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 # undef bn_mul_comba8
436 # undef bn_mul_comba4
437 # undef bn_sqr_comba8
438 # undef bn_sqr_comba4
439
440 /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
441 /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
442 /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
443 /*
444 * sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number
445 * c=(c2,c1,c0)
446 */
447
448 # ifdef BN_LLONG
449 /*
450 * Keep in mind that additions to multiplication result can not
451 * overflow, because its high half cannot be all-ones.
452 */
453 # define mul_add_c(a,b,c0,c1,c2) do { \
454 BN_ULONG hi; \
455 BN_ULLONG t = (BN_ULLONG)(a)*(b); \
456 t += c0; /* no carry */ \
457 c0 = (BN_ULONG)Lw(t); \
458 hi = (BN_ULONG)Hw(t); \
459 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
460 } while(0)
461
462 # define mul_add_c2(a,b,c0,c1,c2) do { \
463 BN_ULONG hi; \
464 BN_ULLONG t = (BN_ULLONG)(a)*(b); \
465 BN_ULLONG tt = t+c0; /* no carry */ \
466 c0 = (BN_ULONG)Lw(tt); \
467 hi = (BN_ULONG)Hw(tt); \
468 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
469 t += c0; /* no carry */ \
470 c0 = (BN_ULONG)Lw(t); \
471 hi = (BN_ULONG)Hw(t); \
472 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
473 } while(0)
474
475 # define sqr_add_c(a,i,c0,c1,c2) do { \
476 BN_ULONG hi; \
477 BN_ULLONG t = (BN_ULLONG)a[i]*a[i]; \
478 t += c0; /* no carry */ \
479 c0 = (BN_ULONG)Lw(t); \
480 hi = (BN_ULONG)Hw(t); \
481 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
482 } while(0)
483
484 # define sqr_add_c2(a,i,j,c0,c1,c2) \
485 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
486
487 # elif defined(BN_UMULT_LOHI)
488 /*
489 * Keep in mind that additions to hi can not overflow, because
490 * the high word of a multiplication result cannot be all-ones.
491 */
492 # define mul_add_c(a,b,c0,c1,c2) do { \
493 BN_ULONG ta = (a), tb = (b); \
494 BN_ULONG lo, hi; \
495 BN_UMULT_LOHI(lo,hi,ta,tb); \
496 c0 += lo; hi += (c0<lo); \
497 c1 += hi; c2 += (c1<hi); \
498 } while(0)
499
500 # define mul_add_c2(a,b,c0,c1,c2) do { \
501 BN_ULONG ta = (a), tb = (b); \
502 BN_ULONG lo, hi, tt; \
503 BN_UMULT_LOHI(lo,hi,ta,tb); \
504 c0 += lo; tt = hi + (c0<lo); \
505 c1 += tt; c2 += (c1<tt); \
506 c0 += lo; hi += (c0<lo); \
507 c1 += hi; c2 += (c1<hi); \
508 } while(0)
509
510 # define sqr_add_c(a,i,c0,c1,c2) do { \
511 BN_ULONG ta = (a)[i]; \
512 BN_ULONG lo, hi; \
513 BN_UMULT_LOHI(lo,hi,ta,ta); \
514 c0 += lo; hi += (c0<lo); \
515 c1 += hi; c2 += (c1<hi); \
516 } while(0)
517
518 # define sqr_add_c2(a,i,j,c0,c1,c2) \
519 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
520
521 # elif defined(BN_UMULT_HIGH)
522 /*
523 * Keep in mind that additions to hi can not overflow, because
524 * the high word of a multiplication result cannot be all-ones.
525 */
526 # define mul_add_c(a,b,c0,c1,c2) do { \
527 BN_ULONG ta = (a), tb = (b); \
528 BN_ULONG lo = ta * tb; \
529 BN_ULONG hi = BN_UMULT_HIGH(ta,tb); \
530 c0 += lo; hi += (c0<lo); \
531 c1 += hi; c2 += (c1<hi); \
532 } while(0)
533
534 # define mul_add_c2(a,b,c0,c1,c2) do { \
535 BN_ULONG ta = (a), tb = (b), tt; \
536 BN_ULONG lo = ta * tb; \
537 BN_ULONG hi = BN_UMULT_HIGH(ta,tb); \
538 c0 += lo; tt = hi + (c0<lo); \
539 c1 += tt; c2 += (c1<tt); \
540 c0 += lo; hi += (c0<lo); \
541 c1 += hi; c2 += (c1<hi); \
542 } while(0)
543
544 # define sqr_add_c(a,i,c0,c1,c2) do { \
545 BN_ULONG ta = (a)[i]; \
546 BN_ULONG lo = ta * ta; \
547 BN_ULONG hi = BN_UMULT_HIGH(ta,ta); \
548 c0 += lo; hi += (c0<lo); \
549 c1 += hi; c2 += (c1<hi); \
550 } while(0)
551
552 # define sqr_add_c2(a,i,j,c0,c1,c2) \
553 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
554
555 # else /* !BN_LLONG */
556 /*
557 * Keep in mind that additions to hi can not overflow, because
558 * the high word of a multiplication result cannot be all-ones.
