1 /* crypto/ec/ec_mult.c */
3 * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
5 /* ====================================================================
6 * Copyright (c) 1998-2007 The OpenSSL Project. All rights reserved.
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in
17 * the documentation and/or other materials provided with the
20 * 3. All advertising materials mentioning features or use of this
21 * software must display the following acknowledgment:
22 * "This product includes software developed by the OpenSSL Project
23 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
25 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
26 * endorse or promote products derived from this software without
27 * prior written permission. For written permission, please contact
28 * openssl-core@openssl.org.
30 * 5. Products derived from this software may not be called "OpenSSL"
31 * nor may "OpenSSL" appear in their names without prior written
32 * permission of the OpenSSL Project.
34 * 6. Redistributions of any form whatsoever must retain the following
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
44 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
45 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
46 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
48 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
49 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
50 * OF THE POSSIBILITY OF SUCH DAMAGE.
51 * ====================================================================
53 * This product includes cryptographic software written by Eric Young
54 * (eay@cryptsoft.com). This product includes software written by Tim
55 * Hudson (tjh@cryptsoft.com).
58 /* ====================================================================
59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
60 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
61 * and contributed to the OpenSSL project.
65 #include <openssl/err.h>
67 #include "internal/bn_int.h"
71 * This file implements the wNAF-based interleaving multi-exponentation method
72 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
73 * for multiplication with precomputation, we use wNAF splitting
74 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
77 /* structure for precomputed multiples of the generator */
78 struct ec_pre_comp_st
{
79 const EC_GROUP
*group
; /* parent EC_GROUP object */
80 size_t blocksize
; /* block size for wNAF splitting */
81 size_t numblocks
; /* max. number of blocks for which we have
83 size_t w
; /* window size */
84 EC_POINT
**points
; /* array with pre-calculated multiples of
85 * generator: 'num' pointers to EC_POINT
86 * objects followed by a NULL */
87 size_t num
; /* numblocks * 2^(w-1) */
91 static EC_PRE_COMP
*ec_pre_comp_new(const EC_GROUP
*group
)
93 EC_PRE_COMP
*ret
= NULL
;
98 ret
= OPENSSL_zalloc(sizeof(*ret
));
100 ECerr(EC_F_EC_PRE_COMP_NEW
, ERR_R_MALLOC_FAILURE
);
104 ret
->blocksize
= 8; /* default */
105 ret
->w
= 4; /* default */
110 EC_PRE_COMP
*EC_ec_pre_comp_dup(EC_PRE_COMP
*pre
)
113 CRYPTO_add(&pre
->references
, 1, CRYPTO_LOCK_EC_PRE_COMP
);
117 void EC_ec_pre_comp_free(EC_PRE_COMP
*pre
)
120 || CRYPTO_add(&pre
->references
, -1, CRYPTO_LOCK_EC_PRE_COMP
) > 0)
123 if (pre
->points
!= NULL
) {
126 for (pts
= pre
->points
; *pts
!= NULL
; pts
++)
128 OPENSSL_free(pre
->points
);
134 * TODO: table should be optimised for the wNAF-based implementation,
135 * sometimes smaller windows will give better performance (thus the
136 * boundaries should be increased)
138 #define EC_window_bits_for_scalar_size(b) \
149 * \sum scalars[i]*points[i],
152 * in the addition if scalar != NULL
154 int ec_wNAF_mul(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
155 size_t num
, const EC_POINT
*points
[], const BIGNUM
*scalars
[],
158 BN_CTX
*new_ctx
= NULL
;
159 const EC_POINT
*generator
= NULL
;
160 EC_POINT
*tmp
= NULL
;
162 size_t blocksize
= 0, numblocks
= 0; /* for wNAF splitting */
163 size_t pre_points_per_block
= 0;
166 int r_is_inverted
= 0;
167 int r_is_at_infinity
= 1;
168 size_t *wsize
= NULL
; /* individual window sizes */
169 signed char **wNAF
= NULL
; /* individual wNAFs */
170 size_t *wNAF_len
= NULL
;
173 EC_POINT
**val
= NULL
; /* precomputation */
175 EC_POINT
***val_sub
= NULL
; /* pointers to sub-arrays of 'val' or
176 * 'pre_comp->points' */
177 const EC_PRE_COMP
*pre_comp
= NULL
;
178 int num_scalar
= 0; /* flag: will be set to 1 if 'scalar' must be
179 * treated like other scalars, i.e.
