Mercurial > dropbear
comparison pre_gen/mpi.c @ 142:d29b64170cf0 libtommath-orig
import of libtommath 0.32
author | Matt Johnston <matt@ucc.asn.au> |
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date | Sun, 19 Dec 2004 11:33:56 +0000 |
parents | 86e0b50a9b58 |
children | d8254fc979e9 |
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19:e1037a1e12e7 | 142:d29b64170cf0 |
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1 /* Start: bn_error.c */ | 1 /* Start: bn_error.c */ |
2 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2 #include <tommath.h> |
3 * | 3 #ifdef BN_ERROR_C |
4 * LibTomMath is a library that provides multiple-precision | 4 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5 * integer arithmetic as well as number theoretic functionality. | 5 * |
6 * | 6 * LibTomMath is a library that provides multiple-precision |
7 * The library was designed directly after the MPI library by | 7 * integer arithmetic as well as number theoretic functionality. |
8 * Michael Fromberger but has been written from scratch with | 8 * |
9 * additional optimizations in place. | 9 * The library was designed directly after the MPI library by |
10 * | 10 * Michael Fromberger but has been written from scratch with |
11 * The library is free for all purposes without any express | 11 * additional optimizations in place. |
12 * guarantee it works. | 12 * |
13 * | 13 * The library is free for all purposes without any express |
14 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 14 * guarantee it works. |
15 */ | 15 * |
16 #include <tommath.h> | 16 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
17 */ | |
17 | 18 |
18 static const struct { | 19 static const struct { |
19 int code; | 20 int code; |
20 char *msg; | 21 char *msg; |
21 } msgs[] = { | 22 } msgs[] = { |
38 | 39 |
39 /* generic reply for invalid code */ | 40 /* generic reply for invalid code */ |
40 return "Invalid error code"; | 41 return "Invalid error code"; |
41 } | 42 } |
42 | 43 |
44 #endif | |
43 | 45 |
44 /* End: bn_error.c */ | 46 /* End: bn_error.c */ |
45 | 47 |
46 /* Start: bn_fast_mp_invmod.c */ | 48 /* Start: bn_fast_mp_invmod.c */ |
47 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 49 #include <tommath.h> |
48 * | 50 #ifdef BN_FAST_MP_INVMOD_C |
49 * LibTomMath is a library that provides multiple-precision | 51 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
50 * integer arithmetic as well as number theoretic functionality. | 52 * |
51 * | 53 * LibTomMath is a library that provides multiple-precision |
52 * The library was designed directly after the MPI library by | 54 * integer arithmetic as well as number theoretic functionality. |
53 * Michael Fromberger but has been written from scratch with | 55 * |
54 * additional optimizations in place. | 56 * The library was designed directly after the MPI library by |
55 * | 57 * Michael Fromberger but has been written from scratch with |
56 * The library is free for all purposes without any express | 58 * additional optimizations in place. |
57 * guarantee it works. | 59 * |
58 * | 60 * The library is free for all purposes without any express |
59 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 61 * guarantee it works. |
60 */ | 62 * |
61 #include <tommath.h> | 63 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
64 */ | |
62 | 65 |
63 /* computes the modular inverse via binary extended euclidean algorithm, | 66 /* computes the modular inverse via binary extended euclidean algorithm, |
64 * that is c = 1/a mod b | 67 * that is c = 1/a mod b |
65 * | 68 * |
66 * Based on mp_invmod except this is optimized for the case where b is | 69 * Based on slow invmod except this is optimized for the case where b is |
67 * odd as per HAC Note 14.64 on pp. 610 | 70 * odd as per HAC Note 14.64 on pp. 610 |
68 */ | 71 */ |
69 int | 72 int |
70 fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c) | 73 fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c) |
71 { | 74 { |
185 res = MP_OKAY; | 188 res = MP_OKAY; |
186 | 189 |
187 __ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); | 190 __ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); |
188 return res; | 191 return res; |
189 } | 192 } |
193 #endif | |
190 | 194 |
191 /* End: bn_fast_mp_invmod.c */ | 195 /* End: bn_fast_mp_invmod.c */ |
192 | 196 |
193 /* Start: bn_fast_mp_montgomery_reduce.c */ | 197 /* Start: bn_fast_mp_montgomery_reduce.c */ |
194 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 198 #include <tommath.h> |
195 * | 199 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C |
196 * LibTomMath is a library that provides multiple-precision | 200 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
197 * integer arithmetic as well as number theoretic functionality. | 201 * |
198 * | 202 * LibTomMath is a library that provides multiple-precision |
199 * The library was designed directly after the MPI library by | 203 * integer arithmetic as well as number theoretic functionality. |
200 * Michael Fromberger but has been written from scratch with | 204 * |
201 * additional optimizations in place. | 205 * The library was designed directly after the MPI library by |
202 * | 206 * Michael Fromberger but has been written from scratch with |
203 * The library is free for all purposes without any express | 207 * additional optimizations in place. |
204 * guarantee it works. | 208 * |
205 * | 209 * The library is free for all purposes without any express |
206 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 210 * guarantee it works. |
207 */ | 211 * |
208 #include <tommath.h> | 212 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
213 */ | |
209 | 214 |
210 /* computes xR**-1 == x (mod N) via Montgomery Reduction | 215 /* computes xR**-1 == x (mod N) via Montgomery Reduction |
211 * | 216 * |
212 * This is an optimized implementation of mp_montgomery_reduce | 217 * This is an optimized implementation of montgomery_reduce |
213 * which uses the comba method to quickly calculate the columns of the | 218 * which uses the comba method to quickly calculate the columns of the |
214 * reduction. | 219 * reduction. |
215 * | 220 * |
216 * Based on Algorithm 14.32 on pp.601 of HAC. | 221 * Based on Algorithm 14.32 on pp.601 of HAC. |
217 */ | 222 */ |
356 if (mp_cmp_mag (x, n) != MP_LT) { | 361 if (mp_cmp_mag (x, n) != MP_LT) { |
357 return s_mp_sub (x, n, x); | 362 return s_mp_sub (x, n, x); |
358 } | 363 } |
359 return MP_OKAY; | 364 return MP_OKAY; |
360 } | 365 } |
366 #endif | |
361 | 367 |
362 /* End: bn_fast_mp_montgomery_reduce.c */ | 368 /* End: bn_fast_mp_montgomery_reduce.c */ |
363 | 369 |
364 /* Start: bn_fast_s_mp_mul_digs.c */ | 370 /* Start: bn_fast_s_mp_mul_digs.c */ |
365 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 371 #include <tommath.h> |
366 * | 372 #ifdef BN_FAST_S_MP_MUL_DIGS_C |
367 * LibTomMath is a library that provides multiple-precision | 373 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
368 * integer arithmetic as well as number theoretic functionality. | 374 * |
369 * | 375 * LibTomMath is a library that provides multiple-precision |
370 * The library was designed directly after the MPI library by | 376 * integer arithmetic as well as number theoretic functionality. |
371 * Michael Fromberger but has been written from scratch with | 377 * |
372 * additional optimizations in place. | 378 * The library was designed directly after the MPI library by |
373 * | 379 * Michael Fromberger but has been written from scratch with |
374 * The library is free for all purposes without any express | 380 * additional optimizations in place. |
375 * guarantee it works. | 381 * |
376 * | 382 * The library is free for all purposes without any express |
377 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 383 * guarantee it works. |
378 */ | 384 * |
379 #include <tommath.h> | 385 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
386 */ | |
380 | 387 |
381 /* Fast (comba) multiplier | 388 /* Fast (comba) multiplier |
382 * | 389 * |
383 * This is the fast column-array [comba] multiplier. It is | 390 * This is the fast column-array [comba] multiplier. It is |
