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1 /* bigint.c */
2 /*
3     This file is part of the AVR-Crypto-Lib.
4     Copyright (C) 2008  Daniel Otte (daniel.otte@rub.de)
5
6     This program is free software: you can redistribute it and/or modify
7     it under the terms of the GNU General Public License as published by
8     the Free Software Foundation, either version 3 of the License, or
9     (at your option) any later version.
10
11     This program is distributed in the hope that it will be useful,
12     but WITHOUT ANY WARRANTY; without even the implied warranty of
13     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
14     GNU General Public License for more details.
15
16     You should have received a copy of the GNU General Public License
17     along with this program.  If not, see <http://www.gnu.org/licenses/>.
18 */
19 /**
20  * \file                bigint.c
21  * \author              Daniel Otte
22  * \date                2010-02-22
23  * 
24  * \license         GPLv3 or later
25  * 
26  */
27  
28
29 #define STRING2(x) #x
30 #define STRING(x) STRING2(x)
31 #define STR_LINE STRING(__LINE__)
32
33 #include "bigint.h"
34 #include <string.h>
35 /*
36 #include "cli.h"
37 #include "bigint_io.h"
38 */
39 #ifndef MAX
40  #define MAX(a,b) (((a)>(b))?(a):(b))
41 #endif
42
43 #ifndef MIN
44  #define MIN(a,b) (((a)<(b))?(a):(b))
45 #endif
46
47 #define SET_FBS(a, v) do{(a)->info &=0xF8; (a)->info |= (v);}while(0)
48 #define GET_FBS(a)   ((a)->info&BIGINT_FBS_MASK)
49 #define SET_NEG(a)   (a)->info |= BIGINT_NEG_MASK
50 #define SET_POS(a)   (a)->info &= ~BIGINT_NEG_MASK
51 #define XCHG(a,b)    do{(a)^=(b); (b)^=(a); (a)^=(b);}while(0)
52 #define XCHG_PTR(a,b)    do{ a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
53                                  b = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
54                                  a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b)));}while(0)
55
56 #define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
57
58 /******************************************************************************/
59 void bigint_adjust(bigint_t* a){
60         while(a->length_B!=0 && a->wordv[a->length_B-1]==0){
61                 a->length_B--;
62         }
63         if(a->length_B==0){
64                 a->info=0;
65                 return;
66         }
67         uint8_t t;
68         uint8_t i = 0x07;
69         t = a->wordv[a->length_B-1];
70         while((t&0x80)==0 && i){
71                 t<<=1;
72                 i--;
73         }
74         SET_FBS(a, i);
75 }
76
77 /******************************************************************************/
78
79 void bigint_copy(bigint_t* dest, const bigint_t* src){
80         memcpy(dest->wordv, src->wordv, src->length_B);
81         dest->length_B = src->length_B;
82         dest->info = src->info;
83 }
84
85 /******************************************************************************/
86
87 /* this should be implemented in assembly */
88 /*
89 void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
90         uint16_t t=0, i;
91         if(a->length_B < b->length_B){
92                 XCHG_PTR(a,b);
93         }
94         for(i=0; i<b->length_B; ++i){
95                 t = a->wordv[i] + b->wordv[i] + t;
96                 dest->wordv[i] = (uint8_t)t;
97                 t>>=8;
98         }
99         for(; i<a->length_B; ++i){
100                 t = a->wordv[i] + t;
101                 dest->wordv[i] = (uint8_t)t;
102                 t>>=8;
103         }
104         dest->wordv[i++] = t;
105         dest->length_B = i;
106         bigint_adjust(dest);
107 }
108 */
109 /******************************************************************************/
110
111 /* this should be implemented in assembly */
112 void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
113         uint16_t i,j=0;
114         uint16_t t=0;
115         if(scale>dest->length_B)
116                 memset(dest->wordv+dest->length_B, 0, scale-dest->length_B);
117         for(i=scale; i<a->length_B+scale; ++i,++j){
118                 t = a->wordv[j] + t;
119                 if(dest->length_B>i){
120                         t += dest->wordv[i];
121                 }
122                 dest->wordv[i] = (uint8_t)t;
123                 t>>=8;
124         }
125         while(t){
126                 if(dest->length_B>i){
127                         t = dest->wordv[i] + t;
128                 }
129                 dest->wordv[i] = (uint8_t)t;
130                 t>>=8;
131                 ++i;
132         }
133         if(dest->length_B < i){
134                 dest->length_B = i;
135         }
136         bigint_adjust(dest);
137 }
138
139 /******************************************************************************/
140
141 /* this should be implemented in assembly */