559 */
560 # define mul_add_c(a,b,c0,c1,c2) do { \
561 BN_ULONG lo = LBITS(a), hi = HBITS(a); \
562 BN_ULONG bl = LBITS(b), bh = HBITS(b); \
563 mul64(lo,hi,bl,bh); \
564 c0 = (c0+lo)&BN_MASK2; hi += (c0<lo); \
565 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
566 } while(0)
567
568 # define mul_add_c2(a,b,c0,c1,c2) do { \
569 BN_ULONG tt; \
570 BN_ULONG lo = LBITS(a), hi = HBITS(a); \
571 BN_ULONG bl = LBITS(b), bh = HBITS(b); \
572 mul64(lo,hi,bl,bh); \
573 tt = hi; \
574 c0 = (c0+lo)&BN_MASK2; tt += (c0<lo); \
575 c1 = (c1+tt)&BN_MASK2; c2 += (c1<tt); \
576 c0 = (c0+lo)&BN_MASK2; hi += (c0<lo); \
577 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
578 } while(0)
579
580 # define sqr_add_c(a,i,c0,c1,c2) do { \
581 BN_ULONG lo, hi; \
582 sqr64(lo,hi,(a)[i]); \
583 c0 = (c0+lo)&BN_MASK2; hi += (c0<lo); \
584 c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi); \
585 } while(0)
586
587 # define sqr_add_c2(a,i,j,c0,c1,c2) \
588 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
589 # endif /* !BN_LLONG */
590
bn_mul_comba8(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)591 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
592 {
593 BN_ULONG c1, c2, c3;
594
595 c1 = 0;
596 c2 = 0;
597 c3 = 0;
598 mul_add_c(a[0], b[0], c1, c2, c3);
599 r[0] = c1;
600 c1 = 0;
601 mul_add_c(a[0], b[1], c2, c3, c1);
602 mul_add_c(a[1], b[0], c2, c3, c1);
603 r[1] = c2;
604 c2 = 0;
605 mul_add_c(a[2], b[0], c3, c1, c2);
606 mul_add_c(a[1], b[1], c3, c1, c2);
607 mul_add_c(a[0], b[2], c3, c1, c2);
608 r[2] = c3;
609 c3 = 0;
610 mul_add_c(a[0], b[3], c1, c2, c3);
611 mul_add_c(a[1], b[2], c1, c2, c3);
612 mul_add_c(a[2], b[1], c1, c2, c3);
613 mul_add_c(a[3], b[0], c1, c2, c3);
614 r[3] = c1;
615 c1 = 0;
616 mul_add_c(a[4], b[0], c2, c3, c1);
617 mul_add_c(a[3], b[1], c2, c3, c1);
618 mul_add_c(a[2], b[2], c2, c3, c1);
619 mul_add_c(a[1], b[3], c2, c3, c1);
620 mul_add_c(a[0], b[4], c2, c3, c1);
621 r[4] = c2;
622 c2 = 0;
623 mul_add_c(a[0], b[5], c3, c1, c2);
624 mul_add_c(a[1], b[4], c3, c1, c2);
625 mul_add_c(a[2], b[3], c3, c1, c2);
626 mul_add_c(a[3], b[2], c3, c1, c2);
627 mul_add_c(a[4], b[1], c3, c1, c2);
628 mul_add_c(a[5], b[0], c3, c1, c2);
629 r[5] = c3;
630 c3 = 0;
631 mul_add_c(a[6], b[0], c1, c2, c3);
632 mul_add_c(a[5], b[1], c1, c2, c3);
633 mul_add_c(a[4], b[2], c1, c2, c3);
634 mul_add_c(a[3], b[3], c1, c2, c3);
635 mul_add_c(a[2], b[4], c1, c2, c3);
636 mul_add_c(a[1], b[5], c1, c2, c3);
637 mul_add_c(a[0], b[6], c1, c2, c3);
638 r[6] = c1;
639 c1 = 0;
640 mul_add_c(a[0], b[7], c2, c3, c1);
641 mul_add_c(a[1], b[6], c2, c3, c1);
642 mul_add_c(a[2], b[5], c2, c3, c1);
643 mul_add_c(a[3], b[4], c2, c3, c1);
644 mul_add_c(a[4], b[3], c2, c3, c1);