384 * designed to compute the columns of the product first | 391 * designed to compute the columns of the product first |
395 * | 402 * |
396 */ | 403 */ |
397 int | 404 int |
398 fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) | 405 fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) |
399 { | 406 { |
400 int olduse, res, pa, ix; | 407 int olduse, res, pa, ix, iz; |
401 mp_word W[MP_WARRAY]; | 408 mp_digit W[MP_WARRAY]; |
409 register mp_word _W; | |
402 | 410 |
403 /* grow the destination as required */ | 411 /* grow the destination as required */ |
404 if (c->alloc < digs) { | 412 if (c->alloc < digs) { |
405 if ((res = mp_grow (c, digs)) != MP_OKAY) { | 413 if ((res = mp_grow (c, digs)) != MP_OKAY) { |
406 return res; | 414 return res; |
407 } | 415 } |
408 } | 416 } |
409 | 417 |
410 /* clear temp buf (the columns) */ | 418 /* number of output digits to produce */ |
411 memset (W, 0, sizeof (mp_word) * digs); | 419 pa = MIN(digs, a->used + b->used); |
412 | 420 |
413 /* calculate the columns */ | 421 /* clear the carry */ |
414 pa = a->used; | 422 _W = 0; |
415 for (ix = 0; ix < pa; ix++) { | 423 for (ix = 0; ix <= pa; ix++) { |
416 /* this multiplier has been modified to allow you to | 424 int tx, ty; |
417 * control how many digits of output are produced. | 425 int iy; |
418 * So at most we want to make upto "digs" digits of output. | 426 mp_digit *tmpx, *tmpy; |
419 * | 427 |
420 * this adds products to distinct columns (at ix+iy) of W | 428 /* get offsets into the two bignums */ |
421 * note that each step through the loop is not dependent on | 429 ty = MIN(b->used-1, ix); |
422 * the previous which means the compiler can easily unroll | 430 tx = ix - ty; |
423 * the loop without scheduling problems | 431 |
424 */ | 432 /* setup temp aliases */ |
425 { | 433 tmpx = a->dp + tx; |
426 register mp_digit tmpx, *tmpy; | 434 tmpy = b->dp + ty; |
427 register mp_word *_W; | 435 |
428 register int iy, pb; | 436 /* this is the number of times the loop will iterrate, essentially its |
429 | 437 while (tx++ < a->used && ty-- >= 0) { ... } |
430 /* alias for the the word on the left e.g. A[ix] * A[iy] */ | |
431 tmpx = a->dp[ix]; | |
432 | |
433 /* alias for the right side */ | |
434 tmpy = b->dp; | |
435 | |
436 /* alias for the columns, each step through the loop adds a new | |
437 term to each column | |
438 */ | 438 */ |
439 _W = W + ix; | 439 iy = MIN(a->used-tx, ty+1); |
440 | 440 |
441 /* the number of digits is limited by their placement. E.g. | 441 /* execute loop */ |
442 we avoid multiplying digits that will end up above the # of | 442 for (iz = 0; iz < iy; ++iz) { |
443 digits of precision requested | 443 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); |
444 */ | |
445 pb = MIN (b->used, digs - ix); | |
446 | |
447 for (iy = 0; iy < pb; iy++) { | |
448 *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++); | |
449 } | 444 } |
450 } | 445 |
451 | 446 /* store term */ |
447 W[ix] = ((mp_digit)_W) & MP_MASK; | |
448 | |
449 /* make next carry */ | |
450 _W = _W >> ((mp_word)DIGIT_BIT); | |
452 } | 451 } |
453 | 452 |
454 /* setup dest */ | 453 /* setup dest */ |
455 olduse = c->used; | 454 olduse = c->used; |
456 c->used = digs; | 455 c->used = digs; |
457 | 456 |
458 { | 457 { |
459 register mp_digit *tmpc; | 458 register mp_digit *tmpc; |
460 | |
461 /* At this point W[] contains the sums of each column. To get the | |
462 * correct result we must take the extra bits from each column and | |
463 * carry them down | |
464 * | |
465 * Note that while this adds extra code to the multiplier it | |
466 * saves time since the carry propagation is removed from the | |
467 * above nested loop.This has the effect of reducing the work | |
468 * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the | |
469 * cost of the shifting. On very small numbers this is slower | |
470 * but on most cryptographic size numbers it is faster. | |
471 * | |
472 * In this particular implementation we feed the carries from | |
473 * behind which means when the loop terminates we still have one | |
474 * last digit to copy | |
475 */ | |
476 tmpc = c->dp; | 459 tmpc = c->dp; |
477 for (ix = 1; ix < digs; ix++) { | 460 for (ix = 0; ix < digs; ix++) { |
478 /* forward the carry from the previous temp */ | |
479 W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT)); | |
480 | |
481 /* now extract the previous digit [below the carry] */ | 461 /* now extract the previous digit [below the carry] */ |
482 *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); | 462 *tmpc++ = W[ix]; |
483 } | 463 } |
484 /* fetch the last digit */ | |
485 *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK)); | |
486 | 464 |
487 /* clear unused digits [that existed in the old copy of c] */ | 465 /* clear unused digits [that existed in the old copy of c] */ |
488 for (; ix < olduse; ix++) { | 466 for (; ix < olduse; ix++) { |
489 *tmpc++ = 0; | 467 *tmpc++ = 0; |
490 } | 468 } |
491 } | 469 } |
492 mp_clamp (c); | 470 mp_clamp (c); |
493 return MP_OKAY; | 471 return MP_OKAY; |
494 } | 472 } |
473 #endif | |
495 | 474 |
496 /* End: bn_fast_s_mp_mul_digs.c */ | 475 /* End: bn_fast_s_mp_mul_digs.c */ |
497 | 476 |
498 /* Start: bn_fast_s_mp_mul_high_digs.c */ | 477 /* Start: bn_fast_s_mp_mul_high_digs.c */ |
499 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 478 #include <tommath.h> |
500 * | 479 #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C |
501 * LibTomMath is a library that provides multiple-precision | 480 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
502 * integer arithmetic as well as number theoretic functionality. | 481 * |
503 * | 482 * LibTomMath is a library that provides multiple-precision |
504 * The library was designed directly after the MPI library by | 483 * integer arithmetic as well as number theoretic functionality. |
505 * Michael Fromberger but has been written from scratch with | 484 * |
506 * additional optimizations in place. | 485 * The library was designed directly after the MPI library by |
507 * | 486 * Michael Fromberger but has been written from scratch with |
508 * The library is free for all purposes without any express | 487 * additional optimizations in place. |
509 * guarantee it works. | 488 * |
510 * | 489 * The library is free for all purposes without any express |
511 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 490 * guarantee it works. |
512 */ | 491 * |
513 #include <tommath.h> | 492 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
514 | 493 */ |
515 /* this is a modified version of fast_s_mp_mul_digs that only produces | 494 |
516 * output digits *above* digs. See the comments for fast_s_mp_mul_digs | 495 /* this is a modified version of fast_s_mul_digs that only produces |
496 * output digits *above* digs. See the comments for fast_s_mul_digs | |
517 * to see how it works. | 497 * to see how it works. |
518 * | 498 * |
519 * This is used in the Barrett reduction since for one of the multiplications | 499 * This is used in the Barrett reduction since for one of the multiplications |
520 * only the higher digits were needed. This essentially halves the work. | 500 * only the higher digits were needed. This essentially halves the work. |
521 * | 501 * |
522 * Based on Algorithm 14.12 on pp.595 of HAC. | 502 * Based on Algorithm 14.12 on pp.595 of HAC. |
523 */ | 503 */ |
524 int | 504 int |
525 fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) | 505 fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) |
526 { | 506 { |
527 int oldused, newused, res, pa, pb, ix; | 507 int olduse, res, pa, ix, iz; |
528 mp_word W[MP_WARRAY]; | 508 mp_digit W[MP_WARRAY]; |
529 | 509 mp_word _W; |
530 /* calculate size of product and allocate more space if required */ | 510 |
531 newused = a->used + b->used + 1; | 511 /* grow the destination as required */ |
532 if (c->alloc < newused) { | 512 pa = a->used + b->used; |
533 if ((res = mp_grow (c, newused)) != MP_OKAY) { | 513 if (c->alloc < pa) { |
514 if ((res = mp_grow (c, pa)) != MP_OKAY) { | |
534 return res; | 515 return res; |
535 } | 516 } |
536 } | 517 } |
