx
))
587 if (BN_is_zero(order
)) {
588 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, EC_R_UNKNOWN_ORDER
);
592 bits
= BN_num_bits(order
);
594 * The following parameters mean we precompute (approximately) one point
595 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
596 * bit lengths, other parameter combinations might provide better
601 if (EC_window_bits_for_scalar_size(bits
) > w
) {
602 /* let's not make the window too small ... */
603 w
= EC_window_bits_for_scalar_size(bits
);
606 numblocks
= (bits
+ blocksize
- 1) / blocksize
; /* max. number of blocks
610 pre_points_per_block
= (size_t)1 << (w
- 1);
611 num
= pre_points_per_block
* numblocks
; /* number of points to compute
614 points
= OPENSSL_malloc(sizeof(*points
) * (num
+ 1));
615 if (points
== NULL
) {
616 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
621 var
[num
] = NULL
; /* pivot */
622 for (i
= 0; i
< num
; i
++) {
623 if ((var
[i
] = EC_POINT_new(group
)) == NULL
) {
624 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
629 if ((tmp_point
= EC_POINT_new(group
)) == NULL
630 || (base
= EC_POINT_new(group
)) == NULL
) {
631 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
635 if (!EC_POINT_copy(base
, generator
))
638 /* do the precomputation */
639 for (i
= 0; i
< numblocks
; i
++) {
642 if (!EC_POINT_dbl(group
, tmp_point
, base
, ctx
))
645 if (!EC_POINT_copy(*var
++, base
))
648 for (j
= 1; j
< pre_points_per_block
; j
++, var
++) {
650 * calculate odd multiples of the current base point
652 if (!EC_POINT_add(group
, *var
, tmp_point
, *(var
- 1), ctx
))
656 if (i
< numblocks
- 1) {
658 * get the next base (multiply current one by 2^blocksize)
662 if (blocksize
<= 2) {
663 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_INTERNAL_ERROR
);
667 if (!EC_POINT_dbl(group
, base
, tmp_point
, ctx
))
669 for (k
= 2; k
< blocksize
; k
++) {
670 if (!EC_POINT_dbl(group
, base
, base
, ctx
))
676 if (!EC_POINTs_make_affine(group
, num
, points
, ctx
))
679 pre_comp
->group
= group
;
680 pre_comp
->blocksize
= blocksize
;
681 pre_comp
->numblocks
= numblocks
;
683 pre_comp
->points
= points
;
686 SETPRECOMP(group
, ec
, pre_comp
);
693 BN_CTX_free(new_ctx
);
694 EC_ec_pre_comp_free(pre_comp
);
698 for (p
= points
; *p
!= NULL
; p
++)
700 OPENSSL_free(points
);
702 EC_POINT_free(tmp_point
);
707 int ec_wNAF_have_precompute_mult(const EC_GROUP
*group
)
709 return HAVEPRECOMP(group
, ec
);