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1 /* bigint.c */
2 /*
3     This file is part of the ARM-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 #define DEBUG 0
37
38 #if DEBUG || 1
39 #include "cli.h"
40 #include "bigint_io.h"
41 #include <stdio.h>
42 #endif
43
44 #ifndef MAX
45  #define MAX(a,b) (((a)>(b))?(a):(b))
46 #endif
47
48 #ifndef MIN
49  #define MIN(a,b) (((a)<(b))?(a):(b))
50 #endif
51
52 #define SET_FBS(a, v) do{(a)->info &=~BIGINT_FBS_MASK; (a)->info |= (v);}while(0)
53 #define GET_FBS(a)   ((a)->info&BIGINT_FBS_MASK)
54 #define SET_NEG(a)   (a)->info |= BIGINT_NEG_MASK
55 #define SET_POS(a)   (a)->info &= ~BIGINT_NEG_MASK
56 #define XCHG(a,b)    do{(a)^=(b); (b)^=(a); (a)^=(b);}while(0)
57 #define XCHG_PTR(a,b)    do{ a = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b))); \
58                                  b = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b))); \
59                                  a = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b)));}while(0)
60
61 #define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
62
63 /******************************************************************************/
64 void bigint_adjust(bigint_t* a){
65         while(a->length_W!=0 && a->wordv[a->length_W-1]==0){
66                 a->length_W--;
67         }
68         if(a->length_W==0){
69                 a->info=0;
70                 return;
71         }
72         bigint_word_t t;
73         uint8_t i = BIGINT_WORD_SIZE-1;
74         t = a->wordv[a->length_W-1];
75         while((t&(1L<<(BIGINT_WORD_SIZE-1)))==0 && i){
76                 t<<=1;
77                 i--;
78         }
79         SET_FBS(a, i);
80 }
81
82 /******************************************************************************/
83
84 uint16_t bigint_length_b(const bigint_t* a){
85         if(!a->length_W || a->length_W==0){
86                 return 0;
87         }
88         return (a->length_W-1) * BIGINT_WORD_SIZE + GET_FBS(a);
89 }
90
91 /******************************************************************************/
92
93 uint16_t bigint_length_B(const bigint_t* a){
94         return a->length_W * sizeof(bigint_word_t);
95 }
96
97 /******************************************************************************/
98
99 uint32_t bigint_get_first_set_bit(const bigint_t* a){
100         if(a->length_W==0){
101                 return (uint32_t)(-1);
102         }
103         return (a->length_W-1)*sizeof(bigint_word_t)*8+GET_FBS(a);
104 }
105
106
107 /******************************************************************************/
108
109 uint32_t bigint_get_last_set_bit(const bigint_t* a){
110         uint32_t r=0;
111         uint8_t b=0;
112         bigint_word_t x=1;
113         if(a->length_W==0){
114                 return (uint32_t)(-1);
115         }
116         while(a->wordv[r]==0 && r<a->length_W){
117                 ++r;
118         }
119         if(a->wordv[r] == 0){
120                 return (uint32_t)(-1);
121         }
122         while((x&a->wordv[r])==0){
123                 ++b;
124                 x <<= 1;
125         }
126         return r*BIGINT_WORD_SIZE+b;
127 }
128
129 /******************************************************************************/
130
131 void bigint_copy(bigint_t* dest, const bigint_t* src){
132     if(dest->wordv != src->wordv){
133             memcpy(dest->wordv, src->wordv, src->length_W * sizeof(bigint_word_t));
134     }
135     dest->length_W = src->length_W;
136         dest->info = src->info;
137 }
138
139 /******************************************************************************/
140
141 /* this should be implemented in assembly */
142 void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
143         uint16_t i;
144         bigint_wordplus_t t = 0LL;
145         if(a->length_W < b->length_W){
146                 XCHG_PTR(a,b);
147         }
148         for(i = 0; i < b->length_W; ++i){
149 //              t = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t;
150                 t += a->wordv[i];
151                 t += b->wordv[i];
152                 dest->wordv[i] = (bigint_word_t)t;
153                 t >>= BIGINT_WORD_SIZE;
154         }
155         for(; i<a->length_W; ++i){
156                 t += a->wordv[i];
157                 dest->wordv[i] = (bigint_word_t)t;
158                 t >>= BIGINT_WORD_SIZE;
159         }
160         if(t){
161                 dest->wordv[i++] = (bigint_word_t)t;
162         }
163         dest->length_W = i;
164         bigint_adjust(dest);
165 }
166
167 /******************************************************************************/
168
169 /* this should be implemented in assembly */
170 void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
