bigint/bigint.c

   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 #include "bigint.h"
  30 #include <string.h>
  31
  32 #ifndef MAX
  33  #define MAX(a,b) (((a)>(b))?(a):(b))
  34 #endif
  35
  36 #ifndef MIN
  37  #define MIN(a,b) (((a)<(b))?(a):(b))
  38 #endif
  39
  40 #define SET_FBS(a, v) do{(a)->info &=0xF8; (a)->info |= (v);}while(0)
  41 #define GET_FBS(a)   ((a)->info&BIGINT_FBS_MASK)
  42 #define SET_NEG(a)   (a)->info |= BIGINT_NEG_MASK
  43 #define SET_POS(a)   (a)->info &= ~BIGINT_NEG_MASK
  44 #define XCHG(a,b)    do{(a)^=(b); (b)^=(a); (a)^=(b);}while(0)
  45 #define XCHG_PTR(a,b)    do{ a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
  46                                  b = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
  47                                  a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b)));}while(0)
  48
  49 #define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
  50
  51 /******************************************************************************/
  52 void bigint_adjust(bigint_t* a){
  53         while(a->length_B!=0 && a->wordv[a->length_B-1]==0){
  54                 a->length_B--;
  55         }
  56         if(a->length_B==0){
  57                 a->info=0;
  58                 return;
  59         }
  60         uint8_t t;
  61         uint8_t i = 0x07;
  62         t = a->wordv[a->length_B-1];
  63         while((t&0x80)==0 && i){
  64                 t<<=1;
  65                 i--;
  66         }
  67         SET_FBS(a, i);
  68 }
  69
  70 /******************************************************************************/
  71
  72 void bigint_copy(bigint_t* dest, const bigint_t* src){
  73         memcpy(dest->wordv, src->wordv, src->length_B);
  74         dest->length_B = src->length_B;
  75         dest->info = src->info;
  76 }
  77
  78 /******************************************************************************/
  79
  80 /* this should be implemented in assembly */
  81 /*
  82 void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
  83         uint16_t t=0, i;
  84         if(a->length_B < b->length_B){
  85                 XCHG_PTR(a,b);
  86         }
  87         for(i=0; i<b->length_B; ++i){
  88                 t = a->wordv[i] + b->wordv[i] + t;
  89                 dest->wordv[i] = (uint8_t)t;
  90                 t>>=8;
  91         }
  92         for(; i<a->length_B; ++i){
  93                 t = a->wordv[i] + t;
  94                 dest->wordv[i] = (uint8_t)t;
  95                 t>>=8;
  96         }
  97         dest->wordv[i++] = t;
  98         dest->length_B = i;
  99         bigint_adjust(dest);
 100 }
 101 */
 102 /******************************************************************************/
 103
 104 /* this should be implemented in assembly */
 105 void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
 106         uint16_t i,j=0;
 107         uint16_t t=0;
 108         if(scale>dest->length_B)
 109                 memset(dest->wordv+dest->length_B, 0, scale-dest->length_B);
 110         for(i=scale; i<a->length_B+scale; ++i,++j){
 111                 t = a->wordv[j] + t;
 112                 if(dest->length_B>i){
 113                         t += dest->wordv[i];
 114                 }
 115                 dest->wordv[i] = (uint8_t)t;
 116                 t>>=8;
 117         }
 118         while(t){
 119                 if(dest->length_B>i){
 120                         t = dest->wordv[i] + t;
 121                 }
 122                 dest->wordv[i] = (uint8_t)t;
 123                 t>>=8;
 124                 ++i;
 125         }
 126         if(dest->length_B < i){
 127                 dest->length_B = i;
 128         }
 129         bigint_adjust(dest);
 130 }
 131
 132 /******************************************************************************/
 133
 134 /* this should be implemented in assembly */
 135 void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 136         int8_t borrow=0;
 137         int8_t  r;
 138         int16_t t;
 139         uint16_t i, min, max;
