1 /*
2 * Copyright 1995-2023 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the Apache License 2.0 (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
8 */
9
10 #include <assert.h>
11 #include <openssl/crypto.h>
12 #include "internal/cryptlib.h"
13 #include "bn_local.h"
14
15 #if defined(BN_LLONG) || defined(BN_UMULT_HIGH)
16
bn_mul_add_words(BN_ULONG * rp,const BN_ULONG * ap,int num,BN_ULONG w)17 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
18 BN_ULONG w)
19 {
20 BN_ULONG c1 = 0;
21
22 assert(num >= 0);
23 if (num <= 0)
24 return c1;
25
26 # ifndef OPENSSL_SMALL_FOOTPRINT
27 while (num & ~3) {
28 mul_add(rp[0], ap[0], w, c1);
29 mul_add(rp[1], ap[1], w, c1);
30 mul_add(rp[2], ap[2], w, c1);
31 mul_add(rp[3], ap[3], w, c1);
32 ap += 4;
33 rp += 4;
34 num -= 4;
35 }
36 # endif
37 while (num) {
38 mul_add(rp[0], ap[0], w, c1);
39 ap++;
40 rp++;
41 num--;
42 }
43
44 return c1;
45 }
46
bn_mul_words(BN_ULONG * rp,const BN_ULONG * ap,int num,BN_ULONG w)47 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
48 {
49 BN_ULONG c1 = 0;
50
51 assert(num >= 0);
52 if (num <= 0)
53 return c1;
54
55 # ifndef OPENSSL_SMALL_FOOTPRINT
56 while (num & ~3) {
57 mul(rp[0], ap[0], w, c1);
58 mul(rp[1], ap[1], w, c1);
59 mul(rp[2], ap[2], w, c1);
60 mul(rp[3], ap[3], w, c1);
61 ap += 4;
62 rp += 4;
63 num -= 4;
64 }
65 # endif
66 while (num) {
67 mul(rp[0], ap[0], w, c1);
68 ap++;
69 rp++;
70 num--;
71 }
72 return c1;
73 }
74
bn_sqr_words(BN_ULONG * r,const BN_ULONG * a,int n)75 void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
76 {
77 assert(n >= 0);
78 if (n <= 0)
79 return;
80
81 # ifndef OPENSSL_SMALL_FOOTPRINT
82 while (n & ~3) {
83 sqr(r[0], r[1], a[0]);
84 sqr(r[2], r[3], a[1]);
85 sqr(r[4], r[5], a[2]);
86 sqr(r[6], r[7], a[3]);
87 a += 4;
88 r += 8;
89 n -= 4;
90 }
91 # endif
92 while (n) {
93 sqr(r[0], r[1], a[0]);
94 a++;
95 r += 2;
96 n--;
97 }
98 }
99
100 #else /* !(defined(BN_LLONG) ||
101 * defined(BN_UMULT_HIGH)) */
102
bn_mul_add_words(BN_ULONG * rp,const BN_ULONG * ap,int num,BN_ULONG w)103 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
104 BN_ULONG w)
105 {
106 BN_ULONG c = 0;
107 BN_ULONG bl, bh;
108
109 assert(num >= 0);
110 if (num <= 0)
111 return (BN_ULONG)0;
112
113 bl = LBITS(w);
114 bh = HBITS(w);
115
116 # ifndef OPENSSL_SMALL_FOOTPRINT
117 while (num & ~3) {
118 mul_add(rp[0], ap[0], bl, bh, c);
119 mul_add(rp[1], ap[1], bl, bh, c);
120 mul_add(rp[2], ap[2], bl, bh, c);
121 mul_add(rp[3], ap[3], bl, bh, c);
122 ap += 4;
123 rp += 4;
124 num -= 4;
125 }
126 # endif
127 while (num) {
128 mul_add(rp[0], ap[0], bl, bh, c);
129 ap++;
130 rp++;
131 num--;
132 }
133 return c;
134 }
135
bn_mul_words(BN_ULONG * rp,const BN_ULONG * ap,int num,BN_ULONG w)136 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
137 {
138 BN_ULONG carry = 0;
139 BN_ULONG bl, bh;
140
141 assert(num >= 0);
142 if (num <= 0)
143 return (BN_ULONG)0;
144
145 bl = LBITS(w);
146 bh = HBITS(w);
147
148 # ifndef OPENSSL_SMALL_FOOTPRINT
149 while (num & ~3) {
150 mul(rp[0], ap[0], bl, bh, carry);
151 mul(rp[1], ap[1], bl, bh, carry);
152 mul(rp[2], ap[2], bl, bh, carry);
153 mul(rp[3], ap[3], bl, bh, carry);
154 ap += 4;
155 rp += 4;
156 num -= 4;
157 }
158 # endif
159 while (num) {
160 mul(rp[0], ap[0], bl, bh, carry);
161 ap++;
162 rp++;
163 num--;
164 }
165 return carry;
166 }
167
bn_sqr_words(BN_ULONG * r,const BN_ULONG * a,int n)168 void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
169 {
170 assert(n >= 0);
171 if (n <= 0)