171         if(a->length_W == 0){
172                 return;
173         }
174         if(scale == 0){
175                 bigint_add_u(dest, dest, a);
176                 return;
177         }
178         bigint_t x;
179 #if BIGINT_WORD_SIZE == 8
180         memset(dest->wordv + dest->length_W, 0, MAX(dest->length_W, a->length_W + scale) - dest->length_W);
181         x.wordv = dest->wordv + scale;
182         x.length_W = dest->length_W - scale;
183         if((int16_t)x.length_W < 0){
184                 x.length_W = 0;
185                 x.info = 0;
186         } else {
187                 x.info = dest->info;
188         }
189         bigint_add_u(&x, &x, a);
190         dest->length_W = x.length_W + scale;
191         dest->info = 0;
192         bigint_adjust(dest);
193 #else
194         bigint_t s;
195         uint16_t word_shift = scale / sizeof(bigint_word_t), byte_shift = scale % sizeof(bigint_word_t);
196         bigint_word_t bv[a->length_W + 1];
197         s.wordv = bv;
198         bv[0] = bv[a->length_W] = 0;
199         memcpy((uint8_t*)bv + byte_shift, a->wordv, a->length_W * sizeof(bigint_word_t));
200         s.length_W = a->length_W + 1;
201         bigint_adjust(&s);
202         memset(dest->wordv + dest->length_W, 0, (MAX(dest->length_W, s.length_W + word_shift) - dest->length_W) * sizeof(bigint_word_t));
203         x.wordv = dest->wordv + word_shift;
204         x.length_W = dest->length_W - word_shift;
205         if((int16_t)x.length_W < 0){
206                 x.length_W = 0;
207                 x.info = 0;
208         }else{
209                 x.info = dest->info;
210         }
211         bigint_add_u(&x, &x, &s);
212         dest->length_W = x.length_W + word_shift;
213         dest->info = 0;
214         bigint_adjust(dest);
215 #endif
216 }
217
218 /******************************************************************************/
219
220 /* this should be implemented in assembly */
221 void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
222         int8_t borrow=0;
223         int8_t  r;
224         bigint_wordplus_signed_t t=0LL;
225         uint16_t i;
226         if(b->length_W == 0){
227                 bigint_copy(dest, a);
228                 SET_POS(dest);
229                 return;
230         }
231         if(a->length_W == 0){
232                 bigint_copy(dest, b);
233                 SET_NEG(dest);
234                 return;
235         }
236     r = bigint_cmp_u(a,b);
237     if(r == 0){
238         bigint_set_zero(dest);
239         return;
240     }
241         if(r < 0){
242                 bigint_sub_u(dest, b, a);
243                 SET_NEG(dest);
244                 return;
245         }
246         for(i = 0; i < a->length_W; ++i){
247                 t = a->wordv[i];
248                 if(i < b->length_W){
249                         t -= b->wordv[i];
250                 }
251                 t -= borrow;
252                 dest->wordv[i]=(bigint_word_t)t;
253                 if(t<0){
254                         borrow = 1;
255                 }else{
256                         borrow = 0;
257                 }
258         }
259         SET_POS(dest);
260         dest->length_W = i;
261         bigint_adjust(dest);
262 }
263
264 /******************************************************************************/
265
266 int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
267         if(a->length_W > b->length_W){
268                 return 1;
269         }
270         if(a->length_W < b->length_W){
271                 return -1;
272         }
273         if(a->length_W==0){
274                 return 0;
275         }
276         uint16_t i;
277         i = a->length_W-1;
278         do{
279                 if(a->wordv[i] != b->wordv[i]){
280                         if(a->wordv[i] > b->wordv[i]){
281                                 return 1;
282                         }else{
283                                 return -1;
284                         }
285                 }
286         }while(i--);
287         return 0;
288 }
289
290 /******************************************************************************/
291
292 void bigint_add_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
293         uint8_t s;
294         s  = GET_SIGN(a)?2:0;
295         s |= GET_SIGN(b)?1:0;
296         switch(s){
297                 case 0: /* both positive */
298                         bigint_add_u(dest, a,b);
299                         SET_POS(dest);
300                         break;
301                 case 1: /* a positive, b negative */
302                         bigint_sub_u(dest, a, b);
303                         break;
304                 case 2: /* a negative, b positive */