142 void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
143         int8_t borrow=0;
144         int8_t  r;
145         int16_t t;
146         uint16_t i, min, max;
147         min = MIN(a->length_B, b->length_B);
148         max = MAX(a->length_B, b->length_B);
149         r = bigint_cmp_u(a,b);
150         if(r==0){
151                 dest->length_B = 0;
152                 dest->wordv[0] = 0;
153                 bigint_adjust(dest);
154                 return;
155         }
156         if(b->length_B==0){
157                 dest->length_B = a->length_B;
158                 memcpy(dest->wordv, a->wordv, a->length_B);
159                 dest->info = a->info;
160                 SET_POS(dest);
161                 return;
162         }
163         if(a->length_B==0){
164                         dest->length_B = b->length_B;
165                         memcpy(dest->wordv, b->wordv, b->length_B);
166                         dest->info = b->info;
167                         SET_NEG(dest);
168                         return;
169         }
170         if(r<0){
171                 bigint_sub_u(dest, b, a);
172                 SET_NEG(dest);
173         }else{
174                 for(i=0; i<min; ++i){
175                         t = a->wordv[i] - b->wordv[i] - borrow;
176                         if(t<0){
177                                 borrow = 1;
178                                 dest->wordv[i]=(uint8_t)t;
179                         }else{
180                                 borrow = 0;
181                                 dest->wordv[i]=(uint8_t)t;
182                         }
183                 }
184                 for(;i<max; ++i){
185                         t = a->wordv[i] - borrow;
186                         if(t<0){
187                                 borrow = 1;
188                                 dest->wordv[i]=(uint8_t)t;
189                         }else{
190                                 borrow = 0;
191                                 dest->wordv[i]=(uint8_t)t;
192                         }
193
194                 }
195                 SET_POS(dest);
196                 dest->length_B = i;
197                 bigint_adjust(dest);
198         }
199 }
200
201 /******************************************************************************/
202
203 int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
204         if(a->length_B > b->length_B){
205                 return 1;
206         }
207         if(a->length_B < b->length_B){
208                 return -1;
209         }
210         if(a->length_B==0){
211                 return 0;
212         }
213         uint16_t i;
214         i = a->length_B-1;
215         do{
216                 if(a->wordv[i]!=b->wordv[i]){
217                         if(a->wordv[i]>b->wordv[i]){
218                                 return 1;
219                         }else{
220                                 return -1;
221                         }
222                 }
223         }while(i--);
224         return 0;
225 }
226
227 /******************************************************************************/
228
229 void bigint_add_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
230         uint8_t s;
231         s  = GET_SIGN(a)?2:0;
232         s |= GET_SIGN(b)?1:0;
233         switch(s){
234                 case 0: /* both positive */
235                         bigint_add_u(dest, a,b);
236                         SET_POS(dest);
237                         break;
238                 case 1: /* a positive, b negative */
239                         bigint_sub_u(dest, a, b);
240                         break;
241                 case 2: /* a negative, b positive */
242                         bigint_sub_u(dest, b, a);
243                         break;
244                 case 3: /* both negative */
245                         bigint_add_u(dest, a, b);
246                         SET_NEG(dest);
247                         break;
248                 default: /* how can this happen?*/
249                         break;
250         }
251 }
252
253 /******************************************************************************/
254
255 void bigint_sub_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
256         uint8_t s;
257         s  = GET_SIGN(a)?2:0;
258         s |= GET_SIGN(b)?1:0;
259         switch(s){
260                 case 0: /* both positive */
261                         bigint_sub_u(dest, a,b);
262                         break;
263                 case 1: /* a positive, b negative */
264                         bigint_add_u(dest, a, b);
265                         SET_POS(dest);
266                         break;
267                 case 2: /* a negative, b positive */
268                         bigint_add_u(dest, a, b);
269                         SET_NEG(dest);