172 return;
173
174 # ifndef OPENSSL_SMALL_FOOTPRINT
175 while (n & ~3) {
176 sqr64(r[0], r[1], a[0]);
177 sqr64(r[2], r[3], a[1]);
178 sqr64(r[4], r[5], a[2]);
179 sqr64(r[6], r[7], a[3]);
180 a += 4;
181 r += 8;
182 n -= 4;
183 }
184 # endif
185 while (n) {
186 sqr64(r[0], r[1], a[0]);
187 a++;
188 r += 2;
189 n--;
190 }
191 }
192
193 #endif /* !(defined(BN_LLONG) ||
194 * defined(BN_UMULT_HIGH)) */
195
196 #if defined(BN_LLONG) && defined(BN_DIV2W)
197
bn_div_words(BN_ULONG h,BN_ULONG l,BN_ULONG d)198 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
199 {
200 return ((BN_ULONG)(((((BN_ULLONG) h) << BN_BITS2) | l) / (BN_ULLONG) d));
201 }
202
203 #else
204
205 /* Divide h,l by d and return the result. */
206 /* I need to test this some more :-( */
bn_div_words(BN_ULONG h,BN_ULONG l,BN_ULONG d)207 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
208 {
209 BN_ULONG dh, dl, q, ret = 0, th, tl, t;
210 int i, count = 2;
211
212 if (d == 0)
213 return BN_MASK2;
214
215 i = BN_num_bits_word(d);
216 assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i));
217
218 i = BN_BITS2 - i;
219 if (h >= d)
220 h -= d;
221
222 if (i) {
223 d <<= i;
224 h = (h << i) | (l >> (BN_BITS2 - i));
225 l <<= i;
226 }
227 dh = (d & BN_MASK2h) >> BN_BITS4;
228 dl = (d & BN_MASK2l);
229 for (;;) {
230 if ((h >> BN_BITS4) == dh)
231 q = BN_MASK2l;
232 else
233 q = h / dh;
234
235 th = q * dh;
236 tl = dl * q;
237 for (;;) {
238 t = h - th;
239 if ((t & BN_MASK2h) ||
240 ((tl) <= ((t << BN_BITS4) | ((l & BN_MASK2h) >> BN_BITS4))))
241 break;
242 q--;
243 th -= dh;
244 tl -= dl;
245 }
246 t = (tl >> BN_BITS4);
247 tl = (tl << BN_BITS4) & BN_MASK2h;
248 th += t;
249
250 if (l < tl)
251 th++;
252 l -= tl;
253 if (h < th) {
254 h += d;
255 q--;
256 }
257 h -= th;
258
259 if (--count == 0)
260 break;
261
262 ret = q << BN_BITS4;
263 h = ((h << BN_BITS4) | (l >> BN_BITS4)) & BN_MASK2;
264 l = (l & BN_MASK2l) << BN_BITS4;
265 }
266 ret |= q;
267 return ret;
268 }
269 #endif /* !defined(BN_LLONG) && defined(BN_DIV2W) */
270
271 #ifdef BN_LLONG
bn_add_words(BN_ULONG * r,const BN_ULONG * a,const BN_ULONG * b,int n)272 BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
273 int n)
274 {
275 BN_ULLONG ll = 0;
276
277 assert(n >= 0);
278 if (n <= 0)
279 return (BN_ULONG)0;
280
281 # ifndef OPENSSL_SMALL_FOOTPRINT
282 while (n & ~3) {
283 ll += (BN_ULLONG) a[0] + b[0];
284 r[0] = (BN_ULONG)ll & BN_MASK2;
285 ll >>= BN_BITS2;
286 ll += (BN_ULLONG) a[1] + b[1];
287 r[1] = (BN_ULONG)ll & BN_MASK2;
288 ll >>= BN_BITS2;
289 ll += (BN_ULLONG) a[2] + b[2];
290 r[2] = (BN_ULONG)ll & BN_MASK2;
291 ll >>= BN_BITS2;
292 ll += (BN_ULLONG) a[3] + b[3];
293 r[3] = (BN_ULONG)ll & BN_MASK2;
294 ll >>= BN_BITS2;
295 a += 4;
296 b += 4;
297 r += 4;
298 n -= 4;
299 }
300 # endif
301 while (n) {
302 ll += (BN_ULLONG) a[0] + b[0];
303 r[0] = (BN_ULONG)ll & BN_MASK2;
304 ll >>= BN_BITS2;
305 a++;
306 b++;
307 r++;
308 n--;
309 }
310 return (BN_ULONG)ll;
311 }
312 #else /* !BN_LLONG */
bn_add_words(BN_ULONG * r,const BN_ULONG * a,const BN_ULONG * b,int n)313 BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
314 int n)
315 {
316 BN_ULONG c, l, t;
317
318 assert(n >= 0);
319 if (n <= 0)
320 return (BN_ULONG)0;
321
322 c = 0;
323 # ifndef OPENSSL_SMALL_FOOTPRINT
324 while (n & ~3) {
325 t = a[0];
326 t = (t + c) & BN_MASK2;
327 c = (t < c);
328 l = (t + b[0]) & BN_MASK2;
329 c += (l < t);
330 r[0] = l;
331 t = a[1];
332 t = (t + c) & BN_MASK2;
333 c = (t < c);
334 l = (t + b[1]) & BN_MASK2;