180 * precomputation is not available */
183 if (group
->meth
!= r
->meth
) {
184 ECerr(EC_F_EC_WNAF_MUL
, EC_R_INCOMPATIBLE_OBJECTS
);
188 if ((scalar
== NULL
) && (num
== 0)) {
189 return EC_POINT_set_to_infinity(group
, r
);
192 for (i
= 0; i
< num
; i
++) {
193 if (group
->meth
!= points
[i
]->meth
) {
194 ECerr(EC_F_EC_WNAF_MUL
, EC_R_INCOMPATIBLE_OBJECTS
);
200 ctx
= new_ctx
= BN_CTX_new();
205 if (scalar
!= NULL
) {
206 generator
= EC_GROUP_get0_generator(group
);
207 if (generator
== NULL
) {
208 ECerr(EC_F_EC_WNAF_MUL
, EC_R_UNDEFINED_GENERATOR
);
212 /* look if we can use precomputed multiples of generator */
214 pre_comp
= group
->pre_comp
.ec
;
215 if (pre_comp
&& pre_comp
->numblocks
216 && (EC_POINT_cmp(group
, generator
, pre_comp
->points
[0], ctx
) ==
218 blocksize
= pre_comp
->blocksize
;
221 * determine maximum number of blocks that wNAF splitting may
222 * yield (NB: maximum wNAF length is bit length plus one)
224 numblocks
= (BN_num_bits(scalar
) / blocksize
) + 1;
227 * we cannot use more blocks than we have precomputation for
229 if (numblocks
> pre_comp
->numblocks
)
230 numblocks
= pre_comp
->numblocks
;
232 pre_points_per_block
= (size_t)1 << (pre_comp
->w
- 1);
234 /* check that pre_comp looks sane */
235 if (pre_comp
->num
!= (pre_comp
->numblocks
* pre_points_per_block
)) {
236 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
240 /* can't use precomputation */
243 num_scalar
= 1; /* treat 'scalar' like 'num'-th element of
248 totalnum
= num
+ numblocks
;
250 wsize
= OPENSSL_malloc(totalnum
* sizeof wsize
[0]);
251 wNAF_len
= OPENSSL_malloc(totalnum
* sizeof wNAF_len
[0]);
252 wNAF
= OPENSSL_malloc((totalnum
+ 1) * sizeof wNAF
[0]); /* includes space
254 val_sub
= OPENSSL_malloc(totalnum
* sizeof val_sub
[0]);
256 /* Ensure wNAF is initialised in case we end up going to err */
258 wNAF
[0] = NULL
; /* preliminary pivot */
260 if (wsize
== NULL
|| wNAF_len
== NULL
|| wNAF
== NULL
|| val_sub
== NULL
) {
261 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
266 * num_val will be the total number of temporarily precomputed points
270 for (i
= 0; i
< num
+ num_scalar
; i
++) {
273 bits
= i
< num
? BN_num_bits(scalars
[i
]) : BN_num_bits(scalar
);
274 wsize
[i
] = EC_window_bits_for_scalar_size(bits
);
275 num_val
+= (size_t)1 << (wsize
[i
] - 1);
276 wNAF
[i
+ 1] = NULL
; /* make sure we always have a pivot */
278 bn_compute_wNAF((i
< num
? scalars
[i
] : scalar
), wsize
[i
],
282 if (wNAF_len
[i
] > max_len
)
283 max_len
= wNAF_len
[i
];
287 /* we go here iff scalar != NULL */
289 if (pre_comp
== NULL
) {
290 if (num_scalar
!= 1) {
291 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
294 /* we have already generated a wNAF for 'scalar' */
296 signed char *tmp_wNAF
= NULL
;
299 if (num_scalar
!= 0) {
300 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
305 * use the window size for which we have precomputation
307 wsize
[num
] = pre_comp
->w
;
308 tmp_wNAF
= bn_compute_wNAF(scalar
, wsize
[num
], &tmp_len
);
312 if (tmp_len
<= max_len
) {
314 * One of the other wNAFs is at least as long as the wNAF
315 * belonging to the generator, so wNAF splitting will not buy
320 totalnum
= num
+ 1; /* don't use wNAF splitting */
321 wNAF
[num
] = tmp_wNAF
;
322 wNAF
[num
+ 1] = NULL
;
323 wNAF_len
[num
] = tmp_len
;
324 if (tmp_len
> max_len
)
327 * pre_comp->points starts with the points that we need here:
329 val_sub
[num
] = pre_comp
->points
;
332 * don't include tmp_wNAF directly into wNAF array - use wNAF
333 * splitting and include the blocks
337 EC_POINT
**tmp_points
;
339 if (tmp_len
< numblocks
* blocksize
) {
341 * possibly we can do with fewer blocks than estimated
343 numblocks
= (tmp_len
+ blocksize
- 1) / blocksize
;
344 if (numblocks
> pre_comp
->numblocks
) {
345 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
348 totalnum
= num
+ numblocks
;
351 /* split wNAF in 'numblocks' parts */
353 tmp_points
= pre_comp
->points
;
355 for (i
= num
; i
< totalnum
; i
++) {
356 if (i
< totalnum
- 1) {
357 wNAF_len
[i
] = blocksize
;
358 if (tmp_len
< blocksize
) {
359 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
362 tmp_len
-= blocksize
;
365 * last block gets whatever is left (this could be
366 * more or less than 'blocksize'!)