537 | 518 |
538 /* like the other comba method we compute the columns first */ | 519 /* number of output digits to produce */ |
539 pa = a->used; | 520 pa = a->used + b->used; |
540 pb = b->used; | 521 _W = 0; |
541 memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word)); | 522 for (ix = digs; ix <= pa; ix++) { |
542 for (ix = 0; ix < pa; ix++) { | 523 int tx, ty, iy; |
543 { | 524 mp_digit *tmpx, *tmpy; |
544 register mp_digit tmpx, *tmpy; | 525 |
545 register int iy; | 526 /* get offsets into the two bignums */ |
546 register mp_word *_W; | 527 ty = MIN(b->used-1, ix); |
547 | 528 tx = ix - ty; |
548 /* work todo, that is we only calculate digits that are at "digs" or above */ | 529 |
549 iy = digs - ix; | 530 /* setup temp aliases */ |
550 | 531 tmpx = a->dp + tx; |
551 /* copy of word on the left of A[ix] * B[iy] */ | 532 tmpy = b->dp + ty; |
552 tmpx = a->dp[ix]; | 533 |
553 | 534 /* this is the number of times the loop will iterrate, essentially its |
554 /* alias for right side */ | 535 while (tx++ < a->used && ty-- >= 0) { ... } |
555 tmpy = b->dp + iy; | |
556 | |
557 /* alias for the columns of output. Offset to be equal to or above the | |
558 * smallest digit place requested | |
559 */ | 536 */ |
560 _W = W + digs; | 537 iy = MIN(a->used-tx, ty+1); |
561 | 538 |
562 /* skip cases below zero where ix > digs */ | 539 /* execute loop */ |
563 if (iy < 0) { | 540 for (iz = 0; iz < iy; iz++) { |
564 iy = abs(iy); | 541 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); |
565 tmpy += iy; | |
566 _W += iy; | |
567 iy = 0; | |
568 } | 542 } |
569 | 543 |
570 /* compute column products for digits above the minimum */ | 544 /* store term */ |
571 for (; iy < pb; iy++) { | 545 W[ix] = ((mp_digit)_W) & MP_MASK; |
572 *_W++ += ((mp_word) tmpx) * ((mp_word)*tmpy++); | 546 |
573 } | 547 /* make next carry */ |
574 } | 548 _W = _W >> ((mp_word)DIGIT_BIT); |
575 } | 549 } |
576 | 550 |
577 /* setup dest */ | 551 /* setup dest */ |
578 oldused = c->used; | 552 olduse = c->used; |
579 c->used = newused; | 553 c->used = pa; |
580 | 554 |
581 /* now convert the array W downto what we need | 555 { |
582 * | 556 register mp_digit *tmpc; |
583 * See comments in bn_fast_s_mp_mul_digs.c | 557 |
584 */ | 558 tmpc = c->dp + digs; |
585 for (ix = digs + 1; ix < newused; ix++) { | 559 for (ix = digs; ix <= pa; ix++) { |
586 W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT)); | 560 /* now extract the previous digit [below the carry] */ |
587 c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); | 561 *tmpc++ = W[ix]; |
588 } | 562 } |
589 c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK)); | 563 |
590 | 564 /* clear unused digits [that existed in the old copy of c] */ |
591 for (; ix < oldused; ix++) { | 565 for (; ix < olduse; ix++) { |
592 c->dp[ix] = 0; | 566 *tmpc++ = 0; |
567 } | |
593 } | 568 } |
594 mp_clamp (c); | 569 mp_clamp (c); |
595 return MP_OKAY; | 570 return MP_OKAY; |
596 } | 571 } |
572 #endif | |
597 | 573 |
598 /* End: bn_fast_s_mp_mul_high_digs.c */ | 574 /* End: bn_fast_s_mp_mul_high_digs.c */ |
599 | 575 |
600 /* Start: bn_fast_s_mp_sqr.c */ | 576 /* Start: bn_fast_s_mp_sqr.c */ |
601 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 577 #include <tommath.h> |
602 * | 578 #ifdef BN_FAST_S_MP_SQR_C |
603 * LibTomMath is a library that provides multiple-precision | 579 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
604 * integer arithmetic as well as number theoretic functionality. | 580 * |
605 * | 581 * LibTomMath is a library that provides multiple-precision |
606 * The library was designed directly after the MPI library by | 582 * integer arithmetic as well as number theoretic functionality. |
607 * Michael Fromberger but has been written from scratch with | 583 * |
608 * additional optimizations in place. | 584 * The library was designed directly after the MPI library by |
609 * | 585 * Michael Fromberger but has been written from scratch with |
610 * The library is free for all purposes without any express | 586 * additional optimizations in place. |
611 * guarantee it works. | 587 * |
612 * | 588 * The library is free for all purposes without any express |
613 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 589 * guarantee it works. |
614 */ | 590 * |
615 #include <tommath.h> | 591 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
592 */ | |
616 | 593 |
617 /* fast squaring | 594 /* fast squaring |
618 * | 595 * |
619 * This is the comba method where the columns of the product | 596 * This is the comba method where the columns of the product |
620 * are computed first then the carries are computed. This | 597 * are computed first then the carries are computed. This |
629 * because 64-bit shifts are slow! | 606 * because 64-bit shifts are slow! |
630 * | 607 * |
631 * Based on Algorithm 14.16 on pp.597 of HAC. | 608 * Based on Algorithm 14.16 on pp.597 of HAC. |
632 * | 609 * |
633 */ | 610 */ |
611 /* the jist of squaring... | |
612 | |
613 you do like mult except the offset of the tmpx [one that starts closer to zero] | |
614 can't equal the offset of tmpy. So basically you set up iy like before then you min it with | |
615 (ty-tx) so that it never happens. You double all those you add in the inner loop | |
616 | |
617 After that loop you do the squares and add them in. | |
618 | |
619 Remove W2 and don't memset W | |
620 | |
621 */ | |
622 | |
634 int fast_s_mp_sqr (mp_int * a, mp_int * b) | 623 int fast_s_mp_sqr (mp_int * a, mp_int * b) |
635 { | 624 { |
636 int olduse, newused, res, ix, pa; | 625 int olduse, res, pa, ix, iz; |
637 mp_word W2[MP_WARRAY], W[MP_WARRAY]; | 626 mp_digit W[MP_WARRAY], *tmpx; |
638 | 627 mp_word W1; |
639 /* calculate size of product and allocate as required */ | 628 |
640 pa = a->used; | 629 /* grow the destination as required */ |
641 newused = pa + pa + 1; | 630 pa = a->used + a->used; |
642 if (b->alloc < newused) { | 631 if (b->alloc < pa) { |
643 if ((res = mp_grow (b, newused)) != MP_OKAY) { | 632 if ((res = mp_grow (b, pa)) != MP_OKAY) { |
644 return res; | 633 return res; |
645 } | 634 } |
646 } | 635 } |
647 | 636 |
648 /* zero temp buffer (columns) | 637 /* number of output digits to produce */ |
649 * Note that there are two buffers. Since squaring requires | 638 W1 = 0; |
650 * a outer and inner product and the inner product requires | 639 for (ix = 0; ix <= pa; ix++) { |
651 * computing a product and doubling it (a relatively expensive | 640 int tx, ty, iy; |
652 * op to perform n**2 times if you don't have to) the inner and | 641 mp_word _W; |
653 * outer products are computed in different buffers. This way | 642 mp_digit *tmpy; |
654 * the inner product can be doubled using n doublings instead of | 643 |
655 * n**2 | 644 /* clear counter */ |
656 */ | 645 _W = 0; |
657 memset (W, 0, newused * sizeof (mp_word)); | 646 |
658 memset (W2, 0, newused * sizeof (mp_word)); | 647 /* get offsets into the two bignums */ |
659 | 648 ty = MIN(a->used-1, ix); |
660 /* This computes the inner product. To simplify the inner N**2 loop | 649 tx = ix - ty; |
661 * the multiplication by two is done afterwards in the N loop. | 650 |
662 */ | 651 /* setup temp aliases */ |
663 for (ix = 0; ix < pa; ix++) { | 652 tmpx = a->dp + tx; |
664 /* compute the outer product | 653 tmpy = a->dp + ty; |
665 * | 654 |
666 * Note that every outer product is computed | 655 /* this is the number of times the loop will iterrate, essentially its |
667 * for a particular column only once which means that | 656 while (tx++ < a->used && ty-- >= 0) { ... } |
668 * there is no need todo a double precision addition | 657 */ |
669 * into the W2[] array. | 658 iy = MIN(a->used-tx, ty+1); |
670 */ | 659 |
671 W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]); | 660 /* now for squaring tx can never equal ty |
672 | 661 * we halve the distance since they approach at a rate of 2x |
673 { | 662 * and we have to round because odd cases need to be executed |
674 register mp_digit tmpx, *tmpy; | 663 */ |
675 register mp_word *_W; | 664 iy = MIN(iy, (ty-tx+1)>>1); |
676 register int iy; | 665 |
677 | 666 /* execute loop */ |