335 c += (l < t);
336 r[1] = l;
337 t = a[2];
338 t = (t + c) & BN_MASK2;
339 c = (t < c);
340 l = (t + b[2]) & BN_MASK2;
341 c += (l < t);
342 r[2] = l;
343 t = a[3];
344 t = (t + c) & BN_MASK2;
345 c = (t < c);
346 l = (t + b[3]) & BN_MASK2;
347 c += (l < t);
348 r[3] = l;
349 a += 4;
350 b += 4;
351 r += 4;
352 n -= 4;
353 }
354 # endif
355 while (n) {
356 t = a[0];
357 t = (t + c) & BN_MASK2;
358 c = (t < c);
359 l = (t + b[0]) & BN_MASK2;
360 c += (l < t);
361 r[0] = l;
362 a++;
363 b++;
364 r++;
365 n--;
366 }
367 return (BN_ULONG)c;
368 }
369 #endif /* !BN_LLONG */
370
bn_sub_words(BN_ULONG * r,const BN_ULONG * a,const BN_ULONG * b,int n)371 BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
372 int n)
373 {
374 BN_ULONG t1, t2;
375 int c = 0;
376
377 assert(n >= 0);
378 if (n <= 0)
379 return (BN_ULONG)0;
380
381 #ifndef OPENSSL_SMALL_FOOTPRINT
382 while (n & ~3) {
383 t1 = a[0];
384 t2 = (t1 - c) & BN_MASK2;
385 c = (t2 > t1);
386 t1 = b[0];
387 t1 = (t2 - t1) & BN_MASK2;
388 r[0] = t1;
389 c += (t1 > t2);
390 t1 = a[1];
391 t2 = (t1 - c) & BN_MASK2;
392 c = (t2 > t1);
393 t1 = b[1];
394 t1 = (t2 - t1) & BN_MASK2;
395 r[1] = t1;
396 c += (t1 > t2);
397 t1 = a[2];
398 t2 = (t1 - c) & BN_MASK2;
399 c = (t2 > t1);
400 t1 = b[2];
401 t1 = (t2 - t1) & BN_MASK2;
402 r[2] = t1;
403 c += (t1 > t2);
404 t1 = a[3];
405 t2 = (t1 - c) & BN_MASK2;
406 c = (t2 > t1);
407 t1 = b[3];
408 t1 = (t2 - t1) & BN_MASK2;
409 r[3] = t1;
410 c += (t1 > t2);
411 a += 4;
412 b += 4;
413 r += 4;
414 n -= 4;
415 }
416 #endif
417 while (n) {
418 t1 = a[0];
419 t2 = (t1 - c) & BN_MASK2;
420 c = (t2 > t1);
421 t1 = b[0];
422 t1 = (t2 - t1) & BN_MASK2;
423 r[0] = t1;
424 c += (t1 > t2);
425 a++;
426 b++;
427 r++;
428 n--;
429 }
430 return c;
431 }
432
433 #if defined(BN_MUL_COMBA) && !defined(OPENSSL_SMALL_FOOTPRINT)
434
435 /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
436 /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
437 /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
438 /*
439 * sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number
440 * c=(c2,c1,c0)
441 */
442
443 # ifdef BN_LLONG
444 /*
445 * Keep in mind that additions to multiplication result can not
446 * overflow, because its high half cannot be all-ones.
447 */
448 # define mul_add_c(a,b,c0,c1,c2) do { \
449 BN_ULONG hi; \
450 BN_ULLONG t = (BN_ULLONG)(a)*(b); \
451 t += c0; /* no carry */ \
452 c0 = (BN_ULONG)Lw(t); \
453 hi = (BN_ULONG)Hw(t); \
454 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
455 } while(0)
456
457 # define mul_add_c2(a,b,c0,c1,c2) do { \
458 BN_ULONG hi; \
459 BN_ULLONG t = (BN_ULLONG)(a)*(b); \
460 BN_ULLONG tt = t+c0; /* no carry */ \
461 c0 = (BN_ULONG)Lw(tt); \
462 hi = (BN_ULONG)Hw(tt); \
463 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
464 t += c0; /* no carry */ \
465 c0 = (BN_ULONG)Lw(t); \
466 hi = (BN_ULONG)Hw(t); \
467 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
468 } while(0)
469
470 # define sqr_add_c(a,i,c0,c1,c2) do { \
471 BN_ULONG hi; \
472 BN_ULLONG t = (BN_ULLONG)a[i]*a[i]; \
473 t += c0; /* no carry */ \
474 c0 = (BN_ULONG)Lw(t); \
475 hi = (BN_ULONG)Hw(t); \
476 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
477 } while(0)
478
479 # define sqr_add_c2(a,i,j,c0,c1,c2) \
480 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
481
482 # elif defined(BN_UMULT_LOHI)
483 /*
484 * Keep in mind that additions to hi can not overflow, because
485 * the high word of a multiplication result cannot be all-ones.