270                         break;
271                 case 3: /* both negative */
272                         bigint_sub_u(dest, b, a);
273                         break;
274                 default: /* how can this happen?*/
275                                         break;
276         }
277
278 }
279
280 /******************************************************************************/
281
282 int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){
283         uint8_t s;
284         if(a->length_B==0 && b->length_B==0){
285                 return 0;
286         }
287         s  = GET_SIGN(a)?2:0;
288         s |= GET_SIGN(b)?1:0;
289         switch(s){
290                 case 0: /* both positive */
291                         return bigint_cmp_u(a, b);
292                         break;
293                 case 1: /* a positive, b negative */
294                         return 1;
295                         break;
296                 case 2: /* a negative, b positive */
297                         return -1;
298                         break;
299                 case 3: /* both negative */
300                         return bigint_cmp_u(b, a);
301                         break;
302                 default: /* how can this happen?*/
303                                         break;
304         }
305         return 0; /* just to satisfy the compiler */
306 }
307
308 /******************************************************************************/
309
310 void bigint_shiftleft(bigint_t* a, uint16_t shift){
311         uint16_t byteshift;
312         uint16_t i;
313         uint8_t bitshift;
314         uint16_t t=0;
315         byteshift = (shift+3)/8;
316         bitshift = shift&7;
317         memmove(a->wordv+byteshift, a->wordv, a->length_B);
318         memset(a->wordv, 0, byteshift);
319         if(bitshift!=0){
320                 if(bitshift<=4){ /* shift to the left */
321                         for(i=byteshift; i<a->length_B+byteshift; ++i){
322                                 t |= (a->wordv[i])<<bitshift;
323                                 a->wordv[i] = (uint8_t)t;
324                                 t >>= 8;
325                         }
326                         a->wordv[i] = (uint8_t)t;
327                         byteshift++;
328                 }else{ /* shift to the right */
329                         for(i=a->length_B+byteshift-1; i>byteshift-1; --i){
330                                 t |= (a->wordv[i])<<(bitshift);
331                                 a->wordv[i] = (uint8_t)(t>>8);
332                                 t <<= 8;
333                         }
334                         t |= (a->wordv[i])<<(bitshift);
335                         a->wordv[i] = (uint8_t)(t>>8);
336                 }
337         }
338         a->length_B += byteshift;
339         bigint_adjust(a);
340 }
341
342 /******************************************************************************/
343
344 void bigint_shiftright(bigint_t* a, uint16_t shift){
345         uint16_t byteshift;
346         uint16_t i;
347         uint8_t bitshift;
348         uint16_t t=0;
349         byteshift = shift/8;
350         bitshift = shift&7;
351         if(byteshift >= a->length_B){ /* we would shift out more than we have */
352                 bigint_set_zero(a);
353                 return;
354         }
355         if(byteshift == a->length_B-1 && bitshift>GET_FBS(a)){
356                 bigint_set_zero(a);
357                 return;
358         }
359         if(byteshift){
360                 memmove(a->wordv, a->wordv+byteshift, a->length_B-byteshift);
361                 memset(a->wordv+a->length_B-byteshift, 0,  byteshift);
362         }
363         if(bitshift!=0){
364          /* shift to the right */
365                 for(i=a->length_B-byteshift-1; i>0; --i){
366                         t |= (a->wordv[i])<<(8-bitshift);
367                         a->wordv[i] = (uint8_t)(t>>8);
368                         t <<= 8;
369                 }
370                 t |= (a->wordv[0])<<(8-bitshift);
371                 a->wordv[0] = (uint8_t)(t>>8);
372         }
373         a->length_B -= byteshift;
374         bigint_adjust(a);
375 }
376
377 /******************************************************************************/
378
379 void bigint_xor(bigint_t* dest, const bigint_t* a){
380         uint16_t i;
381         for(i=0; i<a->length_B; ++i){
382                 dest->wordv[i] ^= a->wordv[i];
383         }
384         bigint_adjust(dest);
385 }
386
387 /******************************************************************************/
388
389 void bigint_set_zero(bigint_t* a){
390         a->length_B=0;
391 }
392
393 /******************************************************************************/
394
395 /* using the Karatsuba-Algorithm */
