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 #include "bigint_io.h"
  33 #include "cli.h"
  34
  35 #ifndef MAX
  36  #define MAX(a,b) (((a)>(b))?(a):(b))
  37 #endif
  38
  39 #ifndef MIN
  40  #define MIN(a,b) (((a)<(b))?(a):(b))
  41 #endif
  42
  43 #define SET_FBS(a, v) do{(a)->info &=0xF8; (a)->info |= (v);}while(0)
  44 #define GET_FBS(a)   ((a)->info&BIGINT_FBS_MASK)
  45 #define SET_NEG(a)   (a)->info |= BIGINT_NEG_MASK
  46 #define SET_POS(a)   (a)->info &= ~BIGINT_NEG_MASK
  47 #define XCHG(a,b)    do{(a)^=(b); (b)^=(a); (a)^=(b);}while(0)
  48 #define XCHG_PTR(a,b)    do{ a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
  49                                  b = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \
  50                                  a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b)));}while(0)
  51
  52 #define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
  53
  54 /******************************************************************************/
  55 void bigint_adjust(bigint_t* a){
  56         while(a->length_B!=0 && a->wordv[a->length_B-1]==0){
  57                 a->length_B--;
  58         }
  59         if(a->length_B==0){
  60                 a->info=0;
  61                 return;
  62         }
  63         uint8_t t;
  64         uint8_t i = 0x07;
  65         t = a->wordv[a->length_B-1];
  66         while((t&0x80)==0 && i){
  67                 t<<=1;
  68                 i--;
  69         }
  70         SET_FBS(a, i);
  71 }
  72
  73 /******************************************************************************/
  74
  75 void bigint_copy(bigint_t* dest, const bigint_t* src){
  76         memcpy(dest->wordv, src->wordv, src->length_B);
  77         dest->length_B = src->length_B;
  78         dest->info = src->info;
  79 }
  80
  81 /******************************************************************************/
  82
  83 /* this should be implemented in assembly */
  84 /*
  85 void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
  86         uint16_t t=0, i;
  87         if(a->length_B < b->length_B){
  88                 XCHG_PTR(a,b);
  89         }
  90         for(i=0; i<b->length_B; ++i){
  91                 t = a->wordv[i] + b->wordv[i] + t;
  92                 dest->wordv[i] = (uint8_t)t;
  93                 t>>=8;
  94         }
  95         for(; i<a->length_B; ++i){
  96                 t = a->wordv[i] + t;
  97                 dest->wordv[i] = (uint8_t)t;
  98                 t>>=8;
  99         }
 100         dest->wordv[i++] = t;
 101         dest->length_B = i;
 102         bigint_adjust(dest);
 103 }
 104 */
 105 /******************************************************************************/
 106
 107 /* this should be implemented in assembly */
 108 void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
 109         uint16_t i,j=0;
 110         uint16_t t=0;
 111         if(scale>dest->length_B)
 112                 memset(dest->wordv+dest->length_B, 0, scale-dest->length_B);
 113         for(i=scale; i<a->length_B+scale; ++i,++j){
 114                 t = a->wordv[j] + t;
 115                 if(dest->length_B>i){
 116                         t += dest->wordv[i];
 117                 }
 118                 dest->wordv[i] = (uint8_t)t;
 119                 t>>=8;
 120         }
 121         while(t){
 122                 if(dest->length_B>i){
 123                         t = dest->wordv[i] + t;
 124                 }
 125                 dest->wordv[i] = (uint8_t)t;
 126                 t>>=8;
 127                 ++i;
 128         }
 129         if(dest->length_B < i){
 130                 dest->length_B = i;
 131         }
 132         bigint_adjust(dest);
 133 }
 134
 135 /******************************************************************************/
 136
 137 /* this should be implemented in assembly */
 138 void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 139         int8_t borrow=0;