678 /* copy of left side */ | 667 for (iz = 0; iz < iy; iz++) { |
679 tmpx = a->dp[ix]; | 668 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); |
680 | |
681 /* alias for right side */ | |
682 tmpy = a->dp + (ix + 1); | |
683 | |
684 /* the column to store the result in */ | |
685 _W = W + (ix + ix + 1); | |
686 | |
687 /* inner products */ | |
688 for (iy = ix + 1; iy < pa; iy++) { | |
689 *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++); | |
690 } | 669 } |
691 } | 670 |
671 /* double the inner product and add carry */ | |
672 _W = _W + _W + W1; | |
673 | |
674 /* even columns have the square term in them */ | |
675 if ((ix&1) == 0) { | |
676 _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]); | |
677 } | |
678 | |
679 /* store it */ | |
680 W[ix] = _W; | |
681 | |
682 /* make next carry */ | |
683 W1 = _W >> ((mp_word)DIGIT_BIT); | |
692 } | 684 } |
693 | 685 |
694 /* setup dest */ | 686 /* setup dest */ |
695 olduse = b->used; | 687 olduse = b->used; |
696 b->used = newused; | 688 b->used = a->used+a->used; |
697 | 689 |
698 /* now compute digits | |
699 * | |
700 * We have to double the inner product sums, add in the | |
701 * outer product sums, propagate carries and convert | |
702 * to single precision. | |
703 */ | |
704 { | 690 { |
705 register mp_digit *tmpb; | 691 mp_digit *tmpb; |
706 | |
707 /* double first value, since the inner products are | |
708 * half of what they should be | |
709 */ | |
710 W[0] += W[0] + W2[0]; | |
711 | |
712 tmpb = b->dp; | 692 tmpb = b->dp; |
713 for (ix = 1; ix < newused; ix++) { | 693 for (ix = 0; ix < pa; ix++) { |
714 /* double/add next digit */ | 694 *tmpb++ = W[ix] & MP_MASK; |
715 W[ix] += W[ix] + W2[ix]; | 695 } |
716 | 696 |
717 /* propagate carry forwards [from the previous digit] */ | 697 /* clear unused digits [that existed in the old copy of c] */ |
718 W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT)); | |
719 | |
720 /* store the current digit now that the carry isn't | |
721 * needed | |
722 */ | |
723 *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); | |
724 } | |
725 /* set the last value. Note even if the carry is zero | |
726 * this is required since the next step will not zero | |
727 * it if b originally had a value at b->dp[2*a.used] | |
728 */ | |
729 *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK)); | |
730 | |
731 /* clear high digits of b if there were any originally */ | |
732 for (; ix < olduse; ix++) { | 698 for (; ix < olduse; ix++) { |
733 *tmpb++ = 0; | 699 *tmpb++ = 0; |
734 } | 700 } |
735 } | 701 } |
736 | |
737 mp_clamp (b); | 702 mp_clamp (b); |
738 return MP_OKAY; | 703 return MP_OKAY; |
739 } | 704 } |
705 #endif | |
740 | 706 |
741 /* End: bn_fast_s_mp_sqr.c */ | 707 /* End: bn_fast_s_mp_sqr.c */ |
742 | 708 |
743 /* Start: bn_mp_2expt.c */ | 709 /* Start: bn_mp_2expt.c */ |
744 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 710 #include <tommath.h> |
745 * | 711 #ifdef BN_MP_2EXPT_C |
746 * LibTomMath is a library that provides multiple-precision | 712 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
747 * integer arithmetic as well as number theoretic functionality. | 713 * |
748 * | 714 * LibTomMath is a library that provides multiple-precision |
749 * The library was designed directly after the MPI library by | 715 * integer arithmetic as well as number theoretic functionality. |
750 * Michael Fromberger but has been written from scratch with | 716 * |
751 * additional optimizations in place. | 717 * The library was designed directly after the MPI library by |
752 * | 718 * Michael Fromberger but has been written from scratch with |
753 * The library is free for all purposes without any express | 719 * additional optimizations in place. |
754 * guarantee it works. | 720 * |
755 * | 721 * The library is free for all purposes without any express |
756 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 722 * guarantee it works. |
757 */ | 723 * |
758 #include <tommath.h> | 724 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
725 */ | |
759 | 726 |
760 /* computes a = 2**b | 727 /* computes a = 2**b |
761 * | 728 * |
762 * Simple algorithm which zeroes the int, grows it then just sets one bit | 729 * Simple algorithm which zeroes the int, grows it then just sets one bit |
763 * as required. | 730 * as required. |
777 | 744 |
778 /* set the used count of where the bit will go */ | 745 /* set the used count of where the bit will go */ |
779 a->used = b / DIGIT_BIT + 1; | 746 a->used = b / DIGIT_BIT + 1; |
780 | 747 |
781 /* put the single bit in its place */ | 748 /* put the single bit in its place */ |
782 a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT); | 749 a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); |
783 | 750 |
784 return MP_OKAY; | 751 return MP_OKAY; |
785 } | 752 } |
753 #endif | |
786 | 754 |
787 /* End: bn_mp_2expt.c */ | 755 /* End: bn_mp_2expt.c */ |
788 | 756 |
789 /* Start: bn_mp_abs.c */ | 757 /* Start: bn_mp_abs.c */ |
790 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 758 #include <tommath.h> |
791 * | 759 #ifdef BN_MP_ABS_C |
792 * LibTomMath is a library that provides multiple-precision | 760 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
793 * integer arithmetic as well as number theoretic functionality. | 761 * |
794 * | 762 * LibTomMath is a library that provides multiple-precision |
795 * The library was designed directly after the MPI library by | 763 * integer arithmetic as well as number theoretic functionality. |
796 * Michael Fromberger but has been written from scratch with | 764 * |
797 * additional optimizations in place. | 765 * The library was designed directly after the MPI library by |
798 * | 766 * Michael Fromberger but has been written from scratch with |
799 * The library is free for all purposes without any express | 767 * additional optimizations in place. |
800 * guarantee it works. | 768 * |
801 * | 769 * The library is free for all purposes without any express |
802 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 770 * guarantee it works. |
803 */ | 771 * |
804 #include <tommath.h> | 772 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
773 */ | |
805 | 774 |
806 /* b = |a| | 775 /* b = |a| |
807 * | 776 * |
808 * Simple function copies the input and fixes the sign to positive | 777 * Simple function copies the input and fixes the sign to positive |
809 */ | 778 */ |
822 /* force the sign of b to positive */ | 791 /* force the sign of b to positive */ |
823 b->sign = MP_ZPOS; | 792 b->sign = MP_ZPOS; |
824 | 793 |
825 return MP_OKAY; | 794 return MP_OKAY; |
826 } | 795 } |
796 #endif | |
827 | 797 |
828 /* End: bn_mp_abs.c */ | 798 /* End: bn_mp_abs.c */ |
829 | 799 |
830 /* Start: bn_mp_add.c */ | 800 /* Start: bn_mp_add.c */ |
831 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 801 #include <tommath.h> |
832 * | 802 #ifdef BN_MP_ADD_C |
833 * LibTomMath is a library that provides multiple-precision | 803 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
834 * integer arithmetic as well as number theoretic functionality. | 804 * |
835 * | 805 * LibTomMath is a library that provides multiple-precision |
836 * The library was designed directly after the MPI library by | 806 * integer arithmetic as well as number theoretic functionality. |
837 * Michael Fromberger but has been written from scratch with | 807 * |
838 * additional optimizations in place. | 808 * The library was designed directly after the MPI library by |
839 * | 809 * Michael Fromberger but has been written from scratch with |
840 * The library is free for all purposes without any express | 810 * additional optimizations in place. |
841 * guarantee it works. | 811 * |
842 * | 812 * The library is free for all purposes without any express |
843 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 813 * guarantee it works. |
844 */ | 814 * |
845 #include <tommath.h> | 815 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
816 */ | |
846 | 817 |
847 /* high level addition (handles signs) */ | 818 /* high level addition (handles signs) */ |
