1 /*
2 * Copyright 1995-2016 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 = b[0];
385 r[0] = (t1 - t2 - c) & BN_MASK2;
386 if (t1 != t2)
387 c = (t1 < t2);
388 t1 = a[1];
389 t2 = b[1];
390 r[1] = (t1 - t2 - c) & BN_MASK2;
391 if (t1 != t2)
392 c = (t1 < t2);
393 t1 = a[2];
394 t2 = b[2];
395 r[2] = (t1 - t2 - c) & BN_MASK2;
396 if (t1 != t2)
397 c = (t1 < t2);
398 t1 = a[3];
399 t2 = b[3];
400 r[3] = (t1 - t2 - c) & BN_MASK2;
401 if (t1 != t2)
402 c = (t1 < t2);
403 a += 4;
404 b += 4;
405 r += 4;
406 n -= 4;
407 }
408 #endif
409 while (n) {
410 t1 = a[0];
411 t2 = b[0];
412 r[0] = (t1 - t2 - c) & BN_MASK2;
413 if (t1 != t2)
414 c = (t1 < t2);
415 a++;
416 b++;
417 r++;
418 n--;
419 }
420 return c;
421 }
422
423 #if defined(BN_MUL_COMBA) && !defined(OPENSSL_SMALL_FOOTPRINT)
424
425 /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
426 /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
427 /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
428 /*
429 * sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number
430 * c=(c2,c1,c0)
431 */
432
433 # ifdef BN_LLONG
434 /*
435 * Keep in mind that additions to multiplication result can not
436 * overflow, because its high half cannot be all-ones.
437 */
438 # define mul_add_c(a,b,c0,c1,c2) do { \
439 BN_ULONG hi; \
440 BN_ULLONG t = (BN_ULLONG)(a)*(b); \
441 t += c0; /* no carry */ \
442 c0 = (BN_ULONG)Lw(t); \
443 hi = (BN_ULONG)Hw(t); \
444 c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
445 } while(0)
446
447 # define mul_add_c2(a,b,c0,c1,c2) do { \
448 BN_ULONG hi; \
449 BN_ULLONG t = (BN_ULLONG)(a)*(b); \
450 BN_ULLONG tt = t+c0; /* no carry */ \
451 c0 = (BN_ULONG)Lw(tt); \
452 hi = (BN_ULONG)Hw(tt); \
453 c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
454 t += c0; /* no carry */ \
455 c0 = (BN_ULONG)Lw(t); \
456 hi = (BN_ULONG)Hw(t); \
457 c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
458 } while(0)
459
460 # define sqr_add_c(a,i,c0,c1,c2) do { \
461 BN_ULONG hi; \
462 BN_ULLONG t = (BN_ULLONG)a[i]*a[i]; \
463 t += c0; /* no carry */ \
464 c0 = (BN_ULONG)Lw(t); \
465 hi = (BN_ULONG)Hw(t); \
466 c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
467 } while(0)
468
469 # define sqr_add_c2(a,i,j,c0,c1,c2) \
470 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
471
472 # elif defined(BN_UMULT_LOHI)
473 /*
474 * Keep in mind that additions to hi can not overflow, because
475 * the high word of a multiplication result cannot be all-ones.