305                         bigint_sub_u(dest, b, a);
306                         break;
307                 case 3: /* both negative */
308                         bigint_add_u(dest, a, b);
309                         SET_NEG(dest);
310                         break;
311                 default: /* how can this happen?*/
312                         break;
313         }
314 }
315
316 /******************************************************************************/
317
318 void bigint_sub_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
319         uint8_t s;
320         s  = GET_SIGN(a)?2:0;
321         s |= GET_SIGN(b)?1:0;
322         switch(s){
323                 case 0: /* both positive */
324                         bigint_sub_u(dest, a,b);
325                         break;
326                 case 1: /* a positive, b negative */
327                         bigint_add_u(dest, a, b);
328                         SET_POS(dest);
329                         break;
330                 case 2: /* a negative, b positive */
331                         bigint_add_u(dest, a, b);
332                         SET_NEG(dest);
333                         break;
334                 case 3: /* both negative */
335                         bigint_sub_u(dest, b, a);
336                         break;
337                 default: /* how can this happen?*/
338                                         break;
339         }
340
341 }
342
343 /******************************************************************************/
344
345 int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){
346         uint8_t s;
347         if(a->length_W==0 && b->length_W==0){
348                 return 0;
349         }
350         s  = GET_SIGN(a)?2:0;
351         s |= GET_SIGN(b)?1:0;
352         switch(s){
353                 case 0: /* both positive */
354                         return bigint_cmp_u(a, b);
355                         break;
356                 case 1: /* a positive, b negative */
357                         return 1;
358                         break;
359                 case 2: /* a negative, b positive */
360                         return -1;
361                         break;
362                 case 3: /* both negative */
363                         return bigint_cmp_u(b, a);
364                         break;
365                 default: /* how can this happen?*/
366                                         break;
367         }
368         return 0; /* just to satisfy the compiler */
369 }
370
371 /******************************************************************************/
372
373 void bigint_shiftleft(bigint_t* a, uint16_t shift){
374         uint16_t byteshift, words_to_shift;
375         int16_t i;
376         uint8_t bitshift;
377         bigint_word_t *p;
378         bigint_wordplus_t t = 0;
379         if(shift == 0){
380                 return;
381         }
382         byteshift = shift / 8;
383         bitshift = shift & 7;
384
385         if(byteshift){
386                 memmove(((uint8_t*)a->wordv) + byteshift, a->wordv, a->length_W * sizeof(bigint_word_t));
387                 memset(a->wordv, 0, byteshift);
388         }
389         if(bitshift == 0){
390             a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
391             bigint_adjust(a);
392             return;
393         }
394         p = a->wordv + byteshift / sizeof(bigint_word_t);
395         words_to_shift = a->length_W + (byteshift % sizeof(bigint_word_t)?1:0);
396     for(i=0; i < words_to_shift; ++i){
397         t |= ((bigint_wordplus_t)p[i]) << bitshift;
398         p[i] = (bigint_word_t)t;
399         t >>= BIGINT_WORD_SIZE;
400     }
401     if(t){
402         p[i] = (bigint_word_t)t;
403         a->length_W += 1;
404     }
405     a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t);
406         bigint_adjust(a);
407 }
408
409 /******************************************************************************/
410
411 void bigint_shiftright(bigint_t* a, uint16_t shift){
412         uint16_t byteshift;
413         uint16_t i;
414         uint8_t bitshift;
415         bigint_wordplus_t t = 0;
416         byteshift = shift / 8;
417         bitshift = shift & 7;
418
419         if(byteshift >= a->length_W * sizeof(bigint_word_t)){ /* we would shift out more than we have */
420                 bigint_set_zero(a);
421                 return;
422         }
423         if(byteshift == a->length_W * sizeof(bigint_word_t) - 1 && bitshift > GET_FBS(a)){
424                 bigint_set_zero(a);
425                 return;
426         }
427
428         if(byteshift){
429                 memmove(a->wordv, (uint8_t*)a->wordv + byteshift, a->length_W * sizeof(bigint_word_t) - byteshift);
430         }