848 int mp_add (mp_int * a, mp_int * b, mp_int * c) | 819 int mp_add (mp_int * a, mp_int * b, mp_int * c) |
849 { | 820 { |
850 int sa, sb, res; | 821 int sa, sb, res; |
873 } | 844 } |
874 } | 845 } |
875 return res; | 846 return res; |
876 } | 847 } |
877 | 848 |
849 #endif | |
878 | 850 |
879 /* End: bn_mp_add.c */ | 851 /* End: bn_mp_add.c */ |
880 | 852 |
881 /* Start: bn_mp_add_d.c */ | 853 /* Start: bn_mp_add_d.c */ |
882 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 854 #include <tommath.h> |
883 * | 855 #ifdef BN_MP_ADD_D_C |
884 * LibTomMath is a library that provides multiple-precision | 856 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
885 * integer arithmetic as well as number theoretic functionality. | 857 * |
886 * | 858 * LibTomMath is a library that provides multiple-precision |
887 * The library was designed directly after the MPI library by | 859 * integer arithmetic as well as number theoretic functionality. |
888 * Michael Fromberger but has been written from scratch with | 860 * |
889 * additional optimizations in place. | 861 * The library was designed directly after the MPI library by |
890 * | 862 * Michael Fromberger but has been written from scratch with |
891 * The library is free for all purposes without any express | 863 * additional optimizations in place. |
892 * guarantee it works. | 864 * |
893 * | 865 * The library is free for all purposes without any express |
894 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 866 * guarantee it works. |
895 */ | 867 * |
896 #include <tommath.h> | 868 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
869 */ | |
897 | 870 |
898 /* single digit addition */ | 871 /* single digit addition */ |
899 int | 872 int |
900 mp_add_d (mp_int * a, mp_digit b, mp_int * c) | 873 mp_add_d (mp_int * a, mp_digit b, mp_int * c) |
901 { | 874 { |
980 mp_clamp(c); | 953 mp_clamp(c); |
981 | 954 |
982 return MP_OKAY; | 955 return MP_OKAY; |
983 } | 956 } |
984 | 957 |
958 #endif | |
985 | 959 |
986 /* End: bn_mp_add_d.c */ | 960 /* End: bn_mp_add_d.c */ |
987 | 961 |
988 /* Start: bn_mp_addmod.c */ | 962 /* Start: bn_mp_addmod.c */ |
989 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 963 #include <tommath.h> |
990 * | 964 #ifdef BN_MP_ADDMOD_C |
991 * LibTomMath is a library that provides multiple-precision | 965 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
992 * integer arithmetic as well as number theoretic functionality. | 966 * |
993 * | 967 * LibTomMath is a library that provides multiple-precision |
994 * The library was designed directly after the MPI library by | 968 * integer arithmetic as well as number theoretic functionality. |
995 * Michael Fromberger but has been written from scratch with | 969 * |
996 * additional optimizations in place. | 970 * The library was designed directly after the MPI library by |
997 * | 971 * Michael Fromberger but has been written from scratch with |
998 * The library is free for all purposes without any express | 972 * additional optimizations in place. |
999 * guarantee it works. | 973 * |
1000 * | 974 * The library is free for all purposes without any express |
1001 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 975 * guarantee it works. |
1002 */ | 976 * |
1003 #include <tommath.h> | 977 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
978 */ | |
1004 | 979 |
1005 /* d = a + b (mod c) */ | 980 /* d = a + b (mod c) */ |
1006 int | 981 int |
1007 mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) | 982 mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) |
1008 { | 983 { |
1019 } | 994 } |
1020 res = mp_mod (&t, c, d); | 995 res = mp_mod (&t, c, d); |
1021 mp_clear (&t); | 996 mp_clear (&t); |
1022 return res; | 997 return res; |
1023 } | 998 } |
999 #endif | |
1024 | 1000 |
1025 /* End: bn_mp_addmod.c */ | 1001 /* End: bn_mp_addmod.c */ |
1026 | 1002 |
1027 /* Start: bn_mp_and.c */ | 1003 /* Start: bn_mp_and.c */ |
1028 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1004 #include <tommath.h> |
1029 * | 1005 #ifdef BN_MP_AND_C |
1030 * LibTomMath is a library that provides multiple-precision | 1006 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1031 * integer arithmetic as well as number theoretic functionality. | 1007 * |
1032 * | 1008 * LibTomMath is a library that provides multiple-precision |
1033 * The library was designed directly after the MPI library by | 1009 * integer arithmetic as well as number theoretic functionality. |
1034 * Michael Fromberger but has been written from scratch with | 1010 * |
1035 * additional optimizations in place. | 1011 * The library was designed directly after the MPI library by |
1036 * | 1012 * Michael Fromberger but has been written from scratch with |
1037 * The library is free for all purposes without any express | 1013 * additional optimizations in place. |
1038 * guarantee it works. | 1014 * |
1039 * | 1015 * The library is free for all purposes without any express |
1040 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1016 * guarantee it works. |
1041 */ | 1017 * |
1042 #include <tommath.h> | 1018 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1019 */ | |
1043 | 1020 |
1044 /* AND two ints together */ | 1021 /* AND two ints together */ |
1045 int | 1022 int |
1046 mp_and (mp_int * a, mp_int * b, mp_int * c) | 1023 mp_and (mp_int * a, mp_int * b, mp_int * c) |
1047 { | 1024 { |
1074 mp_clamp (&t); | 1051 mp_clamp (&t); |
1075 mp_exch (c, &t); | 1052 mp_exch (c, &t); |
1076 mp_clear (&t); | 1053 mp_clear (&t); |
1077 return MP_OKAY; | 1054 return MP_OKAY; |
1078 } | 1055 } |
1056 #endif | |
1079 | 1057 |
1080 /* End: bn_mp_and.c */ | 1058 /* End: bn_mp_and.c */ |
1081 | 1059 |
1082 /* Start: bn_mp_clamp.c */ | 1060 /* Start: bn_mp_clamp.c */ |
1083 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1061 #include <tommath.h> |
1084 * | 1062 #ifdef BN_MP_CLAMP_C |
1085 * LibTomMath is a library that provides multiple-precision | 1063 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1086 * integer arithmetic as well as number theoretic functionality. | 1064 * |
1087 * | 1065 * LibTomMath is a library that provides multiple-precision |
1088 * The library was designed directly after the MPI library by | 1066 * integer arithmetic as well as number theoretic functionality. |
1089 * Michael Fromberger but has been written from scratch with | 1067 * |
1090 * additional optimizations in place. | 1068 * The library was designed directly after the MPI library by |
1091 * | 1069 * Michael Fromberger but has been written from scratch with |
1092 * The library is free for all purposes without any express | 1070 * additional optimizations in place. |
1093 * guarantee it works. | 1071 * |
1094 * | 1072 * The library is free for all purposes without any express |
1095 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1073 * guarantee it works. |
1096 */ | 1074 * |
1097 #include <tommath.h> | 1075 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1076 */ | |
1098 | 1077 |
1099 /* trim unused digits | 1078 /* trim unused digits |
1100 * | 1079 * |
1101 * This is used to ensure that leading zero digits are | 1080 * This is used to ensure that leading zero digits are |
1102 * trimed and the leading "used" digit will be non-zero | 1081 * trimed and the leading "used" digit will be non-zero |
1116 /* reset the sign flag if used == 0 */ | 1095 /* reset the sign flag if used == 0 */ |
1117 if (a->used == 0) { | 1096 if (a->used == 0) { |
1118 a->sign = MP_ZPOS; | 1097 a->sign = MP_ZPOS; |
1119 } | 1098 } |
1120 } | 1099 } |
1100 #endif | |
1121 | 1101 |
1122 /* End: bn_mp_clamp.c */ | 1102 /* End: bn_mp_clamp.c */ |
1123 | 1103 |
1124 /* Start: bn_mp_clear.c */ | 1104 /* Start: bn_mp_clear.c */ |
1125 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1105 #include <tommath.h> |
1126 * | 1106 #ifdef BN_MP_CLEAR_C |
1127 * LibTomMath is a library that provides multiple-precision | 1107 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1128 * integer arithmetic as well as number theoretic functionality. | 1108 * |
1129 * | 1109 * LibTomMath is a library that provides multiple-precision |