476 */
477 # define mul_add_c(a,b,c0,c1,c2) do { \
478 BN_ULONG ta = (a), tb = (b); \
479 BN_ULONG lo, hi; \
480 BN_UMULT_LOHI(lo,hi,ta,tb); \
481 c0 += lo; hi += (c0<lo)?1:0; \
482 c1 += hi; c2 += (c1<hi)?1:0; \
483 } while(0)
484
485 # define mul_add_c2(a,b,c0,c1,c2) do { \
486 BN_ULONG ta = (a), tb = (b); \
487 BN_ULONG lo, hi, tt; \
488 BN_UMULT_LOHI(lo,hi,ta,tb); \
489 c0 += lo; tt = hi+((c0<lo)?1:0); \
490 c1 += tt; c2 += (c1<tt)?1:0; \
491 c0 += lo; hi += (c0<lo)?1:0; \
492 c1 += hi; c2 += (c1<hi)?1:0; \
493 } while(0)
494
495 # define sqr_add_c(a,i,c0,c1,c2) do { \
496 BN_ULONG ta = (a)[i]; \
497 BN_ULONG lo, hi; \
498 BN_UMULT_LOHI(lo,hi,ta,ta); \
499 c0 += lo; hi += (c0<lo)?1:0; \
500 c1 += hi; c2 += (c1<hi)?1:0; \
501 } while(0)
502
503 # define sqr_add_c2(a,i,j,c0,c1,c2) \
504 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
505
506 # elif defined(BN_UMULT_HIGH)
507 /*
508 * Keep in mind that additions to hi can not overflow, because
509 * the high word of a multiplication result cannot be all-ones.
510 */
511 # define mul_add_c(a,b,c0,c1,c2) do { \
512 BN_ULONG ta = (a), tb = (b); \
513 BN_ULONG lo = ta * tb; \
514 BN_ULONG hi = BN_UMULT_HIGH(ta,tb); \
515 c0 += lo; hi += (c0<lo)?1:0; \
516 c1 += hi; c2 += (c1<hi)?1:0; \
517 } while(0)
518
519 # define mul_add_c2(a,b,c0,c1,c2) do { \
520 BN_ULONG ta = (a), tb = (b), tt; \
521 BN_ULONG lo = ta * tb; \
522 BN_ULONG hi = BN_UMULT_HIGH(ta,tb); \
523 c0 += lo; tt = hi + ((c0<lo)?1:0); \
524 c1 += tt; c2 += (c1<tt)?1:0; \
525 c0 += lo; hi += (c0<lo)?1:0; \
526 c1 += hi; c2 += (c1<hi)?1:0; \
527 } while(0)
528
529 # define sqr_add_c(a,i,c0,c1,c2) do { \
530 BN_ULONG ta = (a)[i]; \
531 BN_ULONG lo = ta * ta; \
532 BN_ULONG hi = BN_UMULT_HIGH(ta,ta); \
533 c0 += lo; hi += (c0<lo)?1:0; \
534 c1 += hi; c2 += (c1<hi)?1:0; \
535 } while(0)
536
537 # define sqr_add_c2(a,i,j,c0,c1,c2) \
538 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
539
540 # else /* !BN_LLONG */
541 /*
542 * Keep in mind that additions to hi can not overflow, because
543 * the high word of a multiplication result cannot be all-ones.
544 */
545 # define mul_add_c(a,b,c0,c1,c2) do { \
546 BN_ULONG lo = LBITS(a), hi = HBITS(a); \
547 BN_ULONG bl = LBITS(b), bh = HBITS(b); \
548 mul64(lo,hi,bl,bh); \
549 c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \
550 c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
551 } while(0)
552
553 # define mul_add_c2(a,b,c0,c1,c2) do { \
554 BN_ULONG tt; \
555 BN_ULONG lo = LBITS(a), hi = HBITS(a); \
556 BN_ULONG bl = LBITS(b), bh = HBITS(b); \
557 mul64(lo,hi,bl,bh); \
558 tt = hi; \
559 c0 = (c0+lo)&BN_MASK2; if (c0<lo) tt++; \
560 c1 = (c1+tt)&BN_MASK2; if (c1<tt) c2++; \