396 /* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */
397 void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
398         if(a->length_B==0 || b->length_B==0){
399                 bigint_set_zero(dest);
400                 return;
401         }
402         if(dest==a || dest==b){
403                 bigint_t d;
404                 uint8_t d_b[a->length_B+b->length_B];
405                 d.wordv = d_b;
406                 bigint_mul_u(&d, a, b);
407                 bigint_copy(dest, &d);
408                 return;
409         }
410         if(a->length_B==1 || b->length_B==1){
411                 if(a->length_B!=1){
412                         XCHG_PTR(a,b);
413                 }
414                 uint16_t i, t=0;
415                 uint8_t x = a->wordv[0];
416                 for(i=0; i<b->length_B; ++i){
417                         t += b->wordv[i]*x;
418                         dest->wordv[i] = (uint8_t)t;
419                         t>>=8;
420                 }
421                 dest->wordv[i] = (uint8_t)t;
422                 dest->length_B=i+1;
423                 bigint_adjust(dest);
424                 return;
425         }
426         if(a->length_B<=4 && b->length_B<=4){
427                 uint32_t p=0, q=0;
428                 uint64_t r;
429                 memcpy(&p, a->wordv, a->length_B);
430                 memcpy(&q, b->wordv, b->length_B);
431                 r = (uint64_t)p*(uint64_t)q;
432                 memcpy(dest->wordv, &r, a->length_B+b->length_B);
433                 dest->length_B =  a->length_B+b->length_B;
434                 bigint_adjust(dest);
435                 return;
436         }
437         bigint_set_zero(dest);
438         /* split a in xh & xl; split b in yh & yl */
439         uint16_t n;
440         n=(MAX(a->length_B, b->length_B)+1)/2;
441         bigint_t xl, xh, yl, yh;
442         xl.wordv = a->wordv;
443         yl.wordv = b->wordv;
444         if(a->length_B<=n){
445                 xh.info=0;
446                 xh.length_B = 0;
447                 xl.length_B = a->length_B;
448                 xl.info = 0;
449         }else{
450                 xl.length_B=n;
451                 xl.info = 0;
452                 bigint_adjust(&xl);
453                 xh.wordv = a->wordv+n;
454                 xh.length_B = a->length_B-n;
455                 xh.info = 0;
456         }
457         if(b->length_B<=n){
458                 yh.info=0;
459                 yh.length_B = 0;
460                 yl.length_B = b->length_B;
461                 yl.info = b->info;
462         }else{
463                 yl.length_B=n;
464                 yl.info = 0;
465                 bigint_adjust(&yl);
466                 yh.wordv = b->wordv+n;
467                 yh.length_B = b->length_B-n;
468                 yh.info = 0;
469         }
470         /* now we have split up a and b */
471         uint8_t  tmp_b[2*n+2], m_b[2*(n+1)];
472         bigint_t tmp, tmp2, m;
473         tmp.wordv = tmp_b;
474         tmp2.wordv = tmp_b+n+1;
475         m.wordv = m_b;
476
477         bigint_mul_u(dest, &xl, &yl);  /* dest <= xl*yl     */
478         bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl     */
479         bigint_add_u(&tmp, &yh, &yl);  /* tmp  <= yh+yl     */
480         bigint_mul_u(&m, &tmp2, &tmp); /* m    <= tmp2*tmp  */
481         bigint_mul_u(&tmp, &xh, &yh);  /* h    <= xh*yh     */
482         bigint_sub_u(&m, &m, dest);    /* m    <= m-dest    */
483     bigint_sub_u(&m, &m, &tmp);    /* m    <= m-h       */
484         bigint_add_scale_u(dest, &m, n);
485         bigint_add_scale_u(dest, &tmp, 2*n);
486 }
487
488 /******************************************************************************/
489
490 void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
491         uint8_t s;
492         s  = GET_SIGN(a)?2:0;
493         s |= GET_SIGN(b)?1:0;
494         switch(s){
495                 case 0: /* both positive */
496                         bigint_mul_u(dest, a,b);
497                         SET_POS(dest);
498                         break;
499                 case 1: /* a positive, b negative */
500                         bigint_mul_u(dest, a,b);
501                         SET_NEG(dest);
502                         break;
503                 case 2: /* a negative, b positive */
504                         bigint_mul_u(dest, a,b);
505                         SET_NEG(dest);
506                         break;
507                 case 3: /* both negative */
508                         bigint_mul_u(dest, a,b);
509                         SET_POS(dest);
510                         break;
511                 default: /* how can this happen?*/
512                         break;
513         }
514 }
515
516 /******************************************************************************/
517
518 /* square */