 140         min = MIN(a->length_B, b->length_B);
 141         max = MAX(a->length_B, b->length_B);
 142         r = bigint_cmp_u(a,b);
 143         if(r==0){
 144                 dest->length_B = 0;
 145                 dest->wordv[0] = 0;
 146                 bigint_adjust(dest);
 147                 return;
 148         }
 149         if(b->length_B==0){
 150                 dest->length_B = a->length_B;
 151                 memcpy(dest->wordv, a->wordv, a->length_B);
 152                 dest->info = a->info;
 153                 SET_POS(dest);
 154                 return;
 155         }
 156         if(a->length_B==0){
 157                         dest->length_B = b->length_B;
 158                         memcpy(dest->wordv, b->wordv, b->length_B);
 159                         dest->info = b->info;
 160                         SET_NEG(dest);
 161                         return;
 162         }
 163         if(r<0){
 164                 bigint_sub_u(dest, b, a);
 165                 SET_NEG(dest);
 166         }else{
 167                 for(i=0; i<min; ++i){
 168                         t = a->wordv[i] - b->wordv[i] - borrow;
 169                         if(t<0){
 170                                 borrow = 1;
 171                                 dest->wordv[i]=(uint8_t)t;
 172                         }else{
 173                                 borrow = 0;
 174                                 dest->wordv[i]=(uint8_t)t;
 175                         }
 176                 }
 177                 for(;i<max; ++i){
 178                         t = a->wordv[i] - borrow;
 179                         if(t<0){
 180                                 borrow = 1;
 181                                 dest->wordv[i]=(uint8_t)t;
 182                         }else{
 183                                 borrow = 0;
 184                                 dest->wordv[i]=(uint8_t)t;
 185                         }
 186
 187                 }
 188                 SET_POS(dest);
 189                 dest->length_B = i;
 190                 bigint_adjust(dest);
 191         }
 192 }
 193
 194 /******************************************************************************/
 195
 196 int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
 197         if(a->length_B > b->length_B){
 198                 return 1;
 199         }
 200         if(a->length_B < b->length_B){
 201                 return -1;
 202         }
 203         if(a->length_B==0){
 204                 return 0;
 205         }
 206         uint16_t i;
 207         i = a->length_B-1;
 208         do{
 209                 if(a->wordv[i]!=b->wordv[i]){
 210                         if(a->wordv[i]>b->wordv[i]){
 211                                 return 1;
 212                         }else{
 213                                 return -1;
 214                         }
 215                 }
 216         }while(i--);
 217         return 0;
 218 }
 219
 220 /******************************************************************************/
 221
 222 void bigint_add_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 223         uint8_t s;
 224         s  = GET_SIGN(a)?2:0;
 225         s |= GET_SIGN(b)?1:0;
 226         switch(s){
 227                 case 0: /* both positive */
 228                         bigint_add_u(dest, a,b);
 229                         SET_POS(dest);
 230                         break;
 231                 case 1: /* a positive, b negative */
 232                         bigint_sub_u(dest, a, b);
 233                         break;
 234                 case 2: /* a negative, b positive */
 235                         bigint_sub_u(dest, b, a);
 236                         break;
 237                 case 3: /* both negative */
 238                         bigint_add_u(dest, a, b);
 239                         SET_NEG(dest);
 240                         break;
 241                 default: /* how can this happen?*/
 242                         break;
 243         }
 244 }
 245