486 */
487 # define mul_add_c(a,b,c0,c1,c2) do { \
488 BN_ULONG ta = (a), tb = (b); \
489 BN_ULONG lo, hi; \
490 BN_UMULT_LOHI(lo,hi,ta,tb); \
491 c0 += lo; hi += (c0<lo); \
492 c1 += hi; c2 += (c1<hi); \
493 } while(0)
494
495 # define mul_add_c2(a,b,c0,c1,c2) do { \
496 BN_ULONG ta = (a), tb = (b); \
497 BN_ULONG lo, hi, tt; \
498 BN_UMULT_LOHI(lo,hi,ta,tb); \
499 c0 += lo; tt = hi + (c0<lo); \
500 c1 += tt; c2 += (c1<tt); \
501 c0 += lo; hi += (c0<lo); \
502 c1 += hi; c2 += (c1<hi); \
503 } while(0)
504
505 # define sqr_add_c(a,i,c0,c1,c2) do { \
506 BN_ULONG ta = (a)[i]; \
507 BN_ULONG lo, hi; \
508 BN_UMULT_LOHI(lo,hi,ta,ta); \
509 c0 += lo; hi += (c0<lo); \
510 c1 += hi; c2 += (c1<hi); \
511 } while(0)
512
513 # define sqr_add_c2(a,i,j,c0,c1,c2) \
514 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
515
516 # elif defined(BN_UMULT_HIGH)
517 /*
518 * Keep in mind that additions to hi can not overflow, because
519 * the high word of a multiplication result cannot be all-ones.
520 */
521 # define mul_add_c(a,b,c0,c1,c2) do { \
522 BN_ULONG ta = (a), tb = (b); \
523 BN_ULONG lo = ta * tb; \
524 BN_ULONG hi = BN_UMULT_HIGH(ta,tb); \
525 c0 += lo; hi += (c0<lo); \
526 c1 += hi; c2 += (c1<hi); \
527 } while(0)
528
529 # define mul_add_c2(a,b,c0,c1,c2) do { \
530 BN_ULONG ta = (a), tb = (b), tt; \
531 BN_ULONG lo = ta * tb; \
532 BN_ULONG hi = BN_UMULT_HIGH(ta,tb); \
533 c0 += lo; tt = hi + (c0<lo); \
534 c1 += tt; c2 += (c1<tt); \
535 c0 += lo; hi += (c0<lo); \
536 c1 += hi; c2 += (c1<hi); \
537 } while(0)
538
539 # define sqr_add_c(a,i,c0,c1,c2) do { \
540 BN_ULONG ta = (a)[i]; \
541 BN_ULONG lo = ta * ta; \
542 BN_ULONG hi = BN_UMULT_HIGH(ta,ta); \
543 c0 += lo; hi += (c0<lo); \
544 c1 += hi; c2 += (c1<hi); \
545 } while(0)
546
547 # define sqr_add_c2(a,i,j,c0,c1,c2) \
548 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
549
550 # else /* !BN_LLONG */
551 /*
552 * Keep in mind that additions to hi can not overflow, because
553 * the high word of a multiplication result cannot be all-ones.