519 /* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
520 void bigint_square(bigint_t* dest, const bigint_t* a){
521         if(a->length_B<=4){
522                 uint64_t r=0;
523                 memcpy(&r, a->wordv, a->length_B);
524                 r = r*r;
525                 memcpy(dest->wordv, &r, 2*a->length_B);
526                 SET_POS(dest);
527                 dest->length_B=2*a->length_B;
528                 bigint_adjust(dest);
529                 return;
530         }
531         if(dest==a){
532                 bigint_t d;
533                 uint8_t d_b[a->length_B*2];
534                 d.wordv = d_b;
535                 bigint_square(&d, a);
536                 bigint_copy(dest, &d);
537                 return;
538         }
539         uint16_t n;
540         n=(a->length_B+1)/2;
541         bigint_t xh, xl, tmp; /* x-high, x-low, temp */
542         uint8_t buffer[2*n+1];
543         xl.wordv = a->wordv;
544         xl.length_B = n;
545         xh.wordv = a->wordv+n;
546         xh.length_B = a->length_B-n;
547         tmp.wordv = buffer;
548         bigint_square(dest, &xl);
549         bigint_square(&tmp, &xh);
550         bigint_add_scale_u(dest, &tmp, 2*n);
551         bigint_mul_u(&tmp, &xl, &xh);
552         bigint_shiftleft(&tmp, 1);
553         bigint_add_scale_u(dest, &tmp, n);
554 }
555
556 /******************************************************************************/
557
558 void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
559         bigint_t tmp;
560         uint8_t tmp_b[b->length_B+1];
561         uint16_t i,j,byteshift=bitscale/8;
562         uint8_t borrow=0;
563         int16_t t;
564
565         if(a->length_B < b->length_B+byteshift){
566                 bigint_set_zero(a);
567                 return;
568         }
569
570         tmp.wordv = tmp_b;
571         bigint_copy(&tmp, b);
572         bigint_shiftleft(&tmp, bitscale&7);
573
574         for(j=0,i=byteshift; i<tmp.length_B+byteshift; ++i, ++j){
575                 t = a->wordv[i] - tmp.wordv[j] - borrow;
576                 a->wordv[i] = (uint8_t)t;
577                 if(t<0){
578                         borrow = 1;
579                 }else{
580                         borrow = 0;
581                 }
582         }
583         while(borrow){
584                 if(i+1 > a->length_B){
585                         bigint_set_zero(a);
586                         return;
587                 }
588                 a->wordv[i] -= borrow;
589                 if(a->wordv[i]!=0xff){
590                         borrow=0;
591                 }
592                 ++i;
593         }
594         bigint_adjust(a);
595 }
596
597 /******************************************************************************/
598
599 void bigint_reduce(bigint_t* a, const bigint_t* r){
600 //      bigint_adjust(r);
601         uint8_t rfbs = GET_FBS(r);
602
603         if(r->length_B==0 || a->length_B==0){
604                 return;
605         }
606         while(a->length_B > r->length_B){
607                 bigint_sub_u_bitscale(a, r, (a->length_B-r->length_B)*8+GET_FBS(a)-rfbs-1);
608         }
609         while((GET_FBS(a) > rfbs+1) && (a->length_B == r->length_B)){
610                 bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1);
611         }
612         while(bigint_cmp_u(a,r)>=0){
613                 bigint_sub_u(a,a,r);
614         }
615         bigint_adjust(a);
616 }
617
618 /******************************************************************************/
619
620 /* calculate dest = a**exp % r */
621 /* using square&multiply */
622 void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, const bigint_t* r){
623         if(a->length_B==0 || r->length_B==0){
624                 return;
625         }
626
627         bigint_t res, base;
628         uint8_t base_b[MAX(a->length_B,r->length_B*2)], res_b[r->length_B*2];
629         uint16_t i;
630         uint8_t j, t;
631         res.wordv = res_b;
632         base.wordv = base_b;
633         bigint_copy(&base, a);
634         bigint_reduce(&base, r);
635         res.wordv[0]=1;
636         res.length_B=1;
637         res.info = 0;
638         bigint_adjust(&res);
639         for(i=0; i+1<exp->length_B; ++i){
640                 t=exp->wordv[i];
641                 for(j=0; j<8; ++j){
642                         if(t&1){
643                                 bigint_mul_u(&res, &res, &base);
644                                 bigint_reduce(&res, r);
645                         }
646                         bigint_square(&base, &base);
647                         bigint_reduce(&base, r);
648                         t>>=1;
649                 }
650         }
651         t=exp->wordv[i];
652         while(t){
653                 if(t&1){
654                         bigint_mul_u(&res, &res, &base);