645 mul_add_c(a[5], b[2], c2, c3, c1);
646 mul_add_c(a[6], b[1], c2, c3, c1);
647 mul_add_c(a[7], b[0], c2, c3, c1);
648 r[7] = c2;
649 c2 = 0;
650 mul_add_c(a[7], b[1], c3, c1, c2);
651 mul_add_c(a[6], b[2], c3, c1, c2);
652 mul_add_c(a[5], b[3], c3, c1, c2);
653 mul_add_c(a[4], b[4], c3, c1, c2);
654 mul_add_c(a[3], b[5], c3, c1, c2);
655 mul_add_c(a[2], b[6], c3, c1, c2);
656 mul_add_c(a[1], b[7], c3, c1, c2);
657 r[8] = c3;
658 c3 = 0;
659 mul_add_c(a[2], b[7], c1, c2, c3);
660 mul_add_c(a[3], b[6], c1, c2, c3);
661 mul_add_c(a[4], b[5], c1, c2, c3);
662 mul_add_c(a[5], b[4], c1, c2, c3);
663 mul_add_c(a[6], b[3], c1, c2, c3);
664 mul_add_c(a[7], b[2], c1, c2, c3);
665 r[9] = c1;
666 c1 = 0;
667 mul_add_c(a[7], b[3], c2, c3, c1);
668 mul_add_c(a[6], b[4], c2, c3, c1);
669 mul_add_c(a[5], b[5], c2, c3, c1);
670 mul_add_c(a[4], b[6], c2, c3, c1);
671 mul_add_c(a[3], b[7], c2, c3, c1);
672 r[10] = c2;
673 c2 = 0;
674 mul_add_c(a[4], b[7], c3, c1, c2);
675 mul_add_c(a[5], b[6], c3, c1, c2);
676 mul_add_c(a[6], b[5], c3, c1, c2);
677 mul_add_c(a[7], b[4], c3, c1, c2);
678 r[11] = c3;
679 c3 = 0;
680 mul_add_c(a[7], b[5], c1, c2, c3);
681 mul_add_c(a[6], b[6], c1, c2, c3);
682 mul_add_c(a[5], b[7], c1, c2, c3);
683 r[12] = c1;
684 c1 = 0;
685 mul_add_c(a[6], b[7], c2, c3, c1);
686 mul_add_c(a[7], b[6], c2, c3, c1);
687 r[13] = c2;
688 c2 = 0;
689 mul_add_c(a[7], b[7], c3, c1, c2);
690 r[14] = c3;
691 r[15] = c1;
692 }
693
bn_mul_comba4(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)694 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
695 {
696 BN_ULONG c1, c2, c3;
697
698 c1 = 0;
699 c2 = 0;
700 c3 = 0;
701 mul_add_c(a[0], b[0], c1, c2, c3);
702 r[0] = c1;
703 c1 = 0;
704 mul_add_c(a[0], b[1], c2, c3, c1);
705 mul_add_c(a[1], b[0], c2, c3, c1);
706 r[1] = c2;
707 c2 = 0;
708 mul_add_c(a[2], b[0], c3, c1, c2);
709 mul_add_c(a[1], b[1], c3, c1, c2);
710 mul_add_c(a[0], b[2], c3, c1, c2);
711 r[2] = c3;
712 c3 = 0;
713 mul_add_c(a[0], b[3], c1, c2, c3);
714 mul_add_c(a[1], b[2], c1, c2, c3);
715 mul_add_c(a[2], b[1], c1, c2, c3);
716 mul_add_c(a[3], b[0], c1, c2, c3);
717 r[3] = c1;
718 c1 = 0;
719 mul_add_c(a[3], b[1], c2, c3, c1);
720 mul_add_c(a[2], b[2], c2, c3, c1);
721 mul_add_c(a[1], b[3], c2, c3, c1);
722 r[4] = c2;
723 c2 = 0;
724 mul_add_c(a[2], b[3], c3, c1, c2);
725 mul_add_c(a[3], b[2], c3, c1, c2);
726 r[5] = c3;
727 c3 = 0;
728 mul_add_c(a[3], b[3], c1, c2, c3);
729 r[6] = c1;
730 r[7] = c2;
731 }
732
bn_sqr_comba8(BN_ULONG * r,const BN_ULONG * a)733 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
734 {
735 BN_ULONG c1, c2, c3;
736
737 c1 = 0;
738 c2 = 0;
739 c3 = 0;
740 sqr_add_c(a, 0, c1, c2, c3);
741 r[0] = c1;
742 c1 = 0;
743 sqr_add_c2(a, 1, 0, c2, c3, c1);