 246 /******************************************************************************/
 247
 248 void bigint_sub_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 249         uint8_t s;
 250         s  = GET_SIGN(a)?2:0;
 251         s |= GET_SIGN(b)?1:0;
 252         switch(s){
 253                 case 0: /* both positive */
 254                         bigint_sub_u(dest, a,b);
 255                         break;
 256                 case 1: /* a positive, b negative */
 257                         bigint_add_u(dest, a, b);
 258                         SET_POS(dest);
 259                         break;
 260                 case 2: /* a negative, b positive */
 261                         bigint_add_u(dest, a, b);
 262                         SET_NEG(dest);
 263                         break;
 264                 case 3: /* both negative */
 265                         bigint_sub_u(dest, b, a);
 266                         break;
 267                 default: /* how can this happen?*/
 268                                         break;
 269         }
 270
 271 }
 272
 273 /******************************************************************************/
 274
 275 int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){
 276         uint8_t s;
 277         if(a->length_B==0 && b->length_B==0){
 278                 return 0;
 279         }
 280         s  = GET_SIGN(a)?2:0;
 281         s |= GET_SIGN(b)?1:0;
 282         switch(s){
 283                 case 0: /* both positive */
 284                         return bigint_cmp_u(a, b);
 285                         break;
 286                 case 1: /* a positive, b negative */
 287                         return 1;
 288                         break;
 289                 case 2: /* a negative, b positive */
 290                         return -1;
 291                         break;
 292                 case 3: /* both negative */
 293                         return bigint_cmp_u(b, a);
 294                         break;
 295                 default: /* how can this happen?*/
 296                                         break;
 297         }
 298         return 0; /* just to satisfy the compiler */
 299 }
 300
 301 /******************************************************************************/
 302
 303 void bigint_shiftleft(bigint_t* a, uint16_t shift){
 304         uint16_t byteshift;
 305         uint16_t i;
 306         uint8_t bitshift;
 307         uint16_t t=0;
 308         byteshift = (shift+3)/8;
 309         bitshift = shift&7;
 310         memmove(a->wordv+byteshift, a->wordv, a->length_B);
 311         memset(a->wordv, 0, byteshift);
 312         if(bitshift!=0){
 313                 if(bitshift<=4){ /* shift to the left */
 314                         for(i=byteshift; i<a->length_B+byteshift; ++i){
 315                                 t |= (a->wordv[i])<<bitshift;
 316                                 a->wordv[i] = (uint8_t)t;
 317                                 t >>= 8;
 318                         }
 319                         a->wordv[i] = (uint8_t)t;
 320                         byteshift++;
 321                 }else{ /* shift to the right */
 322                         for(i=a->length_B+byteshift-1; i>byteshift-1; --i){
 323                                 t |= (a->wordv[i])<<(bitshift);
 324                                 a->wordv[i] = (uint8_t)(t>>8);
 325                                 t <<= 8;
 326                         }
 327                         t |= (a->wordv[i])<<(bitshift);
 328                         a->wordv[i] = (uint8_t)(t>>8);
 329                 }
 330         }
 331         a->length_B += byteshift;
 332         bigint_adjust(a);
 333 }
 334
 335 /******************************************************************************/
 336
 337 void bigint_shiftright(bigint_t* a, uint16_t shift){
 338         uint16_t byteshift;
 339         uint16_t i;
 340         uint8_t bitshift;
 341         uint16_t t=0;
 342         byteshift = shift/8;
 343         bitshift = shift&7;
 344         if(byteshift >= a->length_B){ /* we would shift out more than we have */