561 c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \
562 c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
563 } while(0)
564
565 # define sqr_add_c(a,i,c0,c1,c2) do { \
566 BN_ULONG lo, hi; \
567 sqr64(lo,hi,(a)[i]); \
568 c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \
569 c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
570 } while(0)
571
572 # define sqr_add_c2(a,i,j,c0,c1,c2) \
573 mul_add_c2((a)[i],(a)[j],c0,c1,c2)
574 # endif /* !BN_LLONG */
575
bn_mul_comba8(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)576 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
577 {
578 BN_ULONG c1, c2, c3;
579
580 c1 = 0;
581 c2 = 0;
582 c3 = 0;
583 mul_add_c(a[0], b[0], c1, c2, c3);
584 r[0] = c1;
585 c1 = 0;
586 mul_add_c(a[0], b[1], c2, c3, c1);
587 mul_add_c(a[1], b[0], c2, c3, c1);
588 r[1] = c2;
589 c2 = 0;
590 mul_add_c(a[2], b[0], c3, c1, c2);
591 mul_add_c(a[1], b[1], c3, c1, c2);
592 mul_add_c(a[0], b[2], c3, c1, c2);
593 r[2] = c3;
594 c3 = 0;
595 mul_add_c(a[0], b[3], c1, c2, c3);
596 mul_add_c(a[1], b[2], c1, c2, c3);
597 mul_add_c(a[2], b[1], c1, c2, c3);
598 mul_add_c(a[3], b[0], c1, c2, c3);
599 r[3] = c1;
600 c1 = 0;
601 mul_add_c(a[4], b[0], c2, c3, c1);
602 mul_add_c(a[3], b[1], c2, c3, c1);
603 mul_add_c(a[2], b[2], c2, c3, c1);
604 mul_add_c(a[1], b[3], c2, c3, c1);
605 mul_add_c(a[0], b[4], c2, c3, c1);
606 r[4] = c2;
607 c2 = 0;
608 mul_add_c(a[0], b[5], c3, c1, c2);
609 mul_add_c(a[1], b[4], c3, c1, c2);
610 mul_add_c(a[2], b[3], c3, c1, c2);
611 mul_add_c(a[3], b[2], c3, c1, c2);
612 mul_add_c(a[4], b[1], c3, c1, c2);
613 mul_add_c(a[5], b[0], c3, c1, c2);
614 r[5] = c3;
615 c3 = 0;
616 mul_add_c(a[6], b[0], c1, c2, c3);
617 mul_add_c(a[5], b[1], c1, c2, c3);
618 mul_add_c(a[4], b[2], c1, c2, c3);
619 mul_add_c(a[3], b[3], c1, c2, c3);
620 mul_add_c(a[2], b[4], c1, c2, c3);
621 mul_add_c(a[1], b[5], c1, c2, c3);
622 mul_add_c(a[0], b[6], c1, c2, c3);
623 r[6] = c1;
624 c1 = 0;
625 mul_add_c(a[0], b[7], c2, c3, c1);
626 mul_add_c(a[1], b[6], c2, c3, c1);
627 mul_add_c(a[2], b[5], c2, c3, c1);
628 mul_add_c(a[3], b[4], c2, c3, c1);
629 mul_add_c(a[4], b[3], c2, c3, c1);
630 mul_add_c(a[5], b[2], c2, c3, c1);
631 mul_add_c(a[6], b[1], c2, c3, c1);
632 mul_add_c(a[7], b[0], c2, c3, c1);
633 r[7] = c2;
634 c2 = 0;
635 mul_add_c(a[7], b[1], c3, c1, c2);
636 mul_add_c(a[6], b[2], c3, c1, c2);
637 mul_add_c(a[5], b[3], c3, c1, c2);
638 mul_add_c(a[4], b[4], c3, c1, c2);
639 mul_add_c(a[3], b[5], c3, c1, c2);
640 mul_add_c(a[2], b[6], c3, c1, c2);
641 mul_add_c(a[1], b[7], c3, c1, c2);
642 r[8] = c3;
643 c3 = 0;
644 mul_add_c(a[2], b[7], c1, c2, c3);
645 mul_add_c(a[3], b[6], c1, c2, c3);
646 mul_add_c(a[4], b[5], c1, c2, c3);