 140         int8_t  r;
 141         int16_t t;
 142         uint16_t i, min, max;
 143         min = MIN(a->length_B, b->length_B);
 144         max = MAX(a->length_B, b->length_B);
 145         r = bigint_cmp_u(a,b);
 146         if(r==0){
 147                 dest->length_B = 0;
 148                 dest->wordv[0] = 0;
 149                 bigint_adjust(dest);
 150                 return;
 151         }
 152         if(b->length_B==0){
 153                 dest->length_B = a->length_B;
 154                 memcpy(dest->wordv, a->wordv, a->length_B);
 155                 dest->info = a->info;
 156                 SET_POS(dest);
 157                 return;
 158         }
 159         if(a->length_B==0){
 160                         dest->length_B = b->length_B;
 161                         memcpy(dest->wordv, b->wordv, b->length_B);
 162                         dest->info = b->info;
 163                         SET_NEG(dest);
 164                         return;
 165         }
 166         if(r<0){
 167                 bigint_sub_u(dest, b, a);
 168                 SET_NEG(dest);
 169         }else{
 170                 for(i=0; i<min; ++i){
 171                         t = a->wordv[i] - b->wordv[i] - borrow;
 172                         if(t<0){
 173                                 borrow = 1;
 174                                 dest->wordv[i]=(uint8_t)t;
 175                         }else{
 176                                 borrow = 0;
 177                                 dest->wordv[i]=(uint8_t)t;
 178                         }
 179                 }
 180                 for(;i<max; ++i){
 181                         t = a->wordv[i] - borrow;
 182                         if(t<0){
 183                                 borrow = 1;
 184                                 dest->wordv[i]=(uint8_t)t;
 185                         }else{
 186                                 borrow = 0;
 187                                 dest->wordv[i]=(uint8_t)t;
 188                         }
 189
 190                 }
 191                 SET_POS(dest);
 192                 dest->length_B = i;
 193                 bigint_adjust(dest);
 194         }
 195 }
 196
 197 /******************************************************************************/
 198
 199 int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
 200         if(a->length_B > b->length_B){
 201                 return 1;
 202         }
 203         if(a->length_B < b->length_B){
 204                 return -1;
 205         }
 206         if(a->length_B==0){
 207                 return 0;
 208         }
 209         uint16_t i;
 210         i = a->length_B-1;
 211         do{
 212                 if(a->wordv[i]!=b->wordv[i]){
 213                         if(a->wordv[i]>b->wordv[i]){
 214                                 return 1;
 215                         }else{
 216                                 return -1;
 217                         }
 218                 }
 219         }while(i--);
 220         return 0;
 221 }
 222
 223 /******************************************************************************/
 224
 225 void bigint_add_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 226         uint8_t s;
 227         s  = GET_SIGN(a)?2:0;
 228         s |= GET_SIGN(b)?1:0;
 229         switch(s){
 230                 case 0: /* both positive */
 231                         bigint_add_u(dest, a,b);
 232                         SET_POS(dest);
 233                         break;
 234                 case 1: /* a positive, b negative */
 235                         bigint_sub_u(dest, a, b);
 236                         break;
 237                 case 2: /* a negative, b positive */
 238                         bigint_sub_u(dest, b, a);
 239                         break;
 240                 case 3: /* both negative */
 241                         bigint_add_u(dest, a, b);
 242                         SET_NEG(dest);
 243                         break;