554 */
555 # define mul_add_c(a,b,c0,c1,c2) do { \
556 BN_ULONG lo = LBITS(a), hi = HBITS(a); \
557 BN_ULONG bl = LBITS(b), bh = HBITS(b); \
558 mul64(lo,hi,bl,bh); \
559 c0 = (c0+lo)&BN_MASK2; hi += (c0<lo); \
560 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
561 } while(0)
562
563 # define mul_add_c2(a,b,c0,c1,c2) do { \
564 BN_ULONG tt; \
565 BN_ULONG lo = LBITS(a), hi = HBITS(a); \
566 BN_ULONG bl = LBITS(b), bh = HBITS(b); \
567 mul64(lo,hi,bl,bh); \
568 tt = hi; \
569 c0 = (c0+lo)&BN_MASK2; tt += (c0<lo); \
570 c1 = (c1+tt)&BN_MASK2; c2 += (c1<tt); \
571 c0 = (c0+lo)&BN_MASK2; hi += (c0<lo); \
572 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
573 } while(0)
574
575 # define sqr_add_c(a,i,c0,c1,c2) do { \
576 BN_ULONG lo, hi; \
577 sqr64(lo,hi,(a)[i]); \
578 c0 = (c0+lo)&BN_MASK2; hi += (c0<lo); \
579 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
580 } while(0)
581
582 # define sqr_add_c2(a,i,j,c0,c1,c2) \
583 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
584 # endif /* !BN_LLONG */
585
bn_mul_comba8(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)586 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
587 {
588 BN_ULONG c1, c2, c3;
589
590 c1 = 0;
591 c2 = 0;
592 c3 = 0;
593 mul_add_c(a[0], b[0], c1, c2, c3);
594 r[0] = c1;
595 c1 = 0;
596 mul_add_c(a[0], b[1], c2, c3, c1);
597 mul_add_c(a[1], b[0], c2, c3, c1);
598 r[1] = c2;
599 c2 = 0;
600 mul_add_c(a[2], b[0], c3, c1, c2);
601 mul_add_c(a[1], b[1], c3, c1, c2);
602 mul_add_c(a[0], b[2], c3, c1, c2);
603 r[2] = c3;
604 c3 = 0;
605 mul_add_c(a[0], b[3], c1, c2, c3);
606 mul_add_c(a[1], b[2], c1, c2, c3);
607 mul_add_c(a[2], b[1], c1, c2, c3);
608 mul_add_c(a[3], b[0], c1, c2, c3);
609 r[3] = c1;
610 c1 = 0;
611 mul_add_c(a[4], b[0], c2, c3, c1);
612 mul_add_c(a[3], b[1], c2, c3, c1);
613 mul_add_c(a[2], b[2], c2, c3, c1);
614 mul_add_c(a[1], b[3], c2, c3, c1);
615 mul_add_c(a[0], b[4], c2, c3, c1);
616 r[4] = c2;
617 c2 = 0;
618 mul_add_c(a[0], b[5], c3, c1, c2);
619 mul_add_c(a[1], b[4], c3, c1, c2);
620 mul_add_c(a[2], b[3], c3, c1, c2);
621 mul_add_c(a[3], b[2], c3, c1, c2);
622 mul_add_c(a[4], b[1], c3, c1, c2);
623 mul_add_c(a[5], b[0], c3, c1, c2);
624 r[5] = c3;
625 c3 = 0;
626 mul_add_c(a[6], b[0], c1, c2, c3);
627 mul_add_c(a[5], b[1], c1, c2, c3);
628 mul_add_c(a[4], b[2], c1, c2, c3);
629 mul_add_c(a[3], b[3], c1, c2, c3);
630 mul_add_c(a[2], b[4], c1, c2, c3);
631 mul_add_c(a[1], b[5], c1, c2, c3);
632 mul_add_c(a[0], b[6], c1, c2, c3);
633 r[6] = c1;
634 c1 = 0;
635 mul_add_c(a[0], b[7], c2, c3, c1);
636 mul_add_c(a[1], b[6], c2, c3, c1);
637 mul_add_c(a[2], b[5], c2, c3, c1);
638 mul_add_c(a[3], b[4], c2, c3, c1);
639 mul_add_c(a[4], b[3], c2, c3, c1);
640 mul_add_c(a[5], b[2], c2, c3, c1);
641 mul_add_c(a[6], b[1], c2, c3, c1);
642 mul_add_c(a[7], b[0], c2, c3, c1);
643 r[7] = c2;
644 c2 = 0;
645 mul_add_c(a[7], b[1], c3, c1, c2);
646 mul_add_c(a[6], b[2], c3, c1, c2);
647 mul_add_c(a[5], b[3], c3, c1, c2);
648 mul_add_c(a[4], b[4], c3, c1, c2);
649 mul_add_c(a[3], b[5], c3, c1, c2);
650 mul_add_c(a[2], b[6], c3, c1, c2);
651 mul_add_c(a[1], b[7], c3, c1, c2);
652 r[8] = c3;
653 c3 = 0;
654 mul_add_c(a[2], b[7], c1, c2, c3);
655 mul_add_c(a[3], b[6], c1, c2, c3);
656 mul_add_c(a[4], b[5], c1, c2, c3);
657 mul_add_c(a[5], b[4], c1, c2, c3);
658 mul_add_c(a[6], b[3], c1, c2, c3);
659 mul_add_c(a[7], b[2], c1, c2, c3);
660 r[9] = c1;
661 c1 = 0;
662 mul_add_c(a[7], b[3], c2, c3, c1);
663 mul_add_c(a[6], b[4], c2, c3, c1);
664 mul_add_c(a[5], b[5], c2, c3, c1);
665 mul_add_c(a[4], b[6], c2, c3, c1);
666 mul_add_c(a[3], b[7], c2, c3, c1);
667 r[10] = c2;
668 c2 = 0;