744 r[1] = c2;
745 c2 = 0;
746 sqr_add_c(a, 1, c3, c1, c2);
747 sqr_add_c2(a, 2, 0, c3, c1, c2);
748 r[2] = c3;
749 c3 = 0;
750 sqr_add_c2(a, 3, 0, c1, c2, c3);
751 sqr_add_c2(a, 2, 1, c1, c2, c3);
752 r[3] = c1;
753 c1 = 0;
754 sqr_add_c(a, 2, c2, c3, c1);
755 sqr_add_c2(a, 3, 1, c2, c3, c1);
756 sqr_add_c2(a, 4, 0, c2, c3, c1);
757 r[4] = c2;
758 c2 = 0;
759 sqr_add_c2(a, 5, 0, c3, c1, c2);
760 sqr_add_c2(a, 4, 1, c3, c1, c2);
761 sqr_add_c2(a, 3, 2, c3, c1, c2);
762 r[5] = c3;
763 c3 = 0;
764 sqr_add_c(a, 3, c1, c2, c3);
765 sqr_add_c2(a, 4, 2, c1, c2, c3);
766 sqr_add_c2(a, 5, 1, c1, c2, c3);
767 sqr_add_c2(a, 6, 0, c1, c2, c3);
768 r[6] = c1;
769 c1 = 0;
770 sqr_add_c2(a, 7, 0, c2, c3, c1);
771 sqr_add_c2(a, 6, 1, c2, c3, c1);
772 sqr_add_c2(a, 5, 2, c2, c3, c1);
773 sqr_add_c2(a, 4, 3, c2, c3, c1);
774 r[7] = c2;
775 c2 = 0;
776 sqr_add_c(a, 4, c3, c1, c2);
777 sqr_add_c2(a, 5, 3, c3, c1, c2);
778 sqr_add_c2(a, 6, 2, c3, c1, c2);
779 sqr_add_c2(a, 7, 1, c3, c1, c2);
780 r[8] = c3;
781 c3 = 0;
782 sqr_add_c2(a, 7, 2, c1, c2, c3);
783 sqr_add_c2(a, 6, 3, c1, c2, c3);
784 sqr_add_c2(a, 5, 4, c1, c2, c3);
785 r[9] = c1;
786 c1 = 0;
787 sqr_add_c(a, 5, c2, c3, c1);
788 sqr_add_c2(a, 6, 4, c2, c3, c1);
789 sqr_add_c2(a, 7, 3, c2, c3, c1);
790 r[10] = c2;
791 c2 = 0;
792 sqr_add_c2(a, 7, 4, c3, c1, c2);
793 sqr_add_c2(a, 6, 5, c3, c1, c2);
794 r[11] = c3;
795 c3 = 0;
796 sqr_add_c(a, 6, c1, c2, c3);
797 sqr_add_c2(a, 7, 5, c1, c2, c3);
798 r[12] = c1;
799 c1 = 0;
800 sqr_add_c2(a, 7, 6, c2, c3, c1);
801 r[13] = c2;
802 c2 = 0;
803 sqr_add_c(a, 7, c3, c1, c2);
804 r[14] = c3;
805 r[15] = c1;
806 }
807
bn_sqr_comba4(BN_ULONG * r,const BN_ULONG * a)808 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
809 {
810 BN_ULONG c1, c2, c3;
811
812 c1 = 0;
813 c2 = 0;
814 c3 = 0;
815 sqr_add_c(a, 0, c1, c2, c3);
816 r[0] = c1;
817 c1 = 0;
818 sqr_add_c2(a, 1, 0, c2, c3, c1);
819 r[1] = c2;
820 c2 = 0;
821 sqr_add_c(a, 1, c3, c1, c2);
822 sqr_add_c2(a, 2, 0, c3, c1, c2);
823 r[2] = c3;
824 c3 = 0;
825 sqr_add_c2(a, 3, 0, c1, c2, c3);
826 sqr_add_c2(a, 2, 1, c1, c2, c3);
827 r[3] = c1;
828 c1 = 0;
829 sqr_add_c(a, 2, c2, c3, c1);
830 sqr_add_c2(a, 3, 1, c2, c3, c1);
831 r[4] = c2;
832 c2 = 0;
833 sqr_add_c2(a, 3, 2, c3, c1, c2);
834 r[5] = c3;
835 c3 = 0;
836 sqr_add_c(a, 3, c1, c2, c3);
837 r[6] = c1;
838 r[7] = c2;
839 }
840
841 # ifdef OPENSSL_NO_ASM
842 # ifdef OPENSSL_BN_ASM_MONT
843 # include <alloca.h>
844 /*
845 * This is essentially reference implementation, which may or may not
846 * result in performance improvement. E.g. on IA-32 this routine was
847 * observed to give 40% faster rsa1024 private key operations and 10%
848 * faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only