 244                 default: /* how can this happen?*/
 245                         break;
 246         }
 247 }
 248
 249 /******************************************************************************/
 250
 251 void bigint_sub_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 252         uint8_t s;
 253         s  = GET_SIGN(a)?2:0;
 254         s |= GET_SIGN(b)?1:0;
 255         switch(s){
 256                 case 0: /* both positive */
 257                         bigint_sub_u(dest, a,b);
 258                         break;
 259                 case 1: /* a positive, b negative */
 260                         bigint_add_u(dest, a, b);
 261                         SET_POS(dest);
 262                         break;
 263                 case 2: /* a negative, b positive */
 264                         bigint_add_u(dest, a, b);
 265                         SET_NEG(dest);
 266                         break;
 267                 case 3: /* both negative */
 268                         bigint_sub_u(dest, b, a);
 269                         break;
 270                 default: /* how can this happen?*/
 271                                         break;
 272         }
 273
 274 }
 275
 276 /******************************************************************************/
 277
 278 int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){
 279         uint8_t s;
 280         if(a->length_B==0 && b->length_B==0){
 281                 return 0;
 282         }
 283         s  = GET_SIGN(a)?2:0;
 284         s |= GET_SIGN(b)?1:0;
 285         switch(s){
 286                 case 0: /* both positive */
 287                         return bigint_cmp_u(a, b);
 288                         break;
 289                 case 1: /* a positive, b negative */
 290                         return 1;
 291                         break;
 292                 case 2: /* a negative, b positive */
 293                         return -1;
 294                         break;
 295                 case 3: /* both negative */
 296                         return bigint_cmp_u(b, a);
 297                         break;
 298                 default: /* how can this happen?*/
 299                                         break;
 300         }
 301         return 0; /* just to satisfy the compiler */
 302 }
 303
 304 /******************************************************************************/
 305
 306 void bigint_shiftleft(bigint_t* a, uint16_t shift){
 307         uint16_t byteshift;
 308         uint16_t i;
 309         uint8_t bitshift;
 310         uint16_t t=0;
 311         byteshift = (shift+3)/8;
 312         bitshift = shift&7;
 313         memmove(a->wordv+byteshift, a->wordv, a->length_B);
 314         memset(a->wordv, 0, byteshift);
 315         if(bitshift!=0){
 316                 if(bitshift<=4){ /* shift to the left */
 317                         for(i=byteshift; i<a->length_B+byteshift; ++i){
 318                                 t |= (a->wordv[i])<<bitshift;
 319                                 a->wordv[i] = (uint8_t)t;
 320                                 t >>= 8;
 321                         }
 322                         a->wordv[i] = (uint8_t)t;
 323                         byteshift++;
 324                 }else{ /* shift to the right */
 325                         for(i=a->length_B+byteshift-1; i>byteshift-1; --i){
 326                                 t |= (a->wordv[i])<<(bitshift);
 327                                 a->wordv[i] = (uint8_t)(t>>8);
 328                                 t <<= 8;
 329                         }
 330                         t |= (a->wordv[i])<<(bitshift);
 331                         a->wordv[i] = (uint8_t)(t>>8);
 332                 }
 333         }
 334         a->length_B += byteshift;
 335         bigint_adjust(a);
 336 }
 337
 338 /******************************************************************************/
 339
 340 void bigint_shiftright(bigint_t* a, uint16_t shift){
 341         uint16_t byteshift;
