1 /* $OpenBSD: bn_mul.c,v 1.39 2023/07/08 12:21:58 beck Exp $ */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
8 *
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 *
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
52 *
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58
59 #include <assert.h>
60 #include <stdio.h>
61 #include <string.h>
62
63 #include <openssl/opensslconf.h>
64
65 #include "bn_arch.h"
66 #include "bn_internal.h"
67 #include "bn_local.h"
68
69 /*
70 * bn_mul_comba4() computes r[] = a[] * b[] using Comba multiplication
71 * (https://everything2.com/title/Comba+multiplication), where a and b are both
72 * four word arrays, producing an eight word array result.
73 */
74 #ifndef HAVE_BN_MUL_COMBA4
75 void
bn_mul_comba4(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)76 bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
77 {
78 BN_ULONG c0, c1, c2;
79
80 bn_mulw_addtw(a[0], b[0], 0, 0, 0, &c2, &c1, &r[0]);
81
82 bn_mulw_addtw(a[0], b[1], 0, c2, c1, &c2, &c1, &c0);
83 bn_mulw_addtw(a[1], b[0], c2, c1, c0, &c2, &c1, &r[1]);
84
85 bn_mulw_addtw(a[2], b[0], 0, c2, c1, &c2, &c1, &c0);
86 bn_mulw_addtw(a[1], b[1], c2, c1, c0, &c2, &c1, &c0);
87 bn_mulw_addtw(a[0], b[2], c2, c1, c0, &c2, &c1, &r[2]);
88
89 bn_mulw_addtw(a[0], b[3], 0, c2, c1, &c2, &c1, &c0);
90 bn_mulw_addtw(a[1], b[2], c2, c1, c0, &c2, &c1, &c0);
91 bn_mulw_addtw(a[2], b[1], c2, c1, c0, &c2, &c1, &c0);
92 bn_mulw_addtw(a[3], b[0], c2, c1, c0, &c2, &c1, &r[3]);
93
94 bn_mulw_addtw(a[3], b[1], 0, c2, c1, &c2, &c1, &c0);
95 bn_mulw_addtw(a[2], b[2], c2, c1, c0, &c2, &c1, &c0);
96 bn_mulw_addtw(a[1], b[3], c2, c1, c0, &c2, &c1, &r[4]);
97
98 bn_mulw_addtw(a[2], b[3], 0, c2, c1, &c2, &c1, &c0);
99 bn_mulw_addtw(a[3], b[2], c2, c1, c0, &c2, &c1, &r[5]);
100
101 bn_mulw_addtw(a[3], b[3], 0, c2, c1, &c2, &r[7], &r[6]);
102 }
103 #endif
104
105 /*
106 * bn_mul_comba8() computes r[] = a[] * b[] using Comba multiplication
107 * (https://everything2.com/title/Comba+multiplication), where a and b are both
108 * eight word arrays, producing a 16 word array result.
109 */
110 #ifndef HAVE_BN_MUL_COMBA8
111 void
bn_mul_comba8(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)112 bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
113 {
114 BN_ULONG c0, c1, c2;
115
116 bn_mulw_addtw(a[0], b[0], 0, 0, 0, &c2, &c1, &r[0]);
117
118 bn_mulw_addtw(a[0], b[1], 0, c2, c1, &c2, &c1, &c0);
119 bn_mulw_addtw(a[1], b[0], c2, c1, c0, &c2, &c1, &r[1]);
120
121 bn_mulw_addtw(a[2], b[0], 0, c2, c1, &c2, &c1, &c0);
122 bn_mulw_addtw(a[1], b[1], c2, c1, c0, &c2, &c1, &c0);
123 bn_mulw_addtw(a[0], b[2], c2, c1, c0, &c2, &c1, &r[2]);
124
125 bn_mulw_addtw(a[0], b[3], 0, c2, c1, &c2, &c1, &c0);
126 bn_mulw_addtw(a[1], b[2], c2, c1, c0, &c2, &c1, &c0);
127 bn_mulw_addtw(a[2], b[1], c2, c1, c0, &c2, &c1, &c0);
128 bn_mulw_addtw(a[3], b[0], c2, c1, c0, &c2, &c1, &r[3]);
129
130 bn_mulw_addtw(a[4], b[0], 0, c2, c1, &c2, &c1, &c0);
131 bn_mulw_addtw(a[3], b[1], c2, c1, c0, &c2, &c1, &c0);
132 bn_mulw_addtw(a[2], b[2], c2, c1, c0, &c2, &c1, &c0);
133 bn_mulw_addtw(a[1], b[3], c2, c1, c0, &c2, &c1, &c0);
134 bn_mulw_addtw(a[0], b[4], c2, c1, c0, &c2, &c1, &r[4]);
135