431
432     byteshift /= sizeof(bigint_word_t); /* byteshift is now wordshift */
433     a->length_W -= byteshift;
434         if(bitshift != 0 && a->length_W){
435          /* shift to the right */
436                 i = a->length_W - 1;
437                 do{
438                         t |= ((bigint_wordplus_t)(a->wordv[i])) << (BIGINT_WORD_SIZE - bitshift);
439                         a->wordv[i] = (bigint_word_t)(t >> BIGINT_WORD_SIZE);
440                         t <<= BIGINT_WORD_SIZE;
441                 }while(i--);
442         }
443         bigint_adjust(a);
444 }
445
446 /******************************************************************************/
447
448 void bigint_xor(bigint_t* dest, const bigint_t* a){
449         uint16_t i;
450         for(i=0; i<a->length_W; ++i){
451                 dest->wordv[i] ^= a->wordv[i];
452         }
453         bigint_adjust(dest);
454 }
455
456 /******************************************************************************/
457
458 void bigint_set_zero(bigint_t* a){
459         a->length_W=0;
460 }
461
462 /******************************************************************************/
463
464 /* using the Karatsuba-Algorithm */
465 /* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */
466 void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
467         if(a->length_W == 0 || b->length_W == 0){
468                 bigint_set_zero(dest);
469                 return;
470         }
471         if(dest == a || dest == b){
472                 bigint_t d;
473                 bigint_word_t d_b[a->length_W + b->length_W];
474                 d.wordv = d_b;
475                 bigint_mul_u(&d, a, b);
476                 bigint_copy(dest, &d);
477                 return;
478         }
479         if(a->length_W == 1 || b->length_W == 1){
480                 if(a->length_W != 1){
481                         XCHG_PTR(a,b);
482                 }
483                 bigint_wordplus_t t = 0;
484                 uint16_t i;
485                 bigint_word_t x = a->wordv[0];
486                 for(i=0; i < b->length_W; ++i){
487                         t += ((bigint_wordplus_t)b->wordv[i]) * ((bigint_wordplus_t)x);
488                         dest->wordv[i] = (bigint_word_t)t;
489                         t >>= BIGINT_WORD_SIZE;
490                 }
491                 dest->length_W = i;
492                 if(t){
493                     dest->wordv[i] = (bigint_word_t)t;
494                     dest->length_W += 1;
495                 }
496                 dest->info = 0;
497                 bigint_adjust(dest);
498                 return;
499         }
500         if(a->length_W * sizeof(bigint_word_t) <= 4 && b->length_W * sizeof(bigint_word_t) <= 4){
501                 uint32_t p=0, q=0;
502                 uint64_t r;
503                 memcpy(&p, a->wordv, a->length_W*sizeof(bigint_word_t));
504                 memcpy(&q, b->wordv, b->length_W*sizeof(bigint_word_t));
505                 r = (uint64_t)p * (uint64_t)q;
506                 memcpy(dest->wordv, &r, (dest->length_W = a->length_W + b->length_W)*sizeof(bigint_word_t));
507                 bigint_adjust(dest);
508                 return;
509         }
510         /* split a in xh & xl; split b in yh & yl */
511         const uint16_t n = (MAX(a->length_W, b->length_W)+1)/2;
512         bigint_t xl, xh, yl, yh;
513         xl.wordv = a->wordv;
514         yl.wordv = b->wordv;
515         if(a->length_W<=n){
516                 bigint_set_zero(&xh);
517                 xl.length_W = a->length_W;
518                 xl.info = a->info;
519         }else{
520                 xl.length_W=n;
521                 xl.info = 0;
522                 bigint_adjust(&xl);
523                 xh.wordv = &(a->wordv[n]);
524                 xh.length_W = a->length_W-n;
525                 xh.info = a->info;
526         }
527         if(b->length_W<=n){
528                 bigint_set_zero(&yh);
529                 yl.length_W = b->length_W;
530                 yl.info = b->info;
531         }else{
532                 yl.length_W=n;
533                 yl.info = 0;
534                 bigint_adjust(&yl);
535                 yh.wordv = &(b->wordv[n]);
536                 yh.length_W = b->length_W-n;
537                 yh.info = b->info;
538         }
539         /* now we have split up a and b */
540         /* remember we want to do:
541          * x*y = (xh * b**n + xl) * (yh * b**n + yl)
542          *     = (xh * yh) * b**2n + xh * b**n * yl + yh * b**n * xl + xl * yl
543          *     = (xh * yh) * b**2n + (xh * yl + yh * xl) * b**n + xl *yl
544          *     // xh * yl + yh * xl = (xh + yh) * (xl + yl) - xh * yh - xl * yl