669 mul_add_c(a[4], b[7], c3, c1, c2);
670 mul_add_c(a[5], b[6], c3, c1, c2);
671 mul_add_c(a[6], b[5], c3, c1, c2);
672 mul_add_c(a[7], b[4], c3, c1, c2);
673 r[11] = c3;
674 c3 = 0;
675 mul_add_c(a[7], b[5], c1, c2, c3);
676 mul_add_c(a[6], b[6], c1, c2, c3);
677 mul_add_c(a[5], b[7], c1, c2, c3);
678 r[12] = c1;
679 c1 = 0;
680 mul_add_c(a[6], b[7], c2, c3, c1);
681 mul_add_c(a[7], b[6], c2, c3, c1);
682 r[13] = c2;
683 c2 = 0;
684 mul_add_c(a[7], b[7], c3, c1, c2);
685 r[14] = c3;
686 r[15] = c1;
687 }
688
bn_mul_comba4(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)689 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
690 {
691 BN_ULONG c1, c2, c3;
692
693 c1 = 0;
694 c2 = 0;
695 c3 = 0;
696 mul_add_c(a[0], b[0], c1, c2, c3);
697 r[0] = c1;
698 c1 = 0;
699 mul_add_c(a[0], b[1], c2, c3, c1);
700 mul_add_c(a[1], b[0], c2, c3, c1);
701 r[1] = c2;
702 c2 = 0;
703 mul_add_c(a[2], b[0], c3, c1, c2);
704 mul_add_c(a[1], b[1], c3, c1, c2);
705 mul_add_c(a[0], b[2], c3, c1, c2);
706 r[2] = c3;
707 c3 = 0;
708 mul_add_c(a[0], b[3], c1, c2, c3);
709 mul_add_c(a[1], b[2], c1, c2, c3);
710 mul_add_c(a[2], b[1], c1, c2, c3);
711 mul_add_c(a[3], b[0], c1, c2, c3);
712 r[3] = c1;
713 c1 = 0;
714 mul_add_c(a[3], b[1], c2, c3, c1);
715 mul_add_c(a[2], b[2], c2, c3, c1);
716 mul_add_c(a[1], b[3], c2, c3, c1);
717 r[4] = c2;
718 c2 = 0;
719 mul_add_c(a[2], b[3], c3, c1, c2);
720 mul_add_c(a[3], b[2], c3, c1, c2);
721 r[5] = c3;
722 c3 = 0;
723 mul_add_c(a[3], b[3], c1, c2, c3);
724 r[6] = c1;
725 r[7] = c2;
726 }
727
bn_sqr_comba8(BN_ULONG * r,const BN_ULONG * a)728 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
729 {
730 BN_ULONG c1, c2, c3;
731
732 c1 = 0;
733 c2 = 0;
734 c3 = 0;
735 sqr_add_c(a, 0, c1, c2, c3);
736 r[0] = c1;
737 c1 = 0;
738 sqr_add_c2(a, 1, 0, c2, c3, c1);
739 r[1] = c2;
740 c2 = 0;
741 sqr_add_c(a, 1, c3, c1, c2);
742 sqr_add_c2(a, 2, 0, c3, c1, c2);
743 r[2] = c3;
744 c3 = 0;
745 sqr_add_c2(a, 3, 0, c1, c2, c3);
746 sqr_add_c2(a, 2, 1, c1, c2, c3);
747 r[3] = c1;
748 c1 = 0;
749 sqr_add_c(a, 2, c2, c3, c1);
750 sqr_add_c2(a, 3, 1, c2, c3, c1);
751 sqr_add_c2(a, 4, 0, c2, c3, c1);
752 r[4] = c2;
753 c2 = 0;
754 sqr_add_c2(a, 5, 0, c3, c1, c2);
755 sqr_add_c2(a, 4, 1, c3, c1, c2);
756 sqr_add_c2(a, 3, 2, c3, c1, c2);
757 r[5] = c3;
758 c3 = 0;
759 sqr_add_c(a, 3, c1, c2, c3);
760 sqr_add_c2(a, 4, 2, c1, c2, c3);
761 sqr_add_c2(a, 5, 1, c1, c2, c3);
762 sqr_add_c2(a, 6, 0, c1, c2, c3);
763 r[6] = c1;
764 c1 = 0;
765 sqr_add_c2(a, 7, 0, c2, c3, c1);
766 sqr_add_c2(a, 6, 1, c2, c3, c1);
767 sqr_add_c2(a, 5, 2, c2, c3, c1);
768 sqr_add_c2(a, 4, 3, c2, c3, c1);
769 r[7] = c2;
770 c2 = 0;
771 sqr_add_c(a, 4, c3, c1, c2);
772 sqr_add_c2(a, 5, 3, c3, c1, c2);
773 sqr_add_c2(a, 6, 2, c3, c1, c2);
774 sqr_add_c2(a, 7, 1, c3, c1, c2);
775 r[8] = c3;
776 c3 = 0;
777 sqr_add_c2(a, 7, 2, c1, c2, c3);
778 sqr_add_c2(a, 6, 3, c1, c2, c3);
779 sqr_add_c2(a, 5, 4, c1, c2, c3);
780 r[9] = c1;
781 c1 = 0;
782 sqr_add_c(a, 5, c2, c3, c1);
783 sqr_add_c2(a, 6, 4, c2, c3, c1);
784 sqr_add_c2(a, 7, 3, c2, c3, c1);
785 r[10] = c2;
786 c2 = 0;
787 sqr_add_c2(a, 7, 4, c3, c1, c2);
788 sqr_add_c2(a, 6, 5, c3, c1, c2);
789 r[11] = c3;
790 c3 = 0;
791 sqr_add_c(a, 6, c1, c2, c3);
792 sqr_add_c2(a, 7, 5, c1, c2, c3);
793 r[12] = c1;
794 c1 = 0;
795 sqr_add_c2(a, 7, 6, c2, c3, c1);
796 r[13] = c2;
797 c2 = 0;
798 sqr_add_c(a, 7, c3, c1, c2);
799 r[14] = c3;
800 r[15] = c1;
801 }
802
bn_sqr_comba4(BN_ULONG * r,const BN_ULONG * a)803 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
804 {
805 BN_ULONG c1, c2, c3;
806
807 c1 = 0;
808 c2 = 0;
809 c3 = 0;
810 sqr_add_c(a, 0, c1, c2, c3);