 345                 bigint_set_zero(a);
 346                 return;
 347         }
 348         if(byteshift == a->length_B-1 && bitshift>GET_FBS(a)){
 349                 bigint_set_zero(a);
 350                 return;
 351         }
 352         if(byteshift){
 353                 memmove(a->wordv, a->wordv+byteshift, a->length_B-byteshift);
 354                 memset(a->wordv+a->length_B-byteshift, 0,  byteshift);
 355         }
 356         if(bitshift!=0){
 357          /* shift to the right */
 358                 for(i=a->length_B-byteshift-1; i>0; --i){
 359                         t |= (a->wordv[i])<<(8-bitshift);
 360                         a->wordv[i] = (uint8_t)(t>>8);
 361                         t <<= 8;
 362                 }
 363                 t |= (a->wordv[0])<<(8-bitshift);
 364                 a->wordv[0] = (uint8_t)(t>>8);
 365         }
 366         a->length_B -= byteshift;
 367         bigint_adjust(a);
 368 }
 369
 370 /******************************************************************************/
 371
 372 void bigint_xor(bigint_t* dest, const bigint_t* a){
 373         uint16_t i;
 374         for(i=0; i<a->length_B; ++i){
 375                 dest->wordv[i] ^= a->wordv[i];
 376         }
 377         bigint_adjust(dest);
 378 }
 379
 380 /******************************************************************************/
 381
 382 void bigint_set_zero(bigint_t* a){
 383         a->length_B=0;
 384 }
 385
 386 /******************************************************************************/
 387
 388 /* using the Karatsuba-Algorithm */
 389 /* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */
 390 void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 391         if(dest==a || dest==b){
 392                 bigint_t d;
 393                 uint8_t d_b[a->length_B+b->length_B];
 394                 d.wordv = d_b;
 395                 bigint_mul_u(&d, a, b);
 396                 bigint_copy(dest, &d);
 397                 return;
 398         }
 399         if(a->length_B==0 || b->length_B==0){
 400                 bigint_set_zero(dest);
 401                 return;
 402         }
 403         if(a->length_B==1 || b->length_B==1){
 404                 if(a->length_B!=1){
 405                         XCHG_PTR(a,b);
 406                 }
 407                 uint16_t i, t=0;
 408                 uint8_t x = a->wordv[0];
 409                 for(i=0; i<b->length_B; ++i){
 410                         t += b->wordv[i]*x;
 411                         dest->wordv[i] = (uint8_t)t;
 412                         t>>=8;
 413                 }
 414                 dest->wordv[i] = (uint8_t)t;
 415                 dest->length_B=i+1;
 416                 bigint_adjust(dest);
 417                 return;
 418         }
 419         if(a->length_B<=4 && b->length_B<=4){
 420                 uint32_t p=0, q=0;
 421                 uint64_t r;
 422                 memcpy(&p, a->wordv, a->length_B);
 423                 memcpy(&q, b->wordv, b->length_B);
 424                 r = (uint64_t)p*(uint64_t)q;
 425                 memcpy(dest->wordv, &r, a->length_B+b->length_B);
 426                 dest->length_B =  a->length_B+b->length_B;
 427                 bigint_adjust(dest);
 428                 return;
 429         }
 430         bigint_set_zero(dest);
 431         /* split a in xh & xl; split b in yh & yl */
 432         uint16_t n;
 433         n=(MAX(a->length_B, b->length_B)+1)/2;
 434         bigint_t xl, xh, yl, yh;
 435         xl.wordv = a->wordv;
 436         yl.wordv = b->wordv;
 437         if(a->length_B<=n){
 438                 xh.info=0;
 439                 xh.length_B = 0;
 440                 xl.length_B = a->length_B;
 441                 xl.info = 0;
 442         }else{
 443                 xl.length_B=n;
 444                 xl.info = 0;
 445                 bigint_adjust(&xl);
 446                 xh.wordv = a->wordv+n;
 447                 xh.length_B = a->length_B-n;
 448                 xh.info = 0;
 449         }