545          * x*y = (xh * yh) * b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + xl*yl
546          *          5              9     2   4   3    7   5   6   1         8   1
547          */
548         bigint_word_t  tmp_b[2 * n + 2], m_b[2 * (n + 1)];
549         bigint_t tmp, tmp2, m;
550         tmp.wordv = tmp_b;
551         tmp2.wordv = &(tmp_b[n + 1]);
552         m.wordv = m_b;
553
554         bigint_mul_u(dest, &xl, &yl);  /* 1: dest <= xl*yl     */
555         bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh+xl     */
556         bigint_add_u(&tmp, &yh, &yl);  /* 3: tmp  <= yh+yl     */
557         bigint_mul_u(&m, &tmp2, &tmp); /* 4: m    <= tmp2*tmp  */
558         bigint_mul_u(&tmp, &xh, &yh);  /* 5: tmp  <= xh*yh     */
559         bigint_sub_u(&m, &m, dest);    /* 6: m    <= m-dest    */
560     bigint_sub_u(&m, &m, &tmp);    /* 7: m    <= m-tmp     */
561         bigint_add_scale_u(dest, &m, n * sizeof(bigint_word_t));       /* 8: dest <= dest+m**n*/
562         bigint_add_scale_u(dest, &tmp, 2 * n * sizeof(bigint_word_t)); /* 9: dest <= dest+tmp**(2*n) */
563 }
564
565 /******************************************************************************/
566
567 void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
568         uint8_t s;
569         s  = GET_SIGN(a)?2:0;
570         s |= GET_SIGN(b)?1:0;
571         switch(s){
572                 case 0: /* both positive */
573                         bigint_mul_u(dest, a,b);
574                         SET_POS(dest);
575                         break;
576                 case 1: /* a positive, b negative */
577                         bigint_mul_u(dest, a,b);
578                         SET_NEG(dest);
579                         break;
580                 case 2: /* a negative, b positive */
581                         bigint_mul_u(dest, a,b);
582                         SET_NEG(dest);
583                         break;
584                 case 3: /* both negative */
585                         bigint_mul_u(dest, a,b);
586                         SET_POS(dest);
587                         break;
588                 default: /* how can this happen?*/
589                         break;
590         }
591 }
592
593 /******************************************************************************/
594
595
596 #if DEBUG_SQUARE
597 unsigned square_depth = 0;
598 #endif
599
600 /* square */
601 /* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
602 void bigint_square(bigint_t* dest, const bigint_t* a){
603         if(a->length_W * sizeof(bigint_word_t) <= 4){
604                 uint64_t r = 0;
605                 memcpy(&r, a->wordv, a->length_W * sizeof(bigint_word_t));
606                 r = r * r;
607                 memcpy(dest->wordv, &r, 2 * a->length_W * sizeof(bigint_word_t));
608                 SET_POS(dest);
609                 dest->length_W = 2 * a->length_W;
610                 bigint_adjust(dest);
611                 return;
612         }
613         if(dest->wordv == a->wordv){
614                 bigint_t d;
615                 bigint_word_t d_b[a->length_W*2];
616                 d.wordv = d_b;
617                 bigint_square(&d, a);
618                 bigint_copy(dest, &d);
619                 return;
620         }
621
622 #if DEBUG_SQUARE
623         square_depth += 1;
624 #endif
625
626         uint16_t n;
627         n=(a->length_W+1)/2;
628         bigint_t xh, xl, tmp; /* x-high, x-low, temp */
629         bigint_word_t buffer[2*n+1];
630         xl.wordv = a->wordv;
631         xl.length_W = n;
632         xl.info = 0;
633         xh.wordv = &(a->wordv[n]);
634         xh.length_W = a->length_W-n;
635         xh.info = a->info;
636         bigint_adjust(&xl);
637         tmp.wordv = buffer;
638 /* (xh * b**n + xl)**2 = xh**2 * b**2n + 2 * xh * xl * b**n + xl**2 */
639 #if DEBUG_SQUARE
640         if(square_depth == 1){
641         cli_putstr("\r\nDBG (a): xl: "); bigint_print_hex(&xl);
642         cli_putstr("\r\nDBG (b): xh: "); bigint_print_hex(&xh);
643         }
644 #endif
645         bigint_square(dest, &xl);
646 #if DEBUG_SQUARE
647         if(square_depth == 1){
648             cli_putstr("\r\nDBG (1): xl**2: "); bigint_print_hex(dest);
649         }
650 #endif
651     bigint_square(&tmp, &xh);
652 #if DEBUG_SQUARE
653     if(square_depth == 1){
654         cli_putstr("\r\nDBG (2): xh**2: "); bigint_print_hex(&tmp);
655     }
656 #endif
657         bigint_add_scale_u(dest, &tmp, 2 * n * sizeof(bigint_word_t));
658 #if DEBUG_SQUARE
659         if(square_depth == 1){
660             cli_putstr("\r\nDBG (3): xl**2 + xh**2*n**2: "); bigint_print_hex(dest);
661         }
662 #endif
663         bigint_mul_u(&tmp, &xl, &xh);
664 #if DEBUG_SQUARE
665         if(square_depth == 1){