647 mul_add_c(a[5], b[4], c1, c2, c3);
648 mul_add_c(a[6], b[3], c1, c2, c3);
649 mul_add_c(a[7], b[2], c1, c2, c3);
650 r[9] = c1;
651 c1 = 0;
652 mul_add_c(a[7], b[3], c2, c3, c1);
653 mul_add_c(a[6], b[4], c2, c3, c1);
654 mul_add_c(a[5], b[5], c2, c3, c1);
655 mul_add_c(a[4], b[6], c2, c3, c1);
656 mul_add_c(a[3], b[7], c2, c3, c1);
657 r[10] = c2;
658 c2 = 0;
659 mul_add_c(a[4], b[7], c3, c1, c2);
660 mul_add_c(a[5], b[6], c3, c1, c2);
661 mul_add_c(a[6], b[5], c3, c1, c2);
662 mul_add_c(a[7], b[4], c3, c1, c2);
663 r[11] = c3;
664 c3 = 0;
665 mul_add_c(a[7], b[5], c1, c2, c3);
666 mul_add_c(a[6], b[6], c1, c2, c3);
667 mul_add_c(a[5], b[7], c1, c2, c3);
668 r[12] = c1;
669 c1 = 0;
670 mul_add_c(a[6], b[7], c2, c3, c1);
671 mul_add_c(a[7], b[6], c2, c3, c1);
672 r[13] = c2;
673 c2 = 0;
674 mul_add_c(a[7], b[7], c3, c1, c2);
675 r[14] = c3;
676 r[15] = c1;
677 }
678
bn_mul_comba4(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)679 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
680 {
681 BN_ULONG c1, c2, c3;
682
683 c1 = 0;
684 c2 = 0;
685 c3 = 0;
686 mul_add_c(a[0], b[0], c1, c2, c3);
687 r[0] = c1;
688 c1 = 0;
689 mul_add_c(a[0], b[1], c2, c3, c1);
690 mul_add_c(a[1], b[0], c2, c3, c1);
691 r[1] = c2;
692 c2 = 0;
693 mul_add_c(a[2], b[0], c3, c1, c2);
694 mul_add_c(a[1], b[1], c3, c1, c2);
695 mul_add_c(a[0], b[2], c3, c1, c2);
696 r[2] = c3;
697 c3 = 0;
698 mul_add_c(a[0], b[3], c1, c2, c3);
699 mul_add_c(a[1], b[2], c1, c2, c3);
700 mul_add_c(a[2], b[1], c1, c2, c3);
701 mul_add_c(a[3], b[0], c1, c2, c3);
702 r[3] = c1;
703 c1 = 0;
704 mul_add_c(a[3], b[1], c2, c3, c1);
705 mul_add_c(a[2], b[2], c2, c3, c1);
706 mul_add_c(a[1], b[3], c2, c3, c1);
707 r[4] = c2;
708 c2 = 0;
709 mul_add_c(a[2], b[3], c3, c1, c2);
710 mul_add_c(a[3], b[2], c3, c1, c2);
711 r[5] = c3;
712 c3 = 0;
713 mul_add_c(a[3], b[3], c1, c2, c3);
714 r[6] = c1;
715 r[7] = c2;
716 }
717
bn_sqr_comba8(BN_ULONG * r,const BN_ULONG * a)718 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
719 {
720 BN_ULONG c1, c2, c3;
721
722 c1 = 0;
723 c2 = 0;
724 c3 = 0;
725 sqr_add_c(a, 0, c1, c2, c3);
726 r[0] = c1;
727 c1 = 0;
728 sqr_add_c2(a, 1, 0, c2, c3, c1);
729 r[1] = c2;
730 c2 = 0;
731 sqr_add_c(a, 1, c3, c1, c2);
732 sqr_add_c2(a, 2, 0, c3, c1, c2);
733 r[2] = c3;
734 c3 = 0;
735 sqr_add_c2(a, 3, 0, c1, c2, c3);
736 sqr_add_c2(a, 2, 1, c1, c2, c3);
737 r[3] = c1;
738 c1 = 0;
739 sqr_add_c(a, 2, c2, c3, c1);
740 sqr_add_c2(a, 3, 1, c2, c3, c1);
741 sqr_add_c2(a, 4, 0, c2, c3, c1);
742 r[4] = c2;
743 c2 = 0;
744 sqr_add_c2(a, 5, 0, c3, c1, c2);
745 sqr_add_c2(a, 4, 1, c3, c1, c2);
746 sqr_add_c2(a, 3, 2, c3, c1, c2);
747 r[5] = c3;
748 c3 = 0;
749 sqr_add_c(a, 3, c1, c2, c3);
