1 /* crypto/ec/ec_mult.c */
2 /* ====================================================================
3 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in
14 * the documentation and/or other materials provided with the
17 * 3. All advertising materials mentioning features or use of this
18 * software must display the following acknowledgment:
19 * "This product includes software developed by the OpenSSL Project
20 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
22 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
23 * endorse or promote products derived from this software without
24 * prior written permission. For written permission, please contact
25 * openssl-core@openssl.org.
27 * 5. Products derived from this software may not be called "OpenSSL"
28 * nor may "OpenSSL" appear in their names without prior written
29 * permission of the OpenSSL Project.
31 * 6. Redistributions of any form whatsoever must retain the following
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
36 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
37 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
38 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
39 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
40 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
41 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
42 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
43 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
44 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
45 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
46 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
47 * OF THE POSSIBILITY OF SUCH DAMAGE.
48 * ====================================================================
50 * This product includes cryptographic software written by Eric Young
51 * (eay@cryptsoft.com). This product includes software written by Tim
52 * Hudson (tjh@cryptsoft.com).
55 /* ====================================================================
56 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
57 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
58 * and contributed to the OpenSSL project.
61 #include <openssl/err.h>
66 /* TODO: optional precomputation of multiples of the generator */
71 * wNAF-based interleaving multi-exponentation method
72 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>)
76 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
77 * This is an array r[] of values that are either zero or odd with an
78 * absolute value less than 2^w satisfying
79 * scalar = \sum_j r[j]*2^j
80 * where at most one of any w+1 consecutive digits is non-zero
81 * with the exception that the most significant digit may be only
82 * w-1 zeros away from that next non-zero digit.
84 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
88 signed char *r = NULL;
90 int bit, next_bit, mask;
93 if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
95 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
98 bit = 1 << w; /* at most 128 */
99 next_bit = bit << 1; /* at most 256 */
100 mask = next_bit - 1; /* at most 255 */
107 len = BN_num_bits(scalar);
108 r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation */
109 if (r == NULL) goto err;
111 if (scalar->d == NULL || scalar->top == 0)
113 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
116 window_val = scalar->d[0] & mask;
118 while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
122 /* 0 <= window_val <= 2^(w+1) */
126 /* 0 < window_val < 2^(w+1) */
128 if (window_val & bit)
130 digit = window_val - next_bit; /* -2^w < digit < 0 */
132 #if 1 /* modified wNAF */
133 if (j + w + 1 >= len)
135 /* special case for generating modified wNAFs:
136 * no new bits will be added into window_val,
137 * so using a positive digit here will decrease
138 * the total length of the representation */
140 digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
146 digit = window_val; /* 0 < digit < 2^w */
149 if (digit <= -bit || digit >= bit || !(digit & 1))
151 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
157 /* now window_val is 0 or 2^(w+1) in standard wNAF generation;
158 * for modified window NAFs, it may also be 2^w
160 if (window_val != 0 && window_val != next_bit && window_val != bit)
162 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
167 r[j++] = sign * digit;
170 window_val += bit * BN_is_bit_set(scalar, j + w);
172 if (window_val > next_bit)
174 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
181 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
199 /* TODO: table should be optimised for the wNAF-based implementation,
200 * sometimes smaller windows will give better performance
201 * (thus the boundaries should be increased)
203 #define EC_window_bits_for_scalar_size(b) \
212 * \sum scalars[i]*points[i],
215 * in the addition if scalar != NULL
217 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
218 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
220 BN_CTX *new_ctx = NULL;
221 EC_POINT *generator = NULL;
222 EC_POINT *tmp = NULL;
226 int r_is_inverted = 0;
227 int r_is_at_infinity = 1;
228 size_t *wsize = NULL; /* individual window sizes */