 450         if(b->length_B<=n){
 451                 yh.info=0;
 452                 yh.length_B = 0;
 453                 yl.length_B = b->length_B;
 454                 yl.info = b->info;
 455         }else{
 456                 yl.length_B=n;
 457                 yl.info = 0;
 458                 bigint_adjust(&yl);
 459                 yh.wordv = b->wordv+n;
 460                 yh.length_B = b->length_B-n;
 461                 yh.info = 0;
 462         }
 463         /* now we have split up a and b */
 464         uint8_t  tmp_b[2*n+2], m_b[2*(n+1)];
 465         bigint_t tmp, tmp2, m;
 466         tmp.wordv = tmp_b;
 467         tmp2.wordv = tmp_b+n+1;
 468         m.wordv = m_b;
 469
 470         bigint_mul_u(dest, &xl, &yl);  /* dest <= xl*yl     */
 471         bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl     */
 472         bigint_add_u(&tmp, &yh, &yl);  /* tmp  <= yh+yl     */
 473         bigint_mul_u(&m, &tmp2, &tmp); /* m    <= tmp2*tmp  */
 474         bigint_mul_u(&tmp, &xh, &yh);  /* h    <= xh*yh     */
 475         bigint_sub_u(&m, &m, dest);    /* m    <= m-dest    */
 476     bigint_sub_u(&m, &m, &tmp);    /* m    <= m-h       */
 477         bigint_add_scale_u(dest, &m, n);
 478         bigint_add_scale_u(dest, &tmp, 2*n);
 479 }
 480
 481 /******************************************************************************/
 482
 483 void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 484         uint8_t s;
 485         s  = GET_SIGN(a)?2:0;
 486         s |= GET_SIGN(b)?1:0;
 487         switch(s){
 488                 case 0: /* both positive */
 489                         bigint_mul_u(dest, a,b);
 490                         SET_POS(dest);
 491                         break;
 492                 case 1: /* a positive, b negative */
 493                         bigint_mul_u(dest, a,b);
 494                         SET_NEG(dest);
 495                         break;
 496                 case 2: /* a negative, b positive */
 497                         bigint_mul_u(dest, a,b);
 498                         SET_NEG(dest);
 499                         break;
 500                 case 3: /* both negative */
 501                         bigint_mul_u(dest, a,b);
 502                         SET_POS(dest);
 503                         break;
 504                 default: /* how can this happen?*/
 505                         break;
 506         }
 507 }
 508
 509 /******************************************************************************/
 510
 511 /* square */
 512 /* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
 513 void bigint_square(bigint_t* dest, const bigint_t* a){
 514         if(a->length_B<=4){
 515                 uint64_t r=0;
 516                 memcpy(&r, a->wordv, a->length_B);
 517                 r = r*r;
 518                 memcpy(dest->wordv, &r, 2*a->length_B);
 519                 SET_POS(dest);
 520                 dest->length_B=2*a->length_B;
 521                 bigint_adjust(dest);
 522                 return;
 523         }
 524         if(dest==a){
 525                 bigint_t d;
 526                 uint8_t d_b[a->length_B*2];
 527                 d.wordv = d_b;
 528                 bigint_square(&d, a);
 529                 bigint_copy(dest, &d);
 530                 return;
 531         }
 532         uint16_t n;
 533         n=(a->length_B+1)/2;
 534         bigint_t xh, xl, tmp; /* x-high, x-low, temp */
 535         uint8_t buffer[2*n+1];
 536         xl.wordv = a->wordv;
 537         xl.length_B = n;
 538         xh.wordv = a->wordv+n;
 539         xh.length_B = a->length_B-n;
 540         tmp.wordv = buffer;
 541         bigint_square(dest, &xl);
 542         bigint_square(&tmp, &xh);
 543         bigint_add_scale_u(dest, &tmp, 2*n);
 544         bigint_mul_u(&tmp, &xl, &xh);
 545         bigint_shiftleft(&tmp, 1);
 546         bigint_add_scale_u(dest, &tmp, n);
 547 }
 548
 549 /******************************************************************************/
 550
 551 void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