136 bn_mulw_addtw(a[0], b[5], 0, c2, c1, &c2, &c1, &c0);
137 bn_mulw_addtw(a[1], b[4], c2, c1, c0, &c2, &c1, &c0);
138 bn_mulw_addtw(a[2], b[3], c2, c1, c0, &c2, &c1, &c0);
139 bn_mulw_addtw(a[3], b[2], c2, c1, c0, &c2, &c1, &c0);
140 bn_mulw_addtw(a[4], b[1], c2, c1, c0, &c2, &c1, &c0);
141 bn_mulw_addtw(a[5], b[0], c2, c1, c0, &c2, &c1, &r[5]);
142
143 bn_mulw_addtw(a[6], b[0], 0, c2, c1, &c2, &c1, &c0);
144 bn_mulw_addtw(a[5], b[1], c2, c1, c0, &c2, &c1, &c0);
145 bn_mulw_addtw(a[4], b[2], c2, c1, c0, &c2, &c1, &c0);
146 bn_mulw_addtw(a[3], b[3], c2, c1, c0, &c2, &c1, &c0);
147 bn_mulw_addtw(a[2], b[4], c2, c1, c0, &c2, &c1, &c0);
148 bn_mulw_addtw(a[1], b[5], c2, c1, c0, &c2, &c1, &c0);
149 bn_mulw_addtw(a[0], b[6], c2, c1, c0, &c2, &c1, &r[6]);
150
151 bn_mulw_addtw(a[0], b[7], 0, c2, c1, &c2, &c1, &c0);
152 bn_mulw_addtw(a[1], b[6], c2, c1, c0, &c2, &c1, &c0);
153 bn_mulw_addtw(a[2], b[5], c2, c1, c0, &c2, &c1, &c0);
154 bn_mulw_addtw(a[3], b[4], c2, c1, c0, &c2, &c1, &c0);
155 bn_mulw_addtw(a[4], b[3], c2, c1, c0, &c2, &c1, &c0);
156 bn_mulw_addtw(a[5], b[2], c2, c1, c0, &c2, &c1, &c0);
157 bn_mulw_addtw(a[6], b[1], c2, c1, c0, &c2, &c1, &c0);
158 bn_mulw_addtw(a[7], b[0], c2, c1, c0, &c2, &c1, &r[7]);
159
160 bn_mulw_addtw(a[7], b[1], 0, c2, c1, &c2, &c1, &c0);
161 bn_mulw_addtw(a[6], b[2], c2, c1, c0, &c2, &c1, &c0);
162 bn_mulw_addtw(a[5], b[3], c2, c1, c0, &c2, &c1, &c0);
163 bn_mulw_addtw(a[4], b[4], c2, c1, c0, &c2, &c1, &c0);
164 bn_mulw_addtw(a[3], b[5], c2, c1, c0, &c2, &c1, &c0);
165 bn_mulw_addtw(a[2], b[6], c2, c1, c0, &c2, &c1, &c0);
166 bn_mulw_addtw(a[1], b[7], c2, c1, c0, &c2, &c1, &r[8]);
167
168 bn_mulw_addtw(a[2], b[7], 0, c2, c1, &c2, &c1, &c0);
169 bn_mulw_addtw(a[3], b[6], c2, c1, c0, &c2, &c1, &c0);
170 bn_mulw_addtw(a[4], b[5], c2, c1, c0, &c2, &c1, &c0);
171 bn_mulw_addtw(a[5], b[4], c2, c1, c0, &c2, &c1, &c0);
172 bn_mulw_addtw(a[6], b[3], c2, c1, c0, &c2, &c1, &c0);
173 bn_mulw_addtw(a[7], b[2], c2, c1, c0, &c2, &c1, &r[9]);
174
175 bn_mulw_addtw(a[7], b[3], 0, c2, c1, &c2, &c1, &c0);
176 bn_mulw_addtw(a[6], b[4], c2, c1, c0, &c2, &c1, &c0);
177 bn_mulw_addtw(a[5], b[5], c2, c1, c0, &c2, &c1, &c0);
178 bn_mulw_addtw(a[4], b[6], c2, c1, c0, &c2, &c1, &c0);
179 bn_mulw_addtw(a[3], b[7], c2, c1, c0, &c2, &c1, &r[10]);
180
181 bn_mulw_addtw(a[4], b[7], 0, c2, c1, &c2, &c1, &c0);
182 bn_mulw_addtw(a[5], b[6], c2, c1, c0, &c2, &c1, &c0);
183 bn_mulw_addtw(a[6], b[5], c2, c1, c0, &c2, &c1, &c0);
184 bn_mulw_addtw(a[7], b[4], c2, c1, c0, &c2, &c1, &r[11]);
185
186 bn_mulw_addtw(a[7], b[5], 0, c2, c1, &c2, &c1, &c0);
187 bn_mulw_addtw(a[6], b[6], c2, c1, c0, &c2, &c1, &c0);
188 bn_mulw_addtw(a[5], b[7], c2, c1, c0, &c2, &c1, &r[12]);
189
190 bn_mulw_addtw(a[6], b[7], 0, c2, c1, &c2, &c1, &c0);
191 bn_mulw_addtw(a[7], b[6], c2, c1, c0, &c2, &c1, &r[13]);
192
193 bn_mulw_addtw(a[7], b[7], 0, c2, c1, &c2, &r[15], &r[14]);
194 }
195 #endif
196
197 /*
198 * bn_mul_words() computes (carry:r[i]) = a[i] * w + carry, where a is an array
199 * of words and w is a single word. This should really be called bn_mulw_words()
200 * since only one input is an array. This is used as a step in the multiplication
201 * of word arrays.