811 r[0] = c1;
812 c1 = 0;
813 sqr_add_c2(a, 1, 0, c2, c3, c1);
814 r[1] = c2;
815 c2 = 0;
816 sqr_add_c(a, 1, c3, c1, c2);
817 sqr_add_c2(a, 2, 0, c3, c1, c2);
818 r[2] = c3;
819 c3 = 0;
820 sqr_add_c2(a, 3, 0, c1, c2, c3);
821 sqr_add_c2(a, 2, 1, c1, c2, c3);
822 r[3] = c1;
823 c1 = 0;
824 sqr_add_c(a, 2, c2, c3, c1);
825 sqr_add_c2(a, 3, 1, c2, c3, c1);
826 r[4] = c2;
827 c2 = 0;
828 sqr_add_c2(a, 3, 2, c3, c1, c2);
829 r[5] = c3;
830 c3 = 0;
831 sqr_add_c(a, 3, c1, c2, c3);
832 r[6] = c1;
833 r[7] = c2;
834 }
835
836 # ifdef OPENSSL_NO_ASM
837 # ifdef OPENSSL_BN_ASM_MONT
838 # include <alloca.h>
839 /*
840 * This is essentially reference implementation, which may or may not
841 * result in performance improvement. E.g. on IA-32 this routine was
842 * observed to give 40% faster rsa1024 private key operations and 10%
843 * faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only
844 * by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a
845 * reference implementation, one to be used as starting point for
846 * platform-specific assembler. Mentioned numbers apply to compiler
847 * generated code compiled with and without -DOPENSSL_BN_ASM_MONT and
848 * can vary not only from platform to platform, but even for compiler
849 * versions. Assembler vs. assembler improvement coefficients can
850 * [and are known to] differ and are to be documented elsewhere.
851 */
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0p,int num)852 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
853 const BN_ULONG *np, const BN_ULONG *n0p, int num)
854 {
855 BN_ULONG c0, c1, ml, *tp, n0;
856 # ifdef mul64
857 BN_ULONG mh;
858 # endif
859 volatile BN_ULONG *vp;
860 int i = 0, j;
861
862 # if 0 /* template for platform-specific
863 * implementation */
864 if (ap == bp)
865 return bn_sqr_mont(rp, ap, np, n0p, num);
866 # endif
867 vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
868
869 n0 = *n0p;
870
871 c0 = 0;
872 ml = bp[0];
873 # ifdef mul64
874 mh = HBITS(ml);
875 ml = LBITS(ml);
876 for (j = 0; j < num; ++j)
877 mul(tp[j], ap[j], ml, mh, c0);
878 # else
879 for (j = 0; j < num; ++j)
880 mul(tp[j], ap[j], ml, c0);
881 # endif
882
883 tp[num] = c0;
884 tp[num + 1] = 0;
885 goto enter;
886
887 for (i = 0; i < num; i++) {
888 c0 = 0;
889 ml = bp[i];
890 # ifdef mul64
891 mh = HBITS(ml);
892 ml = LBITS(ml);
893 for (j = 0; j < num; ++j)
894 mul_add(tp[j], ap[j], ml, mh, c0);
895 # else
896 for (j = 0; j < num; ++j)
897 mul_add(tp[j], ap[j], ml, c0);
898 # endif
899 c1 = (tp[num] + c0) & BN_MASK2;
900 tp[num] = c1;
901 tp[num + 1] = (c1 < c0 ? 1 : 0);
902 enter:
903 c1 = tp[0];
904 ml = (c1 * n0) & BN_MASK2;
905 c0 = 0;
906 # ifdef mul64
907 mh = HBITS(ml);
908 ml = LBITS(ml);
909 mul_add(c1, np[0], ml, mh, c0);
910 # else
911 mul_add(c1, ml, np[0], c0);
912 # endif
913 for (j = 1; j < num; j++) {
914 c1 = tp[j];
915 # ifdef mul64
916 mul_add(c1, np[j], ml, mh, c0);
917 # else
918 mul_add(c1, ml, np[j], c0);
919 # endif
920 tp[j - 1] = c1 & BN_MASK2;
921 }
922 c1 = (tp[num] + c0) & BN_MASK2;
923 tp[num - 1] = c1;
924 tp[num] = tp[num + 1] + (c1 < c0 ? 1 : 0);
925 }
926
927 if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
928 c0 = bn_sub_words(rp, tp, np, num);
929 if (tp[num] != 0 || c0 == 0) {
930 for (i = 0; i < num + 2; i++)
931 vp[i] = 0;
932 return 1;
933 }
934 }
935 for (i = 0; i < num; i++)
936 rp[i] = tp[i], vp[i] = 0;
937 vp[num] = 0;
938 vp[num + 1] = 0;
939 return 1;
940 }
941 # else
942 /*
943 * Return value of 0 indicates that multiplication/convolution was not
944 * performed to signal the caller to fall down to alternative/original
945 * code-path.