 552         bigint_t tmp;
 553         uint8_t tmp_b[b->length_B+1];
 554         uint16_t i,j,byteshift=bitscale/8;
 555         uint8_t borrow=0;
 556         int16_t t;
 557
 558         if(a->length_B < b->length_B+byteshift){
 559                 bigint_set_zero(a);
 560                 return;
 561         }
 562
 563         tmp.wordv = tmp_b;
 564         bigint_copy(&tmp, b);
 565         bigint_shiftleft(&tmp, bitscale&7);
 566
 567         for(j=0,i=byteshift; i<tmp.length_B+byteshift; ++i, ++j){
 568                 t = a->wordv[i] - tmp.wordv[j] - borrow;
 569                 a->wordv[i] = (uint8_t)t;
 570                 if(t<0){
 571                         borrow = 1;
 572                 }else{
 573                         borrow = 0;
 574                 }
 575         }
 576         while(borrow){
 577                 if(i+1 > a->length_B){
 578                         cli_hexdump_rev(&bitscale, 2);
 579                         bigint_set_zero(a);
 580                         return;
 581                 }
 582                 a->wordv[i] -= borrow;
 583                 if(a->wordv[i]!=0xff){
 584                         borrow=0;
 585                 }
 586                 ++i;
 587         }
 588         bigint_adjust(a);
 589 }
 590
 591 /******************************************************************************/
 592
 593 void bigint_reduce(bigint_t* a, const bigint_t* r){
 594         uint8_t rfbs = GET_FBS(r);
 595
 596         if(r->length_B==0){
 597                 return;
 598         }
 599         while(a->length_B > r->length_B){
 600                 bigint_sub_u_bitscale(a, r, (a->length_B-r->length_B)*8+GET_FBS(a)-rfbs-1);
 601         }
 602
 603         while((GET_FBS(a) > rfbs+1) && (a->length_B == r->length_B)){
 604                 bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1);
 605         }
 606
 607         while(bigint_cmp_u(a,r)>=0){
 608                 bigint_sub_u(a,a,r);
 609         }
 610         bigint_adjust(a);
 611 }
 612
 613 /******************************************************************************/
 614
 615 /* calculate dest = a**exp % r */
 616 /* using square&multiply */
 617 void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, const bigint_t* r){
 618         bigint_t tmp, tmp2, x;
 619         uint8_t x_b[MAX(r->length_B, a->length_B)], tmp_b[r->length_B*2], tmp2_b[r->length_B*2];
 620         int16_t i;
 621         uint8_t j;
 622         x.wordv = x_b;
 623         tmp.wordv = tmp_b;
 624         tmp2.wordv = tmp2_b;
 625         bigint_copy(&x, a);
 626         bigint_reduce(&x, r);
 627         bigint_copy(&tmp, &x);
 628         if(a->length_B==0 || exp->length_B==0 || r->length_B==0){
 629                 return;
 630         }
 631         i=exp->length_B-1;
 632         if(exp->wordv[i]!=1){
 633                 for(j=1<<(GET_FBS(exp)-1); j>0; j>>=1){
 634                         bigint_square(&tmp2, &tmp);
 635                         bigint_reduce(&tmp2, r);
 636                         if(exp->wordv[i]&j){
 637                                 bigint_mul_u(&tmp, &tmp2, &x);
 638                                 bigint_reduce(&tmp, r);
 639                         }else{
 640                                 bigint_copy(&tmp, &tmp2);
 641                         }
 642                 }
 643         }
 644         for(--i; i>=0; --i){
 645                 for(j=0x80; j>0; j>>=1){
 646                         bigint_square(&tmp2, &tmp);
 647                         bigint_reduce(&tmp2, r);
 648                         if(exp->wordv[i]&j){
 649                                 bigint_mul_u(&tmp, &tmp2, &x);
 650                                 bigint_reduce(&tmp, r);
 651                         }else{
 652                                 bigint_copy(&tmp, &tmp2);
 653                         }
 654                 }
 655         }
 656         bigint_copy(dest, &tmp);
 657 }
 658
 659 /******************************************************************************/
 660 /* gcd <-- gcd(x,y) a*x+b*y=gcd */