750 sqr_add_c2(a, 4, 2, c1, c2, c3);
751 sqr_add_c2(a, 5, 1, c1, c2, c3);
752 sqr_add_c2(a, 6, 0, c1, c2, c3);
753 r[6] = c1;
754 c1 = 0;
755 sqr_add_c2(a, 7, 0, c2, c3, c1);
756 sqr_add_c2(a, 6, 1, c2, c3, c1);
757 sqr_add_c2(a, 5, 2, c2, c3, c1);
758 sqr_add_c2(a, 4, 3, c2, c3, c1);
759 r[7] = c2;
760 c2 = 0;
761 sqr_add_c(a, 4, c3, c1, c2);
762 sqr_add_c2(a, 5, 3, c3, c1, c2);
763 sqr_add_c2(a, 6, 2, c3, c1, c2);
764 sqr_add_c2(a, 7, 1, c3, c1, c2);
765 r[8] = c3;
766 c3 = 0;
767 sqr_add_c2(a, 7, 2, c1, c2, c3);
768 sqr_add_c2(a, 6, 3, c1, c2, c3);
769 sqr_add_c2(a, 5, 4, c1, c2, c3);
770 r[9] = c1;
771 c1 = 0;
772 sqr_add_c(a, 5, c2, c3, c1);
773 sqr_add_c2(a, 6, 4, c2, c3, c1);
774 sqr_add_c2(a, 7, 3, c2, c3, c1);
775 r[10] = c2;
776 c2 = 0;
777 sqr_add_c2(a, 7, 4, c3, c1, c2);
778 sqr_add_c2(a, 6, 5, c3, c1, c2);
779 r[11] = c3;
780 c3 = 0;
781 sqr_add_c(a, 6, c1, c2, c3);
782 sqr_add_c2(a, 7, 5, c1, c2, c3);
783 r[12] = c1;
784 c1 = 0;
785 sqr_add_c2(a, 7, 6, c2, c3, c1);
786 r[13] = c2;
787 c2 = 0;
788 sqr_add_c(a, 7, c3, c1, c2);
789 r[14] = c3;
790 r[15] = c1;
791 }
792
bn_sqr_comba4(BN_ULONG * r,const BN_ULONG * a)793 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
794 {
795 BN_ULONG c1, c2, c3;
796
797 c1 = 0;
798 c2 = 0;
799 c3 = 0;
800 sqr_add_c(a, 0, c1, c2, c3);
801 r[0] = c1;
802 c1 = 0;
803 sqr_add_c2(a, 1, 0, c2, c3, c1);
804 r[1] = c2;
805 c2 = 0;
806 sqr_add_c(a, 1, c3, c1, c2);
807 sqr_add_c2(a, 2, 0, c3, c1, c2);
808 r[2] = c3;
809 c3 = 0;
810 sqr_add_c2(a, 3, 0, c1, c2, c3);
811 sqr_add_c2(a, 2, 1, c1, c2, c3);
812 r[3] = c1;
813 c1 = 0;
814 sqr_add_c(a, 2, c2, c3, c1);
815 sqr_add_c2(a, 3, 1, c2, c3, c1);
816 r[4] = c2;
817 c2 = 0;
818 sqr_add_c2(a, 3, 2, c3, c1, c2);
819 r[5] = c3;
820 c3 = 0;
821 sqr_add_c(a, 3, c1, c2, c3);
822 r[6] = c1;
823 r[7] = c2;
824 }
825
826 # ifdef OPENSSL_NO_ASM
827 # ifdef OPENSSL_BN_ASM_MONT
828 # include <alloca.h>
829 /*
830 * This is essentially reference implementation, which may or may not
831 * result in performance improvement. E.g. on IA-32 this routine was
832 * observed to give 40% faster rsa1024 private key operations and 10%
833 * faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only
834 * by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a
835 * reference implementation, one to be used as starting point for
836 * platform-specific assembler. Mentioned numbers apply to compiler
837 * generated code compiled with and without -DOPENSSL_BN_ASM_MONT and
838 * can vary not only from platform to platform, but even for compiler
839 * versions. Assembler vs. assembler improvement coefficients can
840 * [and are known to] differ and are to be documented elsewhere.