655                         bigint_reduce(&res, r);
656                 }
657                 bigint_square(&base, &base);
658                 bigint_reduce(&base, r);
659                 t>>=1;
660         }
661         SET_POS(&res);
662         bigint_copy(dest, &res);
663 }
664
665 /******************************************************************************/
666 /* gcd <-- gcd(x,y) a*x+b*y=gcd */
667 void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, const bigint_t* y){
668          bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
669          volatile uint16_t i=0;
670          if(x->length_B==0 || y->length_B==0){
671                  return;
672          }
673          while(x->wordv[i]==0 && y->wordv[i]==0){
674                  ++i;
675          }
676          uint8_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i];
677          uint8_t u_b[x->length_B-i], v_b[y->length_B-i];
678          uint8_t a_b[y->length_B+2], c_b[y->length_B+2];
679          uint8_t b_b[x->length_B+2], d_b[x->length_B+2];
680
681          g.wordv = g_b;
682          x_.wordv = x_b;
683          y_.wordv = y_b;
684          memset(g_b, 0, i);
685          g_b[i]=1;
686          g.length_B = i+1;
687          g.info=0;
688          x_.info = y_.info = 0;
689          x_.length_B = x->length_B-i;
690          y_.length_B = y->length_B-i;
691          memcpy(x_.wordv, x->wordv+i, x_.length_B);
692          memcpy(y_.wordv, y->wordv+i, y_.length_B);
693          for(i=0; (x_.wordv[0]&(1<<i))==0 && (y_.wordv[0]&(1<<i))==0; ++i){
694          }
695
696          bigint_adjust(&x_);
697          bigint_adjust(&y_);
698
699          if(i){
700                  bigint_shiftleft(&g, i);
701                  bigint_shiftright(&x_, i);
702                  bigint_shiftright(&y_, i);
703          }
704          u.wordv = u_b;
705          v.wordv = v_b;
706          a_.wordv = a_b;
707          b_.wordv = b_b;
708          c_.wordv = c_b;
709          d_.wordv = d_b;
710
711          bigint_copy(&u, &x_);
712          bigint_copy(&v, &y_);
713          a_.wordv[0] = 1;
714          a_.length_B = 1;
715          a_.info = 0;
716          d_.wordv[0] = 1;
717          d_.length_B = 1;
718          d_.info = 0;
719          bigint_set_zero(&b_);
720          bigint_set_zero(&c_);
721          do{
722                  while((u.wordv[0]&1)==0){
723                          bigint_shiftright(&u, 1);
724                          if((a_.wordv[0]&1) || (b_.wordv[0]&1)){
725                                  bigint_add_s(&a_, &a_, &y_);
726                                  bigint_sub_s(&b_, &b_, &x_);
727                          }
728                          bigint_shiftright(&a_, 1);
729                          bigint_shiftright(&b_, 1);
730                  }
731                  while((v.wordv[0]&1)==0){
732                          bigint_shiftright(&v, 1);
733                          if((c_.wordv[0]&1) || (d_.wordv[0]&1)){
734                                  bigint_add_s(&c_, &c_, &y_);
735                                  bigint_sub_s(&d_, &d_, &x_);
736                          }
737                          bigint_shiftright(&c_, 1);
738                          bigint_shiftright(&d_, 1);
739
740                  }
741                  if(bigint_cmp_u(&u, &v)>=0){
742                         bigint_sub_u(&u, &u, &v);
743                         bigint_sub_s(&a_, &a_, &c_);
744                         bigint_sub_s(&b_, &b_, &d_);
745                  }else{
746                         bigint_sub_u(&v, &v, &u);
747                         bigint_sub_s(&c_, &c_, &a_);
748                         bigint_sub_s(&d_, &d_, &b_);
749                  }
750          }while(u.length_B);
751          if(gcd){
752                  bigint_mul_s(gcd, &v, &g);
753          }
754          if(a){
755                 bigint_copy(a, &c_);
756          }
757          if(b){
758                  bigint_copy(b, &d_);
759          }
760 }
761
762 /******************************************************************************/
763
764 void bigint_inverse(bigint_t* dest, const bigint_t* a, const bigint_t* m){
765         bigint_gcdext(NULL, dest, NULL, a, m);
766         while(dest->info&BIGINT_NEG_MASK){
767                 bigint_add_s(dest, dest, m);
768         }
769 }
770
771 /******************************************************************************/
772
773 void bigint_changeendianess(bigint_t* a){
774         uint8_t t, *p, *q;
775         p = a->wordv;
776         q = p+a->length_B-1;
777         while(p<q){
778                 t = *p;
779                 *p = *q;
780                 *q = t;
781                 ++p; --q;
782         }
783 }
784
785 /******************************************************************************/
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