 661 void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, const bigint_t* y){
 662          bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
 663          volatile uint16_t i=0;
 664          if(x->length_B==0 || y->length_B==0){
 665                  return;
 666          }
 667          while(x->wordv[i]==0 && y->wordv[i]==0){
 668                  ++i;
 669          }
 670          uint8_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i];
 671          uint8_t u_b[x->length_B-i], v_b[y->length_B-i];
 672          uint8_t a_b[y->length_B+2], c_b[y->length_B+2];
 673          uint8_t b_b[x->length_B+2], d_b[x->length_B+2];
 674
 675          g.wordv = g_b;
 676          x_.wordv = x_b;
 677          y_.wordv = y_b;
 678          memset(g_b, 0, i);
 679          g_b[i]=1;
 680          g.length_B = i+1;
 681          g.info=0;
 682          x_.info = y_.info = 0;
 683          x_.length_B = x->length_B-i;
 684          y_.length_B = y->length_B-i;
 685          memcpy(x_.wordv, x->wordv+i, x_.length_B);
 686          memcpy(y_.wordv, y->wordv+i, y_.length_B);
 687          for(i=0; (x_.wordv[0]&(1<<i))==0 && (y_.wordv[0]&(1<<i))==0; ++i){
 688          }
 689
 690          bigint_adjust(&x_);
 691          bigint_adjust(&y_);
 692
 693          if(i){
 694                  bigint_shiftleft(&g, i);
 695                  bigint_shiftright(&x_, i);
 696                  bigint_shiftright(&y_, i);
 697          }
 698          u.wordv = u_b;
 699          v.wordv = v_b;
 700          a_.wordv = a_b;
 701          b_.wordv = b_b;
 702          c_.wordv = c_b;
 703          d_.wordv = d_b;
 704
 705          bigint_copy(&u, &x_);
 706          bigint_copy(&v, &y_);
 707          a_.wordv[0] = 1;
 708          a_.length_B = 1;
 709          a_.info = 0;
 710          d_.wordv[0] = 1;
 711          d_.length_B = 1;
 712          d_.info = 0;
 713          bigint_set_zero(&b_);
 714          bigint_set_zero(&c_);
 715          do{
 716                  while((u.wordv[0]&1)==0){
 717                          bigint_shiftright(&u, 1);
 718                          if((a_.wordv[0]&1) || (b_.wordv[0]&1)){
 719                                  bigint_add_s(&a_, &a_, &y_);
 720                                  bigint_sub_s(&b_, &b_, &x_);
 721                          }
 722                          bigint_shiftright(&a_, 1);
 723                          bigint_shiftright(&b_, 1);
 724                  }
 725                  while((v.wordv[0]&1)==0){
 726                          bigint_shiftright(&v, 1);
 727                          if((c_.wordv[0]&1) || (d_.wordv[0]&1)){
 728                                  bigint_add_s(&c_, &c_, &y_);
 729                                  bigint_sub_s(&d_, &d_, &x_);
 730                          }
 731                          bigint_shiftright(&c_, 1);
 732                          bigint_shiftright(&d_, 1);
 733
 734                  }
 735                  if(bigint_cmp_u(&u, &v)>=0){
 736                         bigint_sub_u(&u, &u, &v);
 737                         bigint_sub_s(&a_, &a_, &c_);
 738                         bigint_sub_s(&b_, &b_, &d_);
 739                  }else{
 740                         bigint_sub_u(&v, &v, &u);
 741                         bigint_sub_s(&c_, &c_, &a_);
 742                         bigint_sub_s(&d_, &d_, &b_);
 743                  }
 744          }while(u.length_B);
 745          if(gcd){
 746                  bigint_mul_s(gcd, &v, &g);
 747          }
 748          if(a){
 749                 bigint_copy(a, &c_);
 750          }
 751          if(b){
 752                  bigint_copy(b, &d_);
 753          }
 754 }
 755
 756 /******************************************************************************/
 757
 758 void bigint_inverse(bigint_t* dest, bigint_t* a, bigint_t* m){
 759         bigint_gcdext(NULL, dest, NULL, a, m);
 760         while(dest->info&BIGINT_NEG_MASK){
 761                 bigint_add_s(dest, dest, m);
 762         }
 763 }
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