841 */
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0p,int num)842 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
843 const BN_ULONG *np, const BN_ULONG *n0p, int num)
844 {
845 BN_ULONG c0, c1, ml, *tp, n0;
846 # ifdef mul64
847 BN_ULONG mh;
848 # endif
849 volatile BN_ULONG *vp;
850 int i = 0, j;
851
852 # if 0 /* template for platform-specific
853 * implementation */
854 if (ap == bp)
855 return bn_sqr_mont(rp, ap, np, n0p, num);
856 # endif
857 vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
858
859 n0 = *n0p;
860
861 c0 = 0;
862 ml = bp[0];
863 # ifdef mul64
864 mh = HBITS(ml);
865 ml = LBITS(ml);
866 for (j = 0; j < num; ++j)
867 mul(tp[j], ap[j], ml, mh, c0);
868 # else
869 for (j = 0; j < num; ++j)
870 mul(tp[j], ap[j], ml, c0);
871 # endif
872
873 tp[num] = c0;
874 tp[num + 1] = 0;
875 goto enter;
876
877 for (i = 0; i < num; i++) {
878 c0 = 0;
879 ml = bp[i];
880 # ifdef mul64
881 mh = HBITS(ml);
882 ml = LBITS(ml);
883 for (j = 0; j < num; ++j)
884 mul_add(tp[j], ap[j], ml, mh, c0);
885 # else
886 for (j = 0; j < num; ++j)
887 mul_add(tp[j], ap[j], ml, c0);
888 # endif
889 c1 = (tp[num] + c0) & BN_MASK2;
890 tp[num] = c1;
891 tp[num + 1] = (c1 < c0 ? 1 : 0);
892 enter:
893 c1 = tp[0];
894 ml = (c1 * n0) & BN_MASK2;
895 c0 = 0;
896 # ifdef mul64
897 mh = HBITS(ml);
898 ml = LBITS(ml);
899 mul_add(c1, np[0], ml, mh, c0);
900 # else
901 mul_add(c1, ml, np[0], c0);
902 # endif
903 for (j = 1; j < num; j++) {
904 c1 = tp[j];
905 # ifdef mul64
906 mul_add(c1, np[j], ml, mh, c0);
907 # else
908 mul_add(c1, ml, np[j], c0);
909 # endif
910 tp[j - 1] = c1 & BN_MASK2;
911 }
912 c1 = (tp[num] + c0) & BN_MASK2;
913 tp[num - 1] = c1;
914 tp[num] = tp[num + 1] + (c1 < c0 ? 1 : 0);
915 }
916
917 if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
918 c0 = bn_sub_words(rp, tp, np, num);
919 if (tp[num] != 0 || c0 == 0) {
920 for (i = 0; i < num + 2; i++)
921 vp[i] = 0;
922 return 1;
923 }
924 }
925 for (i = 0; i < num; i++)
926 rp[i] = tp[i], vp[i] = 0;
927 vp[num] = 0;
928 vp[num + 1] = 0;
929 return 1;
930 }
931 # else
932 /*
933 * Return value of 0 indicates that multiplication/convolution was not
934 * performed to signal the caller to fall down to alternative/original
935 * code-path.
