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