368 wNAF_len
[i
] = tmp_len
;
371 wNAF
[i
] = OPENSSL_malloc(wNAF_len
[i
]);
372 if (wNAF
[i
] == NULL
) {
373 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
374 OPENSSL_free(tmp_wNAF
);
377 memcpy(wNAF
[i
], pp
, wNAF_len
[i
]);
378 if (wNAF_len
[i
] > max_len
)
379 max_len
= wNAF_len
[i
];
381 if (*tmp_points
== NULL
) {
382 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
383 OPENSSL_free(tmp_wNAF
);
386 val_sub
[i
] = tmp_points
;
387 tmp_points
+= pre_points_per_block
;
390 OPENSSL_free(tmp_wNAF
);
396 * All points we precompute now go into a single array 'val'.
397 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
398 * subarray of 'pre_comp->points' if we already have precomputation.
400 val
= OPENSSL_malloc((num_val
+ 1) * sizeof val
[0]);
402 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_MALLOC_FAILURE
);
405 val
[num_val
] = NULL
; /* pivot element */
407 /* allocate points for precomputation */
409 for (i
= 0; i
< num
+ num_scalar
; i
++) {
411 for (j
= 0; j
< ((size_t)1 << (wsize
[i
] - 1)); j
++) {
412 *v
= EC_POINT_new(group
);
418 if (!(v
== val
+ num_val
)) {
419 ECerr(EC_F_EC_WNAF_MUL
, ERR_R_INTERNAL_ERROR
);
423 if ((tmp
= EC_POINT_new(group
)) == NULL
)
427 * prepare precomputed values:
428 * val_sub[i][0] := points[i]
429 * val_sub[i][1] := 3 * points[i]
430 * val_sub[i][2] := 5 * points[i]
433 for (i
= 0; i
< num
+ num_scalar
; i
++) {
435 if (!EC_POINT_copy(val_sub
[i
][0], points
[i
]))
438 if (!EC_POINT_copy(val_sub
[i
][0], generator
))
443 if (!EC_POINT_dbl(group
, tmp
, val_sub
[i
][0], ctx
))
445 for (j
= 1; j
< ((size_t)1 << (wsize
[i
] - 1)); j
++) {
447 (group
, val_sub
[i
][j
], val_sub
[i
][j
- 1], tmp
, ctx
))
453 if (!EC_POINTs_make_affine(group
, num_val
, val
, ctx
))
456 r_is_at_infinity
= 1;
458 for (k
= max_len
- 1; k
>= 0; k
--) {
459 if (!r_is_at_infinity
) {
460 if (!EC_POINT_dbl(group
, r
, r
, ctx
))
464 for (i
= 0; i
< totalnum
; i
++) {
465 if (wNAF_len
[i
] > (size_t)k
) {
466 int digit
= wNAF
[i
][k
];
475 if (is_neg
!= r_is_inverted
) {
476 if (!r_is_at_infinity
) {
477 if (!EC_POINT_invert(group
, r
, ctx
))
480 r_is_inverted
= !r_is_inverted
;
485 if (r_is_at_infinity
) {
486 if (!EC_POINT_copy(r
, val_sub
[i
][digit
>> 1]))
488 r_is_at_infinity
= 0;
491 (group
, r
, r
, val_sub
[i
][digit
>> 1], ctx
))
499 if (r_is_at_infinity
) {
500 if (!EC_POINT_set_to_infinity(group
, r
))
504 if (!EC_POINT_invert(group
, r
, ctx
))
511 BN_CTX_free(new_ctx
);
514 OPENSSL_free(wNAF_len
);
518 for (w
= wNAF
; *w
!= NULL
; w
++)
524 for (v
= val
; *v
!= NULL
; v
++)
525 EC_POINT_clear_free(*v
);
529 OPENSSL_free(val_sub
);
534 * ec_wNAF_precompute_mult()
535 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
536 * for use with wNAF splitting as implemented in ec_wNAF_mul().