 342         uint16_t i;
 343         uint8_t bitshift;
 344         uint16_t t=0;
 345         byteshift = shift/8;
 346         bitshift = shift&7;
 347         if(byteshift >= a->length_B){ /* we would shift out more than we have */
 348                 bigint_set_zero(a);
 349                 return;
 350         }
 351         if(byteshift == a->length_B-1 && bitshift>GET_FBS(a)){
 352                 bigint_set_zero(a);
 353                 return;
 354         }
 355         if(byteshift){
 356                 memmove(a->wordv, a->wordv+byteshift, a->length_B-byteshift);
 357                 memset(a->wordv+a->length_B-byteshift, 0,  byteshift);
 358         }
 359         if(bitshift!=0){
 360          /* shift to the right */
 361                 for(i=a->length_B-byteshift-1; i>0; --i){
 362                         t |= (a->wordv[i])<<(8-bitshift);
 363                         a->wordv[i] = (uint8_t)(t>>8);
 364                         t <<= 8;
 365                 }
 366                 t |= (a->wordv[0])<<(8-bitshift);
 367                 a->wordv[0] = (uint8_t)(t>>8);
 368         }
 369         a->length_B -= byteshift;
 370         bigint_adjust(a);
 371 }
 372
 373 /******************************************************************************/
 374
 375 void bigint_xor(bigint_t* dest, const bigint_t* a){
 376         uint16_t i;
 377         for(i=0; i<a->length_B; ++i){
 378                 dest->wordv[i] ^= a->wordv[i];
 379         }
 380         bigint_adjust(dest);
 381 }
 382
 383 /******************************************************************************/
 384
 385 void bigint_set_zero(bigint_t* a){
 386         a->length_B=0;
 387 }
 388
 389 /******************************************************************************/
 390
 391 /* using the Karatsuba-Algorithm */
 392 /* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */
 393 void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 394         if(dest==a || dest==b){
 395                 bigint_t d;
 396                 uint8_t d_b[a->length_B+b->length_B];
 397                 d.wordv = d_b;
 398                 bigint_mul_u(&d, a, b);
 399                 bigint_copy(dest, &d);
 400                 return;
 401         }
 402         if(a->length_B==0 || b->length_B==0){
 403                 bigint_set_zero(dest);
 404                 return;
 405         }
 406         if(a->length_B==1 || b->length_B==1){
 407                 if(a->length_B!=1){
 408                         XCHG_PTR(a,b);
 409                 }
 410                 uint16_t i, t=0;
 411                 uint8_t x = a->wordv[0];
 412                 for(i=0; i<b->length_B; ++i){
 413                         t += b->wordv[i]*x;
 414                         dest->wordv[i] = (uint8_t)t;
 415                         t>>=8;
 416                 }
 417                 dest->wordv[i] = (uint8_t)t;
 418                 dest->length_B=i+1;
 419                 bigint_adjust(dest);
 420                 return;
 421         }
 422         if(a->length_B<=4 && b->length_B<=4){
 423                 uint32_t p=0, q=0;
 424                 uint64_t r;
 425                 memcpy(&p, a->wordv, a->length_B);
 426                 memcpy(&q, b->wordv, b->length_B);
 427                 r = (uint64_t)p*(uint64_t)q;
 428                 memcpy(dest->wordv, &r, a->length_B+b->length_B);
 429                 dest->length_B =  a->length_B+b->length_B;
 430                 bigint_adjust(dest);
 431                 return;
 432         }
 433         bigint_set_zero(dest);
 434         /* split a in xh & xl; split b in yh & yl */
 435         uint16_t n;
 436         n=(MAX(a->length_B, b->length_B)+1)/2;
 437         bigint_t xl, xh, yl, yh;
 438         xl.wordv = a->wordv;
 439         yl.wordv = b->wordv;
 440         if(a->length_B<=n){
 441                 xh.info=0;
 442                 xh.length_B = 0;
 443                 xl.length_B = a->length_B;