849 * by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a
850 * reference implementation, one to be used as starting point for
851 * platform-specific assembler. Mentioned numbers apply to compiler
852 * generated code compiled with and without -DOPENSSL_BN_ASM_MONT and
853 * can vary not only from platform to platform, but even for compiler
854 * versions. Assembler vs. assembler improvement coefficients can
855 * [and are known to] differ and are to be documented elsewhere.
856 */
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0p,int num)857 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
858 const BN_ULONG *np, const BN_ULONG *n0p, int num)
859 {
860 BN_ULONG c0, c1, ml, *tp, n0;
861 # ifdef mul64
862 BN_ULONG mh;
863 # endif
864 volatile BN_ULONG *vp;
865 int i = 0, j;
866
867 # if 0 /* template for platform-specific
868 * implementation */
869 if (ap == bp)
870 return bn_sqr_mont(rp, ap, np, n0p, num);
871 # endif
872 vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
873
874 n0 = *n0p;
875
876 c0 = 0;
877 ml = bp[0];
878 # ifdef mul64
879 mh = HBITS(ml);
880 ml = LBITS(ml);
881 for (j = 0; j < num; ++j)
882 mul(tp[j], ap[j], ml, mh, c0);
883 # else
884 for (j = 0; j < num; ++j)
885 mul(tp[j], ap[j], ml, c0);
886 # endif
887
888 tp[num] = c0;
889 tp[num + 1] = 0;
890 goto enter;
891
892 for (i = 0; i < num; i++) {
893 c0 = 0;
894 ml = bp[i];
895 # ifdef mul64
896 mh = HBITS(ml);
897 ml = LBITS(ml);
898 for (j = 0; j < num; ++j)
899 mul_add(tp[j], ap[j], ml, mh, c0);
900 # else
901 for (j = 0; j < num; ++j)
902 mul_add(tp[j], ap[j], ml, c0);
903 # endif
904 c1 = (tp[num] + c0) & BN_MASK2;
905 tp[num] = c1;
906 tp[num + 1] = (c1 < c0 ? 1 : 0);
907 enter:
908 c1 = tp[0];
909 ml = (c1 * n0) & BN_MASK2;
910 c0 = 0;
911 # ifdef mul64
912 mh = HBITS(ml);
913 ml = LBITS(ml);
914 mul_add(c1, np[0], ml, mh, c0);
915 # else
916 mul_add(c1, ml, np[0], c0);
917 # endif
918 for (j = 1; j < num; j++) {
919 c1 = tp[j];
920 # ifdef mul64
921 mul_add(c1, np[j], ml, mh, c0);
922 # else
923 mul_add(c1, ml, np[j], c0);
924 # endif
925 tp[j - 1] = c1 & BN_MASK2;
926 }
927 c1 = (tp[num] + c0) & BN_MASK2;
928 tp[num - 1] = c1;
929 tp[num] = tp[num + 1] + (c1 < c0 ? 1 : 0);
930 }
931
932 if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
933 c0 = bn_sub_words(rp, tp, np, num);
934 if (tp[num] != 0 || c0 == 0) {
935 for (i = 0; i < num + 2; i++)
936 vp[i] = 0;
937 return 1;
938 }
939 }
940 for (i = 0; i < num; i++)
941 rp[i] = tp[i], vp[i] = 0;
942 vp[num] = 0;
943 vp[num + 1] = 0;
944 return 1;
945 }
946 # else
947 /*
948 * Return value of 0 indicates that multiplication/convolution was not
949 * performed to signal the caller to fall down to alternative/original
950 * code-path.