1130 * The library was designed directly after the MPI library by | 1110 * integer arithmetic as well as number theoretic functionality. |
1131 * Michael Fromberger but has been written from scratch with | 1111 * |
1132 * additional optimizations in place. | 1112 * The library was designed directly after the MPI library by |
1133 * | 1113 * Michael Fromberger but has been written from scratch with |
1134 * The library is free for all purposes without any express | 1114 * additional optimizations in place. |
1135 * guarantee it works. | 1115 * |
1136 * | 1116 * The library is free for all purposes without any express |
1137 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1117 * guarantee it works. |
1138 */ | 1118 * |
1139 #include <tommath.h> | 1119 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1120 */ | |
1140 | 1121 |
1141 /* clear one (frees) */ | 1122 /* clear one (frees) */ |
1142 void | 1123 void |
1143 mp_clear (mp_int * a) | 1124 mp_clear (mp_int * a) |
1144 { | 1125 { |
1126 int i; | |
1127 | |
1145 /* only do anything if a hasn't been freed previously */ | 1128 /* only do anything if a hasn't been freed previously */ |
1146 if (a->dp != NULL) { | 1129 if (a->dp != NULL) { |
1147 /* first zero the digits */ | 1130 /* first zero the digits */ |
1148 memset (a->dp, 0, sizeof (mp_digit) * a->used); | 1131 for (i = 0; i < a->used; i++) { |
1132 a->dp[i] = 0; | |
1133 } | |
1149 | 1134 |
1150 /* free ram */ | 1135 /* free ram */ |
1151 XFREE(a->dp); | 1136 XFREE(a->dp); |
1152 | 1137 |
1153 /* reset members to make debugging easier */ | 1138 /* reset members to make debugging easier */ |
1154 a->dp = NULL; | 1139 a->dp = NULL; |
1155 a->alloc = a->used = 0; | 1140 a->alloc = a->used = 0; |
1156 a->sign = MP_ZPOS; | 1141 a->sign = MP_ZPOS; |
1157 } | 1142 } |
1158 } | 1143 } |
1144 #endif | |
1159 | 1145 |
1160 /* End: bn_mp_clear.c */ | 1146 /* End: bn_mp_clear.c */ |
1161 | 1147 |
1162 /* Start: bn_mp_clear_multi.c */ | 1148 /* Start: bn_mp_clear_multi.c */ |
1163 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1149 #include <tommath.h> |
1164 * | 1150 #ifdef BN_MP_CLEAR_MULTI_C |
1165 * LibTomMath is a library that provides multiple-precision | 1151 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1166 * integer arithmetic as well as number theoretic functionality. | 1152 * |
1167 * | 1153 * LibTomMath is a library that provides multiple-precision |
1168 * The library was designed directly after the MPI library by | 1154 * integer arithmetic as well as number theoretic functionality. |
1169 * Michael Fromberger but has been written from scratch with | 1155 * |
1170 * additional optimizations in place. | 1156 * The library was designed directly after the MPI library by |
1171 * | 1157 * Michael Fromberger but has been written from scratch with |
1172 * The library is free for all purposes without any express | 1158 * additional optimizations in place. |
1173 * guarantee it works. | 1159 * |
1174 * | 1160 * The library is free for all purposes without any express |
1175 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1161 * guarantee it works. |
1176 */ | 1162 * |
1177 #include <tommath.h> | 1163 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1164 */ | |
1178 #include <stdarg.h> | 1165 #include <stdarg.h> |
1179 | 1166 |
1180 void mp_clear_multi(mp_int *mp, ...) | 1167 void mp_clear_multi(mp_int *mp, ...) |
1181 { | 1168 { |
1182 mp_int* next_mp = mp; | 1169 mp_int* next_mp = mp; |
1186 mp_clear(next_mp); | 1173 mp_clear(next_mp); |
1187 next_mp = va_arg(args, mp_int*); | 1174 next_mp = va_arg(args, mp_int*); |
1188 } | 1175 } |
1189 va_end(args); | 1176 va_end(args); |
1190 } | 1177 } |
1178 #endif | |
1191 | 1179 |
1192 /* End: bn_mp_clear_multi.c */ | 1180 /* End: bn_mp_clear_multi.c */ |
1193 | 1181 |
1194 /* Start: bn_mp_cmp.c */ | 1182 /* Start: bn_mp_cmp.c */ |
1195 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1183 #include <tommath.h> |
1196 * | 1184 #ifdef BN_MP_CMP_C |
1197 * LibTomMath is a library that provides multiple-precision | 1185 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1198 * integer arithmetic as well as number theoretic functionality. | 1186 * |
1199 * | 1187 * LibTomMath is a library that provides multiple-precision |
1200 * The library was designed directly after the MPI library by | 1188 * integer arithmetic as well as number theoretic functionality. |
1201 * Michael Fromberger but has been written from scratch with | 1189 * |
1202 * additional optimizations in place. | 1190 * The library was designed directly after the MPI library by |
1203 * | 1191 * Michael Fromberger but has been written from scratch with |
1204 * The library is free for all purposes without any express | 1192 * additional optimizations in place. |
1205 * guarantee it works. | 1193 * |
1206 * | 1194 * The library is free for all purposes without any express |
1207 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1195 * guarantee it works. |
1208 */ | 1196 * |
1209 #include <tommath.h> | 1197 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1198 */ | |
1210 | 1199 |
1211 /* compare two ints (signed)*/ | 1200 /* compare two ints (signed)*/ |
1212 int | 1201 int |
1213 mp_cmp (mp_int * a, mp_int * b) | 1202 mp_cmp (mp_int * a, mp_int * b) |
1214 { | 1203 { |
1227 return mp_cmp_mag(b, a); | 1216 return mp_cmp_mag(b, a); |
1228 } else { | 1217 } else { |
1229 return mp_cmp_mag(a, b); | 1218 return mp_cmp_mag(a, b); |
1230 } | 1219 } |
1231 } | 1220 } |
1221 #endif | |
1232 | 1222 |
1233 /* End: bn_mp_cmp.c */ | 1223 /* End: bn_mp_cmp.c */ |
1234 | 1224 |
1235 /* Start: bn_mp_cmp_d.c */ | 1225 /* Start: bn_mp_cmp_d.c */ |
1236 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1226 #include <tommath.h> |
1237 * | 1227 #ifdef BN_MP_CMP_D_C |
1238 * LibTomMath is a library that provides multiple-precision | 1228 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1239 * integer arithmetic as well as number theoretic functionality. | 1229 * |
1240 * | 1230 * LibTomMath is a library that provides multiple-precision |
1241 * The library was designed directly after the MPI library by | 1231 * integer arithmetic as well as number theoretic functionality. |
1242 * Michael Fromberger but has been written from scratch with | 1232 * |
1243 * additional optimizations in place. | 1233 * The library was designed directly after the MPI library by |
1244 * | 1234 * Michael Fromberger but has been written from scratch with |
1245 * The library is free for all purposes without any express | 1235 * additional optimizations in place. |
1246 * guarantee it works. | 1236 * |
1247 * | 1237 * The library is free for all purposes without any express |
1248 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1238 * guarantee it works. |
1249 */ | 1239 * |
1250 #include <tommath.h> | 1240 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1241 */ | |
1251 | 1242 |
1252 /* compare a digit */ | 1243 /* compare a digit */ |
1253 int mp_cmp_d(mp_int * a, mp_digit b) | 1244 int mp_cmp_d(mp_int * a, mp_digit b) |
1254 { | 1245 { |
1255 /* compare based on sign */ | 1246 /* compare based on sign */ |
1269 return MP_LT; | 1260 return MP_LT; |
1270 } else { | 1261 } else { |
1271 return MP_EQ; | 1262 return MP_EQ; |
1272 } | 1263 } |
1273 } | 1264 } |
1265 #endif | |
1274 | 1266 |
1275 /* End: bn_mp_cmp_d.c */ | 1267 /* End: bn_mp_cmp_d.c */ |
1276 | 1268 |
1277 /* Start: bn_mp_cmp_mag.c */ | 1269 /* Start: bn_mp_cmp_mag.c */ |
1278 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1270 #include <tommath.h> |
1279 * | 1271 #ifdef BN_MP_CMP_MAG_C |
1280 * LibTomMath is a library that provides multiple-precision | 1272 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1281 * integer arithmetic as well as number theoretic functionality. | 1273 * |
1282 * | 1274 * LibTomMath is a library that provides multiple-precision |
1283 * The library was designed directly after the MPI library by | 1275 * integer arithmetic as well as number theoretic functionality. |
1284 * Michael Fromberger but has been written from scratch with | 1276 * |
1285 * additional optimizations in place. | 1277 * The library was designed directly after the MPI library by |