936 */
bn_mul_mont(BN_ULONG * rp,const BN_ULONG * ap,const BN_ULONG * bp,const BN_ULONG * np,const BN_ULONG * n0,int num)937 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
938 const BN_ULONG *np, const BN_ULONG *n0, int num)
939 {
940 return 0;
941 }
942 # endif /* OPENSSL_BN_ASM_MONT */
943 # endif
944
945 #else /* !BN_MUL_COMBA */
946
947 /* hmm... is it faster just to do a multiply? */
bn_sqr_comba4(BN_ULONG * r,const BN_ULONG * a)948 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
949 {
950 BN_ULONG t[8];
951 bn_sqr_normal(r, a, 4, t);
952 }
953
bn_sqr_comba8(BN_ULONG * r,const BN_ULONG * a)954 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
955 {
956 BN_ULONG t[16];
957 bn_sqr_normal(r, a, 8, t);
958 }
959
bn_mul_comba4(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)960 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
961 {
962 r[4] = bn_mul_words(&(r[0]), a, 4, b[0]);
963 r[5] = bn_mul_add_words(&(r[1]), a, 4, b[1]);
964 r[6] = bn_mul_add_words(&(r[2]), a, 4, b[2]);
965 r[7] = bn_mul_add_words(&(r[3]), a, 4, b[3]);
966 }
967
bn_mul_comba8(BN_ULONG * r,BN_ULONG * a,BN_ULONG * b)968 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
969 {
970 r[8] = bn_mul_words(&(r[0]), a, 8, b[0]);
971 r[9] = bn_mul_add_words(&(r[1]), a, 8, b[1]);
972 r[10] = bn_mul_add_words(&(r[2]), a, 8, b[2]);
973 r[11] = bn_mul_add_words(&(r[3]), a, 8, b[3]);
974 r[12] = bn_mul_add_words(&(r[4]), a, 8, b[4]);
975 r[13] = bn_mul_add_words(&(r[5]), a, 8, b[5]);
976 r[14] = bn_mul_add_words(&(r[6]), a, 8, b[6]);
977 r[15] = bn_mul_add_words(&(r[7]), a, 8, b[7]);
978 }
979
980 # ifdef OPENSSL_NO_ASM
981 # ifdef OPENSSL_BN_ASM_MONT
982 # 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)983 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
984 const BN_ULONG *np, const BN_ULONG *n0p, int num)
985 {
986 BN_ULONG c0, c1, *tp, n0 = *n0p;
987 volatile BN_ULONG *vp;
988 int i = 0, j;
989
990 vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
991
992 for (i = 0; i <= num; i++)
993 tp[i] = 0;
994
995 for (i = 0; i < num; i++) {
996 c0 = bn_mul_add_words(tp, ap, num, bp[i]);
997 c1 = (tp[num] + c0) & BN_MASK2;
998 tp[num] = c1;
999 tp[num + 1] = (c1 < c0 ? 1 : 0);
1000
1001 c0 = bn_mul_add_words(tp, np, num, tp[0] * n0);
1002 c1 = (tp[num] + c0) & BN_MASK2;
1003 tp[num] = c1;
1004 tp[num + 1] += (c1 < c0 ? 1 : 0);
1005 for (j = 0; j <= num; j++)
1006 tp[j] = tp[j + 1];
1007 }
1008
1009 if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
1010 c0 = bn_sub_words(rp, tp, np, num);
1011 if (tp[num] != 0 || c0 == 0) {
1012 for (i = 0; i < num + 2; i++)
1013 vp[i] = 0;
1014 return 1;
1015 }
1016 }
1017 for (i = 0; i < num; i++)
1018 rp[i] = tp[i], vp[i] = 0;
1019 vp[num] = 0;
1020 vp[num + 1] = 0;
1021 return 1;
1022 }
1023 # 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)1024 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
1025 const BN_ULONG *np, const BN_ULONG *n0, int num)
1026 {
1027 return 0;
1028 }
1029 # endif /* OPENSSL_BN_ASM_MONT */
1030 # endif
1031
1032 #endif /* !BN_MUL_COMBA */
1033