666             cli_putstr("\r\nDBG (4): xl*xh: "); bigint_print_hex(&tmp);
667         }
668 #endif
669         bigint_shiftleft(&tmp, 1);
670 #if DEBUG_SQUARE
671         if(square_depth == 1){
672             cli_putstr("\r\nDBG (5): xl*xh*2: "); bigint_print_hex(&tmp);
673         }
674 #endif
675         bigint_add_scale_u(dest, &tmp, n * sizeof(bigint_word_t));
676 #if DEBUG_SQUARE
677         if(square_depth == 1){
678             cli_putstr("\r\nDBG (6): x**2: "); bigint_print_hex(dest);
679             cli_putstr("\r\n");
680         }
681         square_depth -= 1;
682 #endif
683 }
684
685 /******************************************************************************/
686 void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
687         bigint_t tmp, x;
688         bigint_word_t tmp_b[b->length_W + 1];
689         const uint16_t word_shift = bitscale / BIGINT_WORD_SIZE;
690
691         if(a->length_W < b->length_W + word_shift){
692 #if DEBUG
693                 cli_putstr("\r\nDBG: *bang*\r\n");
694 #endif
695                 bigint_set_zero(a);
696                 return;
697         }
698         tmp.wordv = tmp_b;
699         bigint_copy(&tmp, b);
700         bigint_shiftleft(&tmp, bitscale % BIGINT_WORD_SIZE);
701
702         x.info = a->info;
703         x.wordv = &(a->wordv[word_shift]);
704         x.length_W = a->length_W - word_shift;
705
706         bigint_sub_u(&x, &x, &tmp);
707         bigint_adjust(a);
708         return;
709 }
710
711 /******************************************************************************/
712
713 void bigint_reduce(bigint_t* a, const bigint_t* r){
714 //      bigint_adjust((bigint_t*)r);
715         uint8_t rfbs = GET_FBS(r);
716 #if DEBUG
717         cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
718 #endif
719         if(r->length_W==0 || a->length_W==0){
720                 return;
721         }
722         if((r->length_W*sizeof(bigint_word_t)<=4) && (a->length_W*sizeof(bigint_word_t)<=4)){
723                 uint32_t p=0, q=0;
724                 memcpy(&p, a->wordv, a->length_W*sizeof(bigint_word_t));
725                 memcpy(&q, r->wordv, r->length_W*sizeof(bigint_word_t));
726                 p %= q;
727                 memcpy(a->wordv, &p, a->length_W*sizeof(bigint_word_t));
728                 bigint_adjust(a);
729 //              cli_putstr("\r\nDBG: (0) = "); bigint_print_hex(a);
730                 return;
731         }
732         uint16_t shift;
733         while(a->length_W > r->length_W){
734                 shift = (a->length_W - r->length_W) * 8 * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1;
735                 /*
736                 if((a->wordv[a->length_W-1] & ((1LL<<GET_FBS(a)) - 1)) > r->wordv[r->length_W-1]){
737                         // cli_putc('~');
738                         cli_putstr("\r\n ~ [a] = ");
739                         cli_hexdump_rev(&a->wordv[a->length_W-1], 4);
740                         cli_putstr("  [r] = ");
741                         cli_hexdump_rev(&r->wordv[r->length_W-1], 4);
742                         shift += 1;
743                 }
744                 */
745 //              cli_putstr("\r\nDBG: (p) shift = "); cli_hexdump_rev(&shift, 2);
746 //              cli_putstr(" a_len = "); cli_hexdump_rev(&a->length_W, 2);
747 //              cli_putstr(" r_len = "); cli_hexdump_rev(&r->length_W, 2);
748 //              uart_flush(0);
749                 bigint_sub_u_bitscale(a, r, shift);
750 //              cli_putstr("\r\nDBG: (1) = "); bigint_print_hex(a);
751         }
752         while((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)){
753                 shift = GET_FBS(a)-rfbs-1;
754 //              cli_putstr("\r\nDBG: (q) shift = "); cli_hexdump_rev(&shift, 2);
755                 bigint_sub_u_bitscale(a, r, shift);
756 //              cli_putstr("\r\nDBG: (2) = "); bigint_print_hex(a);
757         }
758         while(bigint_cmp_u(a,r)>=0){
759                 bigint_sub_u(a,a,r);
760 //              cli_putstr("\r\nDBG: (3) = "); bigint_print_hex(a);
761         }
762         bigint_adjust(a);
763 //      cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
764 //      cli_putstr("\r\n");
765 }
766
767 /******************************************************************************/
768
769 /* calculate dest = a**exp % r */
770 /* using square&multiply */
771 void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, const bigint_t* r){
772         if(a->length_W==0 || r->length_W==0){
773                 return;
774         }
775
776         bigint_t res, base;
777         bigint_word_t t, base_b[MAX(a->length_W,r->length_W)], res_b[r->length_W*2];
778         uint16_t i;
779         uint8_t j;
780 //      uint16_t *xaddr = &i;