1286 * | 1278 * Michael Fromberger but has been written from scratch with |
1287 * The library is free for all purposes without any express | 1279 * additional optimizations in place. |
1288 * guarantee it works. | 1280 * |
1289 * | 1281 * The library is free for all purposes without any express |
1290 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1282 * guarantee it works. |
1291 */ | 1283 * |
1292 #include <tommath.h> | 1284 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1285 */ | |
1293 | 1286 |
1294 /* compare maginitude of two ints (unsigned) */ | 1287 /* compare maginitude of two ints (unsigned) */ |
1295 int mp_cmp_mag (mp_int * a, mp_int * b) | 1288 int mp_cmp_mag (mp_int * a, mp_int * b) |
1296 { | 1289 { |
1297 int n; | 1290 int n; |
1322 return MP_LT; | 1315 return MP_LT; |
1323 } | 1316 } |
1324 } | 1317 } |
1325 return MP_EQ; | 1318 return MP_EQ; |
1326 } | 1319 } |
1320 #endif | |
1327 | 1321 |
1328 /* End: bn_mp_cmp_mag.c */ | 1322 /* End: bn_mp_cmp_mag.c */ |
1329 | 1323 |
1330 /* Start: bn_mp_cnt_lsb.c */ | 1324 /* Start: bn_mp_cnt_lsb.c */ |
1331 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1325 #include <tommath.h> |
1332 * | 1326 #ifdef BN_MP_CNT_LSB_C |
1333 * LibTomMath is a library that provides multiple-precision | 1327 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1334 * integer arithmetic as well as number theoretic functionality. | 1328 * |
1335 * | 1329 * LibTomMath is a library that provides multiple-precision |
1336 * The library was designed directly after the MPI library by | 1330 * integer arithmetic as well as number theoretic functionality. |
1337 * Michael Fromberger but has been written from scratch with | 1331 * |
1338 * additional optimizations in place. | 1332 * The library was designed directly after the MPI library by |
1339 * | 1333 * Michael Fromberger but has been written from scratch with |
1340 * The library is free for all purposes without any express | 1334 * additional optimizations in place. |
1341 * guarantee it works. | 1335 * |
1342 * | 1336 * The library is free for all purposes without any express |
1343 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1337 * guarantee it works. |
1344 */ | 1338 * |
1345 #include <tommath.h> | 1339 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1340 */ | |
1346 | 1341 |
1347 static const int lnz[16] = { | 1342 static const int lnz[16] = { |
1348 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 | 1343 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 |
1349 }; | 1344 }; |
1350 | 1345 |
1373 } while (qq == 0); | 1368 } while (qq == 0); |
1374 } | 1369 } |
1375 return x; | 1370 return x; |
1376 } | 1371 } |
1377 | 1372 |
1373 #endif | |
1378 | 1374 |
1379 /* End: bn_mp_cnt_lsb.c */ | 1375 /* End: bn_mp_cnt_lsb.c */ |
1380 | 1376 |
1381 /* Start: bn_mp_copy.c */ | 1377 /* Start: bn_mp_copy.c */ |
1382 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1378 #include <tommath.h> |
1383 * | 1379 #ifdef BN_MP_COPY_C |
1384 * LibTomMath is a library that provides multiple-precision | 1380 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1385 * integer arithmetic as well as number theoretic functionality. | 1381 * |
1386 * | 1382 * LibTomMath is a library that provides multiple-precision |
1387 * The library was designed directly after the MPI library by | 1383 * integer arithmetic as well as number theoretic functionality. |
1388 * Michael Fromberger but has been written from scratch with | 1384 * |
1389 * additional optimizations in place. | 1385 * The library was designed directly after the MPI library by |
1390 * | 1386 * Michael Fromberger but has been written from scratch with |
1391 * The library is free for all purposes without any express | 1387 * additional optimizations in place. |
1392 * guarantee it works. | 1388 * |
1393 * | 1389 * The library is free for all purposes without any express |
1394 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1390 * guarantee it works. |
1395 */ | 1391 * |
1396 #include <tommath.h> | 1392 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1393 */ | |
1397 | 1394 |
1398 /* copy, b = a */ | 1395 /* copy, b = a */ |
1399 int | 1396 int |
1400 mp_copy (mp_int * a, mp_int * b) | 1397 mp_copy (mp_int * a, mp_int * b) |
1401 { | 1398 { |
1439 /* copy used count and sign */ | 1436 /* copy used count and sign */ |
1440 b->used = a->used; | 1437 b->used = a->used; |
1441 b->sign = a->sign; | 1438 b->sign = a->sign; |
1442 return MP_OKAY; | 1439 return MP_OKAY; |
1443 } | 1440 } |
1441 #endif | |
1444 | 1442 |
1445 /* End: bn_mp_copy.c */ | 1443 /* End: bn_mp_copy.c */ |
1446 | 1444 |
1447 /* Start: bn_mp_count_bits.c */ | 1445 /* Start: bn_mp_count_bits.c */ |
1448 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1446 #include <tommath.h> |
1449 * | 1447 #ifdef BN_MP_COUNT_BITS_C |
1450 * LibTomMath is a library that provides multiple-precision | 1448 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1451 * integer arithmetic as well as number theoretic functionality. | 1449 * |
1452 * | 1450 * LibTomMath is a library that provides multiple-precision |
1453 * The library was designed directly after the MPI library by | 1451 * integer arithmetic as well as number theoretic functionality. |
1454 * Michael Fromberger but has been written from scratch with | 1452 * |
1455 * additional optimizations in place. | 1453 * The library was designed directly after the MPI library by |
1456 * | 1454 * Michael Fromberger but has been written from scratch with |
1457 * The library is free for all purposes without any express | 1455 * additional optimizations in place. |
1458 * guarantee it works. | 1456 * |
1459 * | 1457 * The library is free for all purposes without any express |
1460 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1458 * guarantee it works. |
1461 */ | 1459 * |
1462 #include <tommath.h> | 1460 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1461 */ | |
1463 | 1462 |
1464 /* returns the number of bits in an int */ | 1463 /* returns the number of bits in an int */ |
1465 int | 1464 int |
1466 mp_count_bits (mp_int * a) | 1465 mp_count_bits (mp_int * a) |
1467 { | 1466 { |
1482 ++r; | 1481 ++r; |
1483 q >>= ((mp_digit) 1); | 1482 q >>= ((mp_digit) 1); |
1484 } | 1483 } |
1485 return r; | 1484 return r; |
1486 } | 1485 } |
1486 #endif | |
1487 | 1487 |
1488 /* End: bn_mp_count_bits.c */ | 1488 /* End: bn_mp_count_bits.c */ |
1489 | 1489 |
1490 /* Start: bn_mp_div.c */ | 1490 /* Start: bn_mp_div.c */ |
1491 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1491 #include <tommath.h> |
1492 * | 1492 #ifdef BN_MP_DIV_C |
1493 * LibTomMath is a library that provides multiple-precision | 1493 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1494 * integer arithmetic as well as number theoretic functionality. | 1494 * |
1495 * | 1495 * LibTomMath is a library that provides multiple-precision |
1496 * The library was designed directly after the MPI library by | 1496 * integer arithmetic as well as number theoretic functionality. |
1497 * Michael Fromberger but has been written from scratch with | 1497 * |
1498 * additional optimizations in place. | 1498 * The library was designed directly after the MPI library by |
1499 * | 1499 * Michael Fromberger but has been written from scratch with |
1500 * The library is free for all purposes without any express | 1500 * additional optimizations in place. |
1501 * guarantee it works. | 1501 * |
1502 * | 1502 * The library is free for all purposes without any express |
1503 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1503 * guarantee it works. |
1504 */ | 1504 * |
1505 #include <tommath.h> | 1505 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1506 */ | |
1507 | |
1508 #ifdef BN_MP_DIV_SMALL | |
1509 | |
1510 /* slower bit-bang division... also smaller */ | |
1511 int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d) | |
1512 { | |
1513 mp_int ta, tb, tq, q; | |
1514 int res, n, n2; | |
1515 | |
1516 /* is divisor zero ? */ | |
1517 if (mp_iszero (b) == 1) { | |
1518 return MP_VAL; | |
1519 } | |