 444                 xl.info = 0;
 445         }else{
 446                 xl.length_B=n;
 447                 xl.info = 0;
 448                 bigint_adjust(&xl);
 449                 xh.wordv = a->wordv+n;
 450                 xh.length_B = a->length_B-n;
 451                 xh.info = 0;
 452         }
 453         if(b->length_B<=n){
 454                 yh.info=0;
 455                 yh.length_B = 0;
 456                 yl.length_B = b->length_B;
 457                 yl.info = b->info;
 458         }else{
 459                 yl.length_B=n;
 460                 yl.info = 0;
 461                 bigint_adjust(&yl);
 462                 yh.wordv = b->wordv+n;
 463                 yh.length_B = b->length_B-n;
 464                 yh.info = 0;
 465         }
 466         /* now we have split up a and b */
 467         uint8_t  tmp_b[2*n+2], m_b[2*(n+1)];
 468         bigint_t tmp, tmp2, m;
 469         tmp.wordv = tmp_b;
 470         tmp2.wordv = tmp_b+n+1;
 471         m.wordv = m_b;
 472
 473         bigint_mul_u(dest, &xl, &yl);  /* dest <= xl*yl     */
 474         bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl     */
 475         bigint_add_u(&tmp, &yh, &yl);  /* tmp  <= yh+yl     */
 476         bigint_mul_u(&m, &tmp2, &tmp); /* m    <= tmp2*tmp  */
 477         bigint_mul_u(&tmp, &xh, &yh);  /* h    <= xh*yh     */
 478         bigint_sub_u(&m, &m, dest);    /* m    <= m-dest    */
 479     bigint_sub_u(&m, &m, &tmp);    /* m    <= m-h       */
 480         bigint_add_scale_u(dest, &m, n);
 481         bigint_add_scale_u(dest, &tmp, 2*n);
 482 }
 483
 484 /******************************************************************************/
 485
 486 void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
 487         uint8_t s;
 488         s  = GET_SIGN(a)?2:0;
 489         s |= GET_SIGN(b)?1:0;
 490         switch(s){
 491                 case 0: /* both positive */
 492                         bigint_mul_u(dest, a,b);
 493                         SET_POS(dest);
 494                         break;
 495                 case 1: /* a positive, b negative */
 496                         bigint_mul_u(dest, a,b);
 497                         SET_NEG(dest);
 498                         break;
 499                 case 2: /* a negative, b positive */
 500                         bigint_mul_u(dest, a,b);
 501                         SET_NEG(dest);
 502                         break;
 503                 case 3: /* both negative */
 504                         bigint_mul_u(dest, a,b);
 505                         SET_POS(dest);
 506                         break;
 507                 default: /* how can this happen?*/
 508                         break;
 509         }
 510 }
 511
 512 /******************************************************************************/
 513
 514 /* square */
 515 /* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
 516 void bigint_square(bigint_t* dest, const bigint_t* a){
 517         if(a->length_B<=4){
 518                 uint64_t r=0;
 519                 memcpy(&r, a->wordv, a->length_B);
 520                 r = r*r;
 521                 memcpy(dest->wordv, &r, 2*a->length_B);
 522                 SET_POS(dest);
 523                 dest->length_B=2*a->length_B;
 524                 bigint_adjust(dest);
 525                 return;
 526         }
 527         if(dest==a){
 528                 bigint_t d;
 529                 uint8_t d_b[a->length_B*2];
 530                 d.wordv = d_b;
 531                 bigint_square(&d, a);
 532                 bigint_copy(dest, &d);
 533                 return;
 534         }
 535         uint16_t n;
 536         n=(a->length_B+1)/2;
 537         bigint_t xh, xl, tmp; /* x-high, x-low, temp */
 538         uint8_t buffer[2*n+1];
 539         xl.wordv = a->wordv;
 540         xl.length_B = n;
 541         xh.wordv = a->wordv+n;
 542         xh.length_B = a->length_B-n;
 543         tmp.wordv = buffer;
 544         bigint_square(dest, &xl);