781 //      cli_putstr("\r\npre-alloc (");
782 //      cli_hexdump_rev(&xaddr, 4);
783 //      cli_putstr(") ...");
784         res.wordv = res_b;
785         base.wordv = base_b;
786         bigint_copy(&base, a);
787 //      cli_putstr("\r\npost-copy");
788         bigint_reduce(&base, r);
789         res.wordv[0]=1;
790         res.length_W=1;
791         res.info = 0;
792         bigint_adjust(&res);
793         if(exp->length_W == 0){
794                 bigint_copy(dest, &res);
795                 return;
796         }
797         uint8_t flag = 0;
798         t=exp->wordv[exp->length_W - 1];
799         for(i=exp->length_W; i > 0; --i){
800                 t = exp->wordv[i - 1];
801                 for(j=BIGINT_WORD_SIZE; j > 0; --j){
802                         if(!flag){
803                                 if(t & (1<<(BIGINT_WORD_SIZE-1))){
804                                         flag = 1;
805                                 }
806                         }
807                         if(flag){
808                                 bigint_square(&res, &res);
809                                 bigint_reduce(&res, r);
810                                 if(t & (1 << (BIGINT_WORD_SIZE - 1))){
811                                         bigint_mul_u(&res, &res, &base);
812                                         bigint_reduce(&res, r);
813                                 }
814                         }
815                         t <<= 1;
816                 }
817         }
818
819 //      cli_putc('+');
820         SET_POS(&res);
821         bigint_copy(dest, &res);
822 }
823
824 /******************************************************************************/
825 #if 1
826 #define cli_putstr(a)
827 #define cli_putstr_P(a)
828 #define bigint_print_hex(a)
829 #define cli_hexdump_rev(a,b)
830 #define uart_flush(a)
831 #define printf_P(...)
832 #endif
833 /* gcd <-- gcd(x,y) a*x+b*y=gcd */
834 void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, const bigint_t* y){
835          uint16_t i = 0;
836          printf_P(PSTR("\nDBG: gcdext( "));
837          bigint_print_hex(x);
838      printf_P(PSTR(", "));
839      bigint_print_hex(y);
840      printf_P(PSTR(")\n"));
841          if(x->length_W == 0 || y->length_W == 0){
842              printf_P(PSTR("\nDBG: got zero in gcd <%s %s %d>\n"), __FILE__, __func__, __LINE__);
843              if(gcd){
844                  bigint_set_zero(gcd);
845              }
846              if(a){
847                  bigint_set_zero(a);
848              }
849          if(b){
850              bigint_set_zero(b);
851          }
852                  return;
853          }
854          if(x->length_W == 1 && x->wordv[0] == 1){
855              if(gcd){
856              gcd->length_W = 1;
857              gcd->wordv[0] = 1;
858              gcd->info = 0;
859              }
860                  if(a){
861                          a->length_W = 1;
862                          a->wordv[0] = 1;
863                          SET_POS(a);
864                          bigint_adjust(a);
865                  }
866                  if(b){
867                          bigint_set_zero(b);
868                  }
869                  return;
870          }
871          if(y->length_W == 1 && y->wordv[0] == 1){
872                  if(gcd){
873              gcd->length_W = 1;
874              gcd->wordv[0] = 1;
875              gcd->info = 0;
876                  }
877                  if(b){
878                          b->length_W = 1;
879                          b->wordv[0] = 1;
880                          SET_POS(b);
881                          bigint_adjust(b);
882                  }
883                  if(a){
884                          bigint_set_zero(a);
885                  }
886                  return;
887          }
888
889          while(x->wordv[i] == 0 && y->wordv[i] == 0){
890                  ++i;
891          }
892          bigint_word_t g_b[i + 2], x_b[x->length_W - i], y_b[y->length_W - i];
893          bigint_word_t u_b[x->length_W - i], v_b[y->length_W - i];
894          bigint_word_t a_b[y->length_W + 2], c_b[y->length_W + 2];
895          bigint_word_t b_b[x->length_W + 2], d_b[x->length_W + 2];
896      bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
897
898          g.wordv = g_b;
899          x_.wordv = x_b;
900          y_.wordv = y_b;
901          memset(g_b, 0, i * sizeof(bigint_word_t));
902          g_b[i] = 1;
903          g.length_W = i + 1;
904          g.info = 0;
905          x_.info = y_.info = 0;
906          x_.length_W = x->length_W - i;
907          y_.length_W = y->length_W - i;
908          memcpy(x_.wordv, x->wordv + i, x_.length_W * sizeof(bigint_word_t));
909          memcpy(y_.wordv, y->wordv + i, y_.length_W * sizeof(bigint_word_t));