946 */
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0,int num)947 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
948 const BN_ULONG *np, const BN_ULONG *n0, int num)
949 {
950 return 0;
951 }
952 # endif /* OPENSSL_BN_ASM_MONT */
953 # endif
954
955 #else /* !BN_MUL_COMBA */
956
957 /* hmm... is it faster just to do a multiply? */
bn_sqr_comba4(BN_ULONG * r,const BN_ULONG * a)958 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
959 {
960 BN_ULONG t[8];
961 bn_sqr_normal(r, a, 4, t);
962 }
963
bn_sqr_comba8(BN_ULONG * r,const BN_ULONG * a)964 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
965 {
966 BN_ULONG t[16];
967 bn_sqr_normal(r, a, 8, t);
968 }
969
bn_mul_comba4(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)970 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
971 {
972 r[4] = bn_mul_words(&(r[0]), a, 4, b[0]);
973 r[5] = bn_mul_add_words(&(r[1]), a, 4, b[1]);
974 r[6] = bn_mul_add_words(&(r[2]), a, 4, b[2]);
975 r[7] = bn_mul_add_words(&(r[3]), a, 4, b[3]);
976 }
977
bn_mul_comba8(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)978 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
979 {
980 r[8] = bn_mul_words(&(r[0]), a, 8, b[0]);
981 r[9] = bn_mul_add_words(&(r[1]), a, 8, b[1]);
982 r[10] = bn_mul_add_words(&(r[2]), a, 8, b[2]);
983 r[11] = bn_mul_add_words(&(r[3]), a, 8, b[3]);
984 r[12] = bn_mul_add_words(&(r[4]), a, 8, b[4]);
985 r[13] = bn_mul_add_words(&(r[5]), a, 8, b[5]);
986 r[14] = bn_mul_add_words(&(r[6]), a, 8, b[6]);
987 r[15] = bn_mul_add_words(&(r[7]), a, 8, b[7]);
988 }
989
990 # ifdef OPENSSL_NO_ASM
991 # ifdef OPENSSL_BN_ASM_MONT
992 # include <alloca.h>
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0p,int num)993 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
994 const BN_ULONG *np, const BN_ULONG *n0p, int num)
995 {
996 BN_ULONG c0, c1, *tp, n0 = *n0p;
997 volatile BN_ULONG *vp;
998 int i = 0, j;
999
1000 vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
1001
1002 for (i = 0; i <= num; i++)
1003 tp[i] = 0;
1004
1005 for (i = 0; i < num; i++) {
1006 c0 = bn_mul_add_words(tp, ap, num, bp[i]);
1007 c1 = (tp[num] + c0) & BN_MASK2;
1008 tp[num] = c1;
1009 tp[num + 1] = (c1 < c0 ? 1 : 0);
1010
1011 c0 = bn_mul_add_words(tp, np, num, tp[0] * n0);
1012 c1 = (tp[num] + c0) & BN_MASK2;
1013 tp[num] = c1;
1014 tp[num + 1] += (c1 < c0 ? 1 : 0);
1015 for (j = 0; j <= num; j++)
1016 tp[j] = tp[j + 1];
1017 }
1018
1019 if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
1020 c0 = bn_sub_words(rp, tp, np, num);
1021 if (tp[num] != 0 || c0 == 0) {
1022 for (i = 0; i < num + 2; i++)
1023 vp[i] = 0;
1024 return 1;
1025 }
1026 }
1027 for (i = 0; i < num; i++)
1028 rp[i] = tp[i], vp[i] = 0;
1029 vp[num] = 0;
1030 vp[num + 1] = 0;
1031 return 1;
1032 }
1033 # else
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0,int num)1034 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
1035 const BN_ULONG *np, const BN_ULONG *n0, int num)
1036 {
1037 return 0;
1038 }
1039 # endif /* OPENSSL_BN_ASM_MONT */
1040 # endif
1041
1042 #endif /* !BN_MUL_COMBA */
1043