 545         bigint_square(&tmp, &xh);
 546         bigint_add_scale_u(dest, &tmp, 2*n);
 547         bigint_mul_u(&tmp, &xl, &xh);
 548         bigint_shiftleft(&tmp, 1);
 549         bigint_add_scale_u(dest, &tmp, n);
 550 }
 551
 552 /******************************************************************************/
 553
 554 void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
 555         bigint_t tmp;
 556         uint8_t tmp_b[b->length_B+1];
 557         uint16_t i,j,byteshift=bitscale/8;
 558         uint8_t borrow=0;
 559         int16_t t;
 560
 561         if(a->length_B < b->length_B+byteshift){
 562                 cli_putstr_P(PSTR("\r\nERROR: bigint_sub_u_bitscale result negative"));
 563                 bigint_set_zero(a);
 564                 return;
 565         }
 566
 567         tmp.wordv = tmp_b;
 568         bigint_copy(&tmp, b);
 569         bigint_shiftleft(&tmp, bitscale&7);
 570
 571         for(j=0,i=byteshift; i<tmp.length_B+byteshift; ++i, ++j){
 572                 t = a->wordv[i] - tmp.wordv[j] - borrow;
 573                 a->wordv[i] = (uint8_t)t;
 574                 if(t<0){
 575                         borrow = 1;
 576                 }else{
 577                         borrow = 0;
 578                 }
 579         }
 580         while(borrow){
 581                 if(i+1 > a->length_B){
 582                         cli_putstr_P(PSTR("\r\nERROR: bigint_sub_u_bitscale result negative (2) shift="));
 583                         cli_hexdump_rev(&bitscale, 2);
 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         uint8_t rfbs = GET_FBS(r);
 600 /*
 601         cli_putstr_P(PSTR("\r\nreduce "));
 602         bigint_print_hex(a);
 603         cli_putstr_P(PSTR(" % "));
 604         bigint_print_hex(r);
 605         cli_putstr_P(PSTR("\r\n"));
 606 */
 607
 608         if(r->length_B==0){
 609                 return;
 610         }
 611         while(a->length_B > r->length_B){
 612                 bigint_sub_u_bitscale(a, r, (a->length_B-r->length_B)*8+GET_FBS(a)-rfbs-1);
 613         }
 614
 615         while((GET_FBS(a) > rfbs+1) && (a->length_B == r->length_B)){
 616                 bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1);
 617         }
 618
 619         while(bigint_cmp_u(a,r)>=0){
 620                 bigint_sub_u(a,a,r);
 621         }
 622         bigint_adjust(a);
 623 }
 624
 625 /******************************************************************************/
 626
 627 /* calculate dest = a**exp % r */
 628 /* using square&multiply */
 629 void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, const bigint_t* r){
 630         bigint_t tmp, tmp2, x;
 631         uint8_t x_b[MAX(r->length_B, a->length_B)], tmp_b[r->length_B*2], tmp2_b[r->length_B*2];
 632         int16_t i;
 633         uint8_t j;
 634         x.wordv = x_b;
 635         tmp.wordv = tmp_b;
 636         tmp2.wordv = tmp2_b;
 637         bigint_copy(&x, a);
 638         bigint_reduce(&x, r);
 639         bigint_copy(&tmp, &x);
 640         if(a->length_B==0 || exp->length_B==0 || r->length_B==0){
 641                 return;
 642         }
 643         i=exp->length_B-1;
 644         if(exp->wordv[i]!=1){
 645                 for(j=1<<(GET_FBS(exp)-1); j>0; j>>=1){
 646         //              cli_putc('Q');
 647                         bigint_square(&tmp2, &tmp);
 648                         bigint_reduce(&tmp2, r);
 649                         if(exp->wordv[i]&j){
 650         //                      cli_putc('M');
 651                                 bigint_mul_u(&tmp, &tmp2, &x);
 652                                 bigint_reduce(&tmp, r);
 653                         }else{
 654                                 bigint_copy(&tmp, &tmp2);
 655                         }
 656                 }
 657         }
 658         for(--i; i>=0; --i){
 659                 for(j=0x80; j>0; j>>=1){
 660 //                      cli_putc('q');
 661                         bigint_square(&tmp2, &tmp);