538 * 'pre_comp->points' is an array of multiples of the generator
539 * of the following form:
540 * points[0] = generator;
541 * points[1] = 3 * generator;
543 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
544 * points[2^(w-1)] = 2^blocksize * generator;
545 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
547 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
548 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
550 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
551 * points[2^(w-1)*numblocks] = NULL
553 int ec_wNAF_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
)
555 const EC_POINT
*generator
;
556 EC_POINT
*tmp_point
= NULL
, *base
= NULL
, **var
;
557 BN_CTX
*new_ctx
= NULL
;
559 size_t i
, bits
, w
, pre_points_per_block
, blocksize
, numblocks
, num
;
560 EC_POINT
**points
= NULL
;
561 EC_PRE_COMP
*pre_comp
;
564 /* if there is an old EC_PRE_COMP object, throw it away */
565 EC_pre_comp_free(group
);
566 if ((pre_comp
= ec_pre_comp_new(group
)) == NULL
)
569 generator
= EC_GROUP_get0_generator(group
);
570 if (generator
== NULL
) {
571 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, EC_R_UNDEFINED_GENERATOR
);
576 ctx
= new_ctx
= BN_CTX_new();
582 order
= BN_CTX_get(ctx
);
586 if (!EC_GROUP_get_order(group
, order
, ctx
))
588 if (BN_is_zero(order
)) {
589 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, EC_R_UNKNOWN_ORDER
);
593 bits
= BN_num_bits(order
);
595 * The following parameters mean we precompute (approximately) one point
596 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
597 * bit lengths, other parameter combinations might provide better
602 if (EC_window_bits_for_scalar_size(bits
) > w
) {
603 /* let's not make the window too small ... */
604 w
= EC_window_bits_for_scalar_size(bits
);
607 numblocks
= (bits
+ blocksize
- 1) / blocksize
; /* max. number of blocks
611 pre_points_per_block
= (size_t)1 << (w
- 1);
612 num
= pre_points_per_block
* numblocks
; /* number of points to compute
615 points
= OPENSSL_malloc(sizeof(*points
) * (num
+ 1));
616 if (points
== NULL
) {
617 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
622 var
[num
] = NULL
; /* pivot */
623 for (i
= 0; i
< num
; i
++) {
624 if ((var
[i
] = EC_POINT_new(group
)) == NULL
) {
625 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
630 if ((tmp_point
= EC_POINT_new(group
)) == NULL
631 || (base
= EC_POINT_new(group
)) == NULL
) {
632 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_MALLOC_FAILURE
);
636 if (!EC_POINT_copy(base
, generator
))
639 /* do the precomputation */
640 for (i
= 0; i
< numblocks
; i
++) {
643 if (!EC_POINT_dbl(group
, tmp_point
, base
, ctx
))
646 if (!EC_POINT_copy(*var
++, base
))
649 for (j
= 1; j
< pre_points_per_block
; j
++, var
++) {
651 * calculate odd multiples of the current base point
653 if (!EC_POINT_add(group
, *var
, tmp_point
, *(var
- 1), ctx
))
657 if (i
< numblocks
- 1) {
659 * get the next base (multiply current one by 2^blocksize)
663 if (blocksize
<= 2) {
664 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT
, ERR_R_INTERNAL_ERROR
);
668 if (!EC_POINT_dbl(group
, base
, tmp_point
, ctx
))
670 for (k
= 2; k
< blocksize
; k
++) {
671 if (!EC_POINT_dbl(group
, base
, base
, ctx
))
677 if (!EC_POINTs_make_affine(group
, num
, points
, ctx
))
680 pre_comp
->group
= group
;
681 pre_comp
->blocksize
= blocksize
;
682 pre_comp
->numblocks
= numblocks
;
684 pre_comp
->points
= points
;
687 SETPRECOMP(group
, ec
, pre_comp
);
694 BN_CTX_free(new_ctx
);
695 EC_ec_pre_comp_free(pre_comp
);
699 for (p
= points
; *p
!= NULL
; p
++)
701 OPENSSL_free(points
);
703 EC_POINT_free(tmp_point
);
708 int ec_wNAF_have_precompute_mult(const EC_GROUP
*group
)
710 return HAVEPRECOMP(group
, ec
);