910          for(i = 0; (x_.wordv[0] & (1 << i)) == 0 && (y_.wordv[0] & (1 << i)) == 0; ++i){
911          }
912
913          bigint_adjust(&x_);
914          bigint_adjust(&y_);
915
916          if(i){
917                  bigint_shiftleft(&g, i);
918                  bigint_shiftright(&x_, i);
919                  bigint_shiftright(&y_, i);
920          }
921
922          u.wordv = u_b;
923          v.wordv = v_b;
924          a_.wordv = a_b;
925          b_.wordv = b_b;
926          c_.wordv = c_b;
927          d_.wordv = d_b;
928
929          bigint_copy(&u, &x_);
930          bigint_copy(&v, &y_);
931          a_.wordv[0] = 1;
932          a_.length_W = 1;
933          a_.info = 0;
934          d_.wordv[0] = 1;
935          d_.length_W = 1;
936          d_.info = 0;
937          bigint_set_zero(&b_);
938          bigint_set_zero(&c_);
939      printf_P(PSTR("\nloop: x_ = "));
940      bigint_print_hex(&x_);
941      printf_P(PSTR("; y_ = "));
942      bigint_print_hex(&y_);
943          do{
944                  printf_P(PSTR("\nDBG (gcdext) 0"));
945                  while((u.wordv[0] & 1) == 0){
946                          printf_P(PSTR("\nDBG (gcdext) 0.1"));
947                          bigint_shiftright(&u, 1);
948                          if((a_.wordv[0] & 1) || (b_.wordv[0] & 1)){
949                                  bigint_add_s(&a_, &a_, &y_);
950                                  bigint_sub_s(&b_, &b_, &x_);
951                          }
952                          bigint_shiftright(&a_, 1);
953                          bigint_shiftright(&b_, 1);
954                          printf_P(PSTR(" a_ = "));
955                          bigint_print_hex(&a_);
956                          printf_P(PSTR("; b_ = "));
957                          bigint_print_hex(&b_);
958                  }
959                  while((v.wordv[0] & 1) == 0){
960                          printf_P(PSTR("\nDBG (gcdext) 0.2"));
961                          bigint_shiftright(&v, 1);
962                          if((c_.wordv[0] & 1) || (d_.wordv[0] & 1)){
963                                  bigint_add_s(&c_, &c_, &y_);
964                                  bigint_sub_s(&d_, &d_, &x_);
965                          }
966              printf_P(PSTR(" c* = "));
967              bigint_print_hex(&c_);
968                          bigint_shiftright(&c_, 1);
969                          bigint_shiftright(&d_, 1);
970              printf_P(PSTR(" c_ = "));
971              bigint_print_hex(&c_);
972              printf_P(PSTR("; d_ = "));
973              bigint_print_hex(&d_);
974                  }
975                  if(bigint_cmp_u(&u, &v) >= 0){
976              printf_P(PSTR("\nDBG (gcdext) 0.3"));
977                         bigint_sub_u(&u, &u, &v);
978                         bigint_sub_s(&a_, &a_, &c_);
979                         bigint_sub_s(&b_, &b_, &d_);
980             printf_P(PSTR(" a_ = "));
981             bigint_print_hex(&a_);
982             printf_P(PSTR("; b_ = "));
983             bigint_print_hex(&b_);
984                  }else{
985              printf_P(PSTR("\nDBG (gcdext) 0.4"));
986                         bigint_sub_u(&v, &v, &u);
987                         bigint_sub_s(&c_, &c_, &a_);
988                         bigint_sub_s(&d_, &d_, &b_);
989             printf_P(PSTR(" c_ = "));
990             bigint_print_hex(&c_);
991             printf_P(PSTR("; d_ = "));
992             bigint_print_hex(&d_);
993                  }
994          }while(u.length_W);
995          if(gcd){
996                  bigint_mul_s(gcd, &v, &g);
997          }
998          if(a){
999                 bigint_copy(a, &c_);
1000          }
1001          if(b){
1002                  bigint_copy(b, &d_);
1003          }
1004 }
1005
1006 /******************************************************************************/
1007
1008 void bigint_inverse(bigint_t* dest, const bigint_t* a, const bigint_t* m){
1009         bigint_gcdext(NULL, dest, NULL, a, m);
1010         while(dest->info&BIGINT_NEG_MASK){
1011                 bigint_add_s(dest, dest, m);
1012         }
1013 }
1014
1015 /******************************************************************************/
1016
1017 void bigint_changeendianess(bigint_t* a){
1018         uint8_t t, *p, *q;
1019         p = (uint8_t*)(a->wordv);
1020         q = p + a->length_W * sizeof(bigint_word_t) - 1;
1021         while(p<q){
1022                 t = *p;
1023                 *p = *q;
1024                 *q = t;
1025                 ++p; --q;
1026         }
1027 }
1028
1029 /******************************************************************************/
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