 662                         bigint_reduce(&tmp2, r);
 663                         if(exp->wordv[i]&j){
 664 //                              cli_putc('m');
 665                                 bigint_mul_u(&tmp, &tmp2, &x);
 666                                 bigint_reduce(&tmp, r);
 667                         }else{
 668                                 bigint_copy(&tmp, &tmp2);
 669                         }
 670                 }
 671         }
 672 //      cli_putstr_P(PSTR("\r\n"));
 673         bigint_copy(dest, &tmp);
 674 }
 675 #define DEBUG 0
 676 /******************************************************************************/
 677 /* gcd <-- gcd(x,y) a*x+b*y=gcd */
 678 void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, const bigint_t* y){
 679          bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
 680          volatile uint16_t i=0;
 681          if(x->length_B==0 || y->length_B==0){
 682                  return;
 683          }
 684          while(x->wordv[i]==0 && y->wordv[i]==0){
 685                  ++i;
 686          }
 687          uint8_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i];
 688          uint8_t u_b[x->length_B-i], v_b[y->length_B-i];
 689          uint8_t a_b[y->length_B+2], c_b[y->length_B+2];
 690          uint8_t b_b[x->length_B+2], d_b[x->length_B+2];
 691
 692          g.wordv = g_b;
 693          x_.wordv = x_b;
 694          y_.wordv = y_b;
 695          memset(g_b, 0, i);
 696          g_b[i]=1;
 697          g.length_B = i+1;
 698          g.info=0;
 699          x_.info = y_.info = 0;
 700          x_.length_B = x->length_B-i;
 701          y_.length_B = y->length_B-i;
 702          memcpy(x_.wordv, x->wordv+i, x_.length_B);
 703          memcpy(y_.wordv, y->wordv+i, y_.length_B);
 704          for(i=0; (x_.wordv[0]&(1<<i))==0 && (y_.wordv[0]&(1<<i))==0; ++i){
 705          }
 706
 707 #if DEBUG
 708          cli_putstr_P(PSTR("\r\nDBG: initshift = "));
 709          cli_hexdump_rev(&i, 2);
 710 #endif
 711          bigint_adjust(&x_);
 712          bigint_adjust(&y_);
 713
 714          if(i){
 715                  bigint_shiftleft(&g, i);
 716 #if DEBUG
 717          cli_putstr_P(PSTR("\r\nDBG: initshift (2) = "));
 718          cli_hexdump_rev(&i, 2);
 719          cli_putstr_P(PSTR("\r\n x' = "));
 720                 bigint_print_hex(&x_);
 721                 cli_putstr_P(PSTR("\r\n y' = "));
 722                 bigint_print_hex(&y_);
 723 #endif
 724                 bigint_shiftright(&x_, i);
 725                 bigint_shiftright(&y_, i);
 726 #if DEBUG
 727                 cli_putstr_P(PSTR("\r\n x' = "));
 728                 bigint_print_hex(&x_);
 729                 cli_putstr_P(PSTR("\r\n y' = "));
 730                 bigint_print_hex(&y_);
 731 #endif
 732          }
 733          u.wordv = u_b;
 734          v.wordv = v_b;
 735          a_.wordv = a_b;
 736          b_.wordv = b_b;
 737          c_.wordv = c_b;
 738          d_.wordv = d_b;
 739
 740          bigint_copy(&u, &x_);
 741          bigint_copy(&v, &y_);
 742          a_.wordv[0] = 1;
 743          a_.length_B = 1;
 744          a_.info = 0;
 745          d_.wordv[0] = 1;
 746          d_.length_B = 1;
 747          d_.info = 0;
 748          bigint_set_zero(&b_);
 749          bigint_set_zero(&c_);
 750          do{
 751 #if DEBUG
 752                  cli_putstr_P(PSTR("\r\n while u%2==0; u = "));
 753                  bigint_print_hex(&u);
 754                  cli_putstr_P(PSTR("\r\nDBG: (10) a = "));
 755                  bigint_print_hex(&a_);
 756                  cli_putstr_P(PSTR("\r\nDBG: (10) b = "));
 757                  bigint_print_hex(&b_);
 758                  cli_putstr_P(PSTR("\r\nDBG: (10) c = "));
 759                  bigint_print_hex(&c_);
 760                  cli_putstr_P(PSTR("\r\nDBG: (10) d = "));
 761                  bigint_print_hex(&d_);
 762 #endif
 763                  while((u.wordv[0]&1)==0){