951 */
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0,int num)952 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
953 const BN_ULONG *np, const BN_ULONG *n0, int num)
954 {
955 return 0;
956 }
957 # endif /* OPENSSL_BN_ASM_MONT */
958 # endif
959
960 #else /* !BN_MUL_COMBA */
961
962 /* hmm... is it faster just to do a multiply? */
963 # undef bn_sqr_comba4
964 # undef bn_sqr_comba8
bn_sqr_comba4(BN_ULONG * r,const BN_ULONG * a)965 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
966 {
967 BN_ULONG t[8];
968 bn_sqr_normal(r, a, 4, t);
969 }
970
bn_sqr_comba8(BN_ULONG * r,const BN_ULONG * a)971 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
972 {
973 BN_ULONG t[16];
974 bn_sqr_normal(r, a, 8, t);
975 }
976
bn_mul_comba4(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)977 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
978 {
979 r[4] = bn_mul_words(&(r[0]), a, 4, b[0]);
980 r[5] = bn_mul_add_words(&(r[1]), a, 4, b[1]);
981 r[6] = bn_mul_add_words(&(r[2]), a, 4, b[2]);
982 r[7] = bn_mul_add_words(&(r[3]), a, 4, b[3]);
983 }
984
bn_mul_comba8(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)985 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
986 {
987 r[8] = bn_mul_words(&(r[0]), a, 8, b[0]);
988 r[9] = bn_mul_add_words(&(r[1]), a, 8, b[1]);
989 r[10] = bn_mul_add_words(&(r[2]), a, 8, b[2]);
990 r[11] = bn_mul_add_words(&(r[3]), a, 8, b[3]);
991 r[12] = bn_mul_add_words(&(r[4]), a, 8, b[4]);
992 r[13] = bn_mul_add_words(&(r[5]), a, 8, b[5]);
993 r[14] = bn_mul_add_words(&(r[6]), a, 8, b[6]);
994 r[15] = bn_mul_add_words(&(r[7]), a, 8, b[7]);
995 }
996
997 # ifdef OPENSSL_NO_ASM
998 # ifdef OPENSSL_BN_ASM_MONT
999 # 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)1000 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
1001 const BN_ULONG *np, const BN_ULONG *n0p, int num)
1002 {
1003 BN_ULONG c0, c1, *tp, n0 = *n0p;
1004 volatile BN_ULONG *vp;
1005 int i = 0, j;
1006
1007 vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
1008
1009 for (i = 0; i <= num; i++)
1010 tp[i] = 0;
1011
1012 for (i = 0; i < num; i++) {
1013 c0 = bn_mul_add_words(tp, ap, num, bp[i]);
1014 c1 = (tp[num] + c0) & BN_MASK2;
1015 tp[num] = c1;
1016 tp[num + 1] = (c1 < c0 ? 1 : 0);
1017
1018 c0 = bn_mul_add_words(tp, np, num, tp[0] * n0);
1019 c1 = (tp[num] + c0) & BN_MASK2;
1020 tp[num] = c1;
1021 tp[num + 1] += (c1 < c0 ? 1 : 0);
1022 for (j = 0; j <= num; j++)
1023 tp[j] = tp[j + 1];
1024 }
1025
1026 if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
1027 c0 = bn_sub_words(rp, tp, np, num);
1028 if (tp[num] != 0 || c0 == 0) {
1029 for (i = 0; i < num + 2; i++)
1030 vp[i] = 0;
1031 return 1;
1032 }
1033 }
1034 for (i = 0; i < num; i++)
1035 rp[i] = tp[i], vp[i] = 0;
1036 vp[num] = 0;
1037 vp[num + 1] = 0;
1038 return 1;
1039 }
1040 # 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)1041 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
1042 const BN_ULONG *np, const BN_ULONG *n0, int num)
1043 {
1044 return 0;
1045 }
1046 # endif /* OPENSSL_BN_ASM_MONT */
1047 # endif
1048
1049 #endif /* !BN_MUL_COMBA */
1050