229 signed char **wNAF = NULL; /* individual wNAFs */
230 size_t *wNAF_len = NULL;
233 EC_POINT **val = NULL; /* precomputation */
235 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */
240 generator = EC_GROUP_get0_generator(group);
241 if (generator == NULL)
243 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
248 for (i = 0; i < num; i++)
250 if (group->meth != points[i]->meth)
252 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
257 totalnum = num + (scalar != NULL);
259 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
260 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
261 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]);
264 wNAF[0] = NULL; /* preliminary pivot */
266 if (wsize == NULL || wNAF_len == NULL || wNAF == NULL) goto err;
268 /* num_val := total number of points to precompute */
270 for (i = 0; i < totalnum; i++)
274 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
275 wsize[i] = EC_window_bits_for_scalar_size(bits);
276 num_val += 1u << (wsize[i] - 1);
279 /* all precomputed points go into a single array 'val',
280 * 'val_sub[i]' is a pointer to the subarray for the i-th point */
281 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
282 if (val == NULL) goto err;
283 val[num_val] = NULL; /* pivot element */
285 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
286 if (val_sub == NULL) goto err;
288 /* allocate points for precomputation */
290 for (i = 0; i < totalnum; i++)
293 for (j = 0; j < (1u << (wsize[i] - 1)); j++)
295 *v = EC_POINT_new(group);
296 if (*v == NULL) goto err;
300 if (!(v == val + num_val))
302 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
308 ctx = new_ctx = BN_CTX_new();
313 tmp = EC_POINT_new(group);
314 if (tmp == NULL) goto err;
316 /* prepare precomputed values:
317 * val_sub[i][0] := points[i]
318 * val_sub[i][1] := 3 * points[i]
319 * val_sub[i][2] := 5 * points[i]
322 for (i = 0; i < totalnum; i++)
326 if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
330 if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
335 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
336 for (j = 1; j < (1u << (wsize[i] - 1)); j++)
338 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
342 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
343 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
344 if (wNAF[i] == NULL) goto err;
345 if (wNAF_len[i] > max_len)
346 max_len = wNAF_len[i];
349 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
350 if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err;
353 r_is_at_infinity = 1;
355 for (k = max_len - 1; k >= 0; k--)
357 if (!r_is_at_infinity)
359 if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
362 for (i = 0; i < totalnum; i++)
364 if (wNAF_len[i] > (size_t)k)
366 int digit = wNAF[i][k];
376 if (is_neg != r_is_inverted)
378 if (!r_is_at_infinity)
380 if (!EC_POINT_invert(group, r, ctx)) goto err;
382 r_is_inverted = !r_is_inverted;
387 if (r_is_at_infinity)
389 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
390 r_is_at_infinity = 0;
394 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
401 if (r_is_at_infinity)
403 if (!EC_POINT_set_to_infinity(group, r)) goto err;
408 if (!EC_POINT_invert(group, r, ctx)) goto err;
415 BN_CTX_free(new_ctx);
420 if (wNAF_len != NULL)
421 OPENSSL_free(wNAF_len);
426 for (w = wNAF; *w != NULL; w++)
433 for (v = val; *v != NULL; v++)
434 EC_POINT_clear_free(*v);
440 OPENSSL_free(val_sub);
446 /* Generic multiplication method.
447 * If group->meth does not provide a multiplication method, default to ec_wNAF_mul;
448 * otherwise use the group->meth's multiplication.
450 int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
451 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
453 if (group->meth->mul == 0)
454 return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
456 return group->meth->mul(group, r, scalar, num, points, scalars, ctx);
460 int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx)
462 const EC_POINT *points[1];
463 const BIGNUM *scalars[1];
466 scalars[0] = p_scalar;
468 return EC_POINTs_mul(group, r, g_scalar, (point != NULL && p_scalar != NULL), points, scalars, ctx);
472 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
474 const EC_POINT *generator;
475 BN_CTX *new_ctx = NULL;
479 generator = EC_GROUP_get0_generator(group);
480 if (generator == NULL)
482 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
488 ctx = new_ctx = BN_CTX_new();
494 order = BN_CTX_get(ctx);
495 if (order == NULL) goto err;
497 if (!EC_GROUP_get_order(group, order, ctx)) return 0;
498 if (BN_is_zero(order))
500 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
511 BN_CTX_free(new_ctx);
516 /* Generic multiplicaiton precomputation method.
517 * If group->meth does not provide a multiplication method, default to ec_wNAF_mul and do its
518 * precomputation; otherwise use the group->meth's precomputation if it exists.
520 int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
522 if (group->meth->mul == 0)
523 return ec_wNAF_precompute_mult(group, ctx);
524 else if (group->meth->precompute_mult != 0)
525 return group->meth->precompute_mult(group, ctx);