 764                          bigint_shiftright(&u, 1);
 765                          if((a_.wordv[0]&1) || (b_.wordv[0]&1)){
 766                                  bigint_add_s(&a_, &a_, &y_);
 767                                  bigint_sub_s(&b_, &b_, &x_);
 768                          }
 769                          bigint_shiftright(&a_, 1);
 770                          bigint_shiftright(&b_, 1);
 771                  }
 772 #if DEBUG
 773                  cli_putstr_P(PSTR("\r\n while v%2==0; v = "));
 774                  bigint_print_hex(&v);
 775                  cli_putstr_P(PSTR("\r\nDBG: (20) a = "));
 776                  bigint_print_hex(&a_);
 777                  cli_putstr_P(PSTR("\r\nDBG: (20) b = "));
 778                  bigint_print_hex(&b_);
 779                  cli_putstr_P(PSTR("\r\nDBG: (20) c = "));
 780                  bigint_print_hex(&c_);
 781                  cli_putstr_P(PSTR("\r\nDBG: (20) d = "));
 782                  bigint_print_hex(&d_);
 783 #endif
 784                  while((v.wordv[0]&1)==0){
 785                          bigint_shiftright(&v, 1);
 786                          if((c_.wordv[0]&1) || (d_.wordv[0]&1)){
 787                                  bigint_add_s(&c_, &c_, &y_);
 788                                  bigint_sub_s(&d_, &d_, &x_);
 789                          }
 790                          bigint_shiftright(&c_, 1);
 791                          bigint_shiftright(&d_, 1);
 792
 793                  }
 794 #if DEBUG
 795                  cli_putstr_P(PSTR("\r\n if u>=v ..."));
 796                  cli_putstr_P(PSTR("\r\nDBG: (30) a = "));
 797                  bigint_print_hex(&a_);
 798                  cli_putstr_P(PSTR("\r\nDBG: (30) b = "));
 799                  bigint_print_hex(&b_);
 800                  cli_putstr_P(PSTR("\r\nDBG: (30) c = "));
 801                  bigint_print_hex(&c_);
 802                  cli_putstr_P(PSTR("\r\nDBG: (30) d = "));
 803                  bigint_print_hex(&d_);
 804 #endif
 805                  if(bigint_cmp_u(&u, &v)>=0){
 806                         bigint_sub_u(&u, &u, &v);
 807                         bigint_sub_s(&a_, &a_, &c_);
 808                         bigint_sub_s(&b_, &b_, &d_);
 809                  }else{
 810                         bigint_sub_u(&v, &v, &u);
 811                         bigint_sub_s(&c_, &c_, &a_);
 812                         bigint_sub_s(&d_, &d_, &b_);
 813                  }
 814 #if DEBUG
 815                  if(GET_SIGN(&u)){
 816                          cli_putstr_P(PSTR("\r\nDBG: u negative! u = "));
 817                          bigint_print_hex(&u);
 818                  }
 819                  if(GET_SIGN(&v)){
 820                          cli_putstr_P(PSTR("\r\nDBG: v negative! v = "));
 821                          bigint_print_hex(&v);
 822                  }
 823 #endif
 824 /*
 825                  cli_putstr_P(PSTR("\r\nDBG: (2) a = "));
 826                  bigint_print_hex(&a_);
 827                  cli_putstr_P(PSTR("\r\nDBG: (2) b = "));
 828                  bigint_print_hex(&b_);
 829                  cli_putstr_P(PSTR("\r\nDBG: (2) c = "));
 830                  bigint_print_hex(&c_);
 831                  cli_putstr_P(PSTR("\r\nDBG: (2) d = "));
 832                  bigint_print_hex(&d_);
 833 */
 834          }while(u.length_B);
 835          if(gcd){
 836                  bigint_mul_s(gcd, &v, &g);
 837          }
 838          if(a){
 839                 bigint_copy(a, &c_);
 840          }
 841          if(b){
 842                  bigint_copy(b, &d_);
 843          }
 844 }
 845
 846 /******************************************************************************/
 847
 848 void bigint_inverse(bigint_t* dest, bigint_t* a, bigint_t* m){
 849         bigint_gcdext(NULL, dest, NULL, a, m);
 850         while(dest->info&BIGINT_NEG_MASK){
 851                 bigint_add_s(dest, dest, m);
 852         }
 853 }
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