202 */
203 #ifndef HAVE_BN_MUL_WORDS
204 BN_ULONG
bn_mul_words(BN_ULONG * r,const BN_ULONG * a,int num,BN_ULONG w)205 bn_mul_words(BN_ULONG *r, const BN_ULONG *a, int num, BN_ULONG w)
206 {
207 BN_ULONG carry = 0;
208
209 assert(num >= 0);
210 if (num <= 0)
211 return 0;
212
213 while (num & ~3) {
214 bn_qwmulw_addw(a[3], a[2], a[1], a[0], w, carry, &carry,
215 &r[3], &r[2], &r[1], &r[0]);
216 a += 4;
217 r += 4;
218 num -= 4;
219 }
220 while (num) {
221 bn_mulw_addw(a[0], w, carry, &carry, &r[0]);
222 a++;
223 r++;
224 num--;
225 }
226 return carry;
227 }
228 #endif
229
230 /*
231 * bn_mul_add_words() computes (carry:r[i]) = a[i] * w + r[i] + carry, where
232 * a is an array of words and w is a single word. This should really be called
233 * bn_mulw_add_words() since only one input is an array. This is used as a step
234 * in the multiplication of word arrays.
235 */
236 #ifndef HAVE_BN_MUL_ADD_WORDS
237 BN_ULONG
bn_mul_add_words(BN_ULONG * r,const BN_ULONG * a,int num,BN_ULONG w)238 bn_mul_add_words(BN_ULONG *r, const BN_ULONG *a, int num, BN_ULONG w)
239 {
240 BN_ULONG carry = 0;
241
242 assert(num >= 0);
243 if (num <= 0)
244 return 0;
245
246 while (num & ~3) {
247 bn_qwmulw_addqw_addw(a[3], a[2], a[1], a[0], w,
248 r[3], r[2], r[1], r[0], carry, &carry,
249 &r[3], &r[2], &r[1], &r[0]);
250 a += 4;
251 r += 4;
252 num -= 4;
253 }
254 while (num) {
255 bn_mulw_addw_addw(a[0], w, r[0], carry, &carry, &r[0]);
256 a++;
257 r++;
258 num--;
259 }
260
261 return carry;
262 }
263 #endif
264
265 void
bn_mul_normal(BN_ULONG * r,BN_ULONG * a,int na,BN_ULONG * b,int nb)266 bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
267 {
268 BN_ULONG *rr;
269
270
271 if (na < nb) {
272 int itmp;
273 BN_ULONG *ltmp;
274
275 itmp = na;
276 na = nb;
277 nb = itmp;
278 ltmp = a;
279 a = b;
280 b = ltmp;
281
282 }
283 rr = &(r[na]);
284 if (nb <= 0) {
285 (void)bn_mul_words(r, a, na, 0);
286 return;
287 } else
288 rr[0] = bn_mul_words(r, a, na, b[0]);
289
290 for (;;) {
291 if (--nb <= 0)
292 return;
293 rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
294 if (--nb <= 0)
295 return;
296 rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
297 if (--nb <= 0)
298 return;
299 rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
300 if (--nb <= 0)
301 return;
302 rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
303 rr += 4;
304 r += 4;
305 b += 4;
306 }
307 }
308
309
310 #ifndef HAVE_BN_MUL
311 int
bn_mul(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,int rn,BN_CTX * ctx)312 bn_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, int rn, BN_CTX *ctx)
313 {
314 bn_mul_normal(r->d, a->d, a->top, b->d, b->top);
315
316 return 1;
317 }
318
319 #endif /* HAVE_BN_MUL */
320
321 int
BN_mul(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)322 BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
323 {
324 BIGNUM *rr;
325 int rn;
326 int ret = 0;
327
328 BN_CTX_start(ctx);
329
330 if (BN_is_zero(a) || BN_is_zero(b)) {
331 BN_zero(r);
332 goto done;
333 }
334
335 rr = r;
336 if (rr == a || rr == b)
337 rr = BN_CTX_get(ctx);
338 if (rr == NULL)
339 goto err;
340
341 rn = a->top + b->top;
342 if (rn < a->top)
343 goto err;
344 if (!bn_wexpand(rr, rn))
345 goto err;
346
347 if (a->top == 4 && b->top == 4) {
348 bn_mul_comba4(rr->d, a->d, b->d);
349 } else if (a->top == 8 && b->top == 8) {
350 bn_mul_comba8(rr->d, a->d, b->d);
351 } else {
352 if (!bn_mul(rr, a, b, rn, ctx))
353 goto err;
354 }
355
356 rr->top = rn;
357 bn_correct_top(rr);
358
359 BN_set_negative(rr, a->neg ^ b->neg);
360
361 if (!bn_copy(r, rr))
362 goto err;
363 done:
364 ret = 1;
365 err:
366 BN_CTX_end(ctx);
367
368 return ret;
369 }
370 LCRYPTO_ALIAS(BN_mul);
371