1520 | |
1521 /* if a < b then q=0, r = a */ | |
1522 if (mp_cmp_mag (a, b) == MP_LT) { | |
1523 if (d != NULL) { | |
1524 res = mp_copy (a, d); | |
1525 } else { | |
1526 res = MP_OKAY; | |
1527 } | |
1528 if (c != NULL) { | |
1529 mp_zero (c); | |
1530 } | |
1531 return res; | |
1532 } | |
1533 | |
1534 /* init our temps */ | |
1535 if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) { | |
1536 return res; | |
1537 } | |
1538 | |
1539 | |
1540 mp_set(&tq, 1); | |
1541 n = mp_count_bits(a) - mp_count_bits(b); | |
1542 if (((res = mp_copy(a, &ta)) != MP_OKAY) || | |
1543 ((res = mp_copy(b, &tb)) != MP_OKAY) || | |
1544 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || | |
1545 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) { | |
1546 goto __ERR; | |
1547 } | |
1548 | |
1549 while (n-- >= 0) { | |
1550 if (mp_cmp(&tb, &ta) != MP_GT) { | |
1551 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || | |
1552 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) { | |
1553 goto __ERR; | |
1554 } | |
1555 } | |
1556 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) || | |
1557 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) { | |
1558 goto __ERR; | |
1559 } | |
1560 } | |
1561 | |
1562 /* now q == quotient and ta == remainder */ | |
1563 n = a->sign; | |
1564 n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG); | |
1565 if (c != NULL) { | |
1566 mp_exch(c, &q); | |
1567 c->sign = n2; | |
1568 } | |
1569 if (d != NULL) { | |
1570 mp_exch(d, &ta); | |
1571 d->sign = n; | |
1572 } | |
1573 __ERR: | |
1574 mp_clear_multi(&ta, &tb, &tq, &q, NULL); | |
1575 return res; | |
1576 } | |
1577 | |
1578 #else | |
1506 | 1579 |
1507 /* integer signed division. | 1580 /* integer signed division. |
1508 * c*b + d == a [e.g. a/b, c=quotient, d=remainder] | 1581 * c*b + d == a [e.g. a/b, c=quotient, d=remainder] |
1509 * HAC pp.598 Algorithm 14.20 | 1582 * HAC pp.598 Algorithm 14.20 |
1510 * | 1583 * |
1675 /* now q is the quotient and x is the remainder | 1748 /* now q is the quotient and x is the remainder |
1676 * [which we have to normalize] | 1749 * [which we have to normalize] |
1677 */ | 1750 */ |
1678 | 1751 |
1679 /* get sign before writing to c */ | 1752 /* get sign before writing to c */ |
1680 x.sign = a->sign; | 1753 x.sign = x.used == 0 ? MP_ZPOS : a->sign; |
1681 | 1754 |
1682 if (c != NULL) { | 1755 if (c != NULL) { |
1683 mp_clamp (&q); | 1756 mp_clamp (&q); |
1684 mp_exch (&q, c); | 1757 mp_exch (&q, c); |
1685 c->sign = neg; | 1758 c->sign = neg; |
1698 __T1:mp_clear (&t1); | 1771 __T1:mp_clear (&t1); |
1699 __Q:mp_clear (&q); | 1772 __Q:mp_clear (&q); |
1700 return res; | 1773 return res; |
1701 } | 1774 } |
1702 | 1775 |
1776 #endif | |
1777 | |
1778 #endif | |
1779 | |
1703 /* End: bn_mp_div.c */ | 1780 /* End: bn_mp_div.c */ |
1704 | 1781 |
1705 /* Start: bn_mp_div_2.c */ | 1782 /* Start: bn_mp_div_2.c */ |
1706 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1783 #include <tommath.h> |
1707 * | 1784 #ifdef BN_MP_DIV_2_C |
1708 * LibTomMath is a library that provides multiple-precision | 1785 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1709 * integer arithmetic as well as number theoretic functionality. | 1786 * |
1710 * | 1787 * LibTomMath is a library that provides multiple-precision |
1711 * The library was designed directly after the MPI library by | 1788 * integer arithmetic as well as number theoretic functionality. |
1712 * Michael Fromberger but has been written from scratch with | 1789 * |
1713 * additional optimizations in place. | 1790 * The library was designed directly after the MPI library by |
1714 * | 1791 * Michael Fromberger but has been written from scratch with |
1715 * The library is free for all purposes without any express | 1792 * additional optimizations in place. |
1716 * guarantee it works. | 1793 * |
1717 * | 1794 * The library is free for all purposes without any express |
1718 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1795 * guarantee it works. |
1719 */ | 1796 * |
1720 #include <tommath.h> | 1797 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1798 */ | |
1721 | 1799 |
1722 /* b = a/2 */ | 1800 /* b = a/2 */ |
1723 int mp_div_2(mp_int * a, mp_int * b) | 1801 int mp_div_2(mp_int * a, mp_int * b) |
1724 { | 1802 { |
1725 int x, res, oldused; | 1803 int x, res, oldused; |
1763 } | 1841 } |
1764 b->sign = a->sign; | 1842 b->sign = a->sign; |
1765 mp_clamp (b); | 1843 mp_clamp (b); |
1766 return MP_OKAY; | 1844 return MP_OKAY; |
1767 } | 1845 } |
1846 #endif | |
1768 | 1847 |
1769 /* End: bn_mp_div_2.c */ | 1848 /* End: bn_mp_div_2.c */ |
1770 | 1849 |
1771 /* Start: bn_mp_div_2d.c */ | 1850 /* Start: bn_mp_div_2d.c */ |
1772 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1851 #include <tommath.h> |
1773 * | 1852 #ifdef BN_MP_DIV_2D_C |
1774 * LibTomMath is a library that provides multiple-precision | 1853 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1775 * integer arithmetic as well as number theoretic functionality. | 1854 * |
1776 * | 1855 * LibTomMath is a library that provides multiple-precision |
1777 * The library was designed directly after the MPI library by | 1856 * integer arithmetic as well as number theoretic functionality. |
1778 * Michael Fromberger but has been written from scratch with | 1857 * |
1779 * additional optimizations in place. | 1858 * The library was designed directly after the MPI library by |
1780 * | 1859 * Michael Fromberger but has been written from scratch with |
1781 * The library is free for all purposes without any express | 1860 * additional optimizations in place. |
1782 * guarantee it works. | 1861 * |
1783 * | 1862 * The library is free for all purposes without any express |
1784 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1863 * guarantee it works. |
1785 */ | 1864 * |
1786 #include <tommath.h> | 1865 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1866 */ | |
1787 | 1867 |
1788 /* shift right by a certain bit count (store quotient in c, optional remainder in d) */ | 1868 /* shift right by a certain bit count (store quotient in c, optional remainder in d) */ |
1789 int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) | 1869 int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) |
1790 { | 1870 { |
1791 mp_digit D, r, rr; | 1871 mp_digit D, r, rr; |
1858 mp_exch (&t, d); | 1938 mp_exch (&t, d); |
1859 } | 1939 } |
1860 mp_clear (&t); | 1940 mp_clear (&t); |
1861 return MP_OKAY; | 1941 return MP_OKAY; |
1862 } | 1942 } |
1943 #endif | |
1863 | 1944 |
1864 /* End: bn_mp_div_2d.c */ | 1945 /* End: bn_mp_div_2d.c */ |
1865 | 1946 |
1866 /* Start: bn_mp_div_3.c */ | 1947 /* Start: bn_mp_div_3.c */ |
1867 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 1948 #include <tommath.h> |
1868 * | 1949 #ifdef BN_MP_DIV_3_C |
1869 * LibTomMath is a library that provides multiple-precision | 1950 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1870 * integer arithmetic as well as number theoretic functionality. | 1951 * |
1871 * | 1952 * LibTomMath is a library that provides multiple-precision |
1872 * The library was designed directly after the MPI library by | 1953 * integer arithmetic as well as number theoretic functionality. |
1873 * Michael Fromberger but has been written from scratch with | 1954 * |
1874 * additional optimizations in place. | 1955 * The library was designed directly after the MPI library by |
1875 * | 1956 * Michael Fromberger but has been written from scratch with |
1876 * The library is free for all purposes without any express | 1957 * additional optimizations in place. |
1877 * guarantee it works. | 1958 * |
1878 * | 1959 * The library is free for all purposes without any express |
1879 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 1960 * guarantee it works. |
1880 */ | 1961 * |
1881 #include <tommath.h> | 1962 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
1963 */ | |
1882 | 1964 |
1883 /* divide by three (based on routine from MPI and the GMP manual) */ | 1965 /* divide by three (based on routine from MPI and the GMP manual) */ |
1884 int | 1966 int |
1885 mp_div_3 (mp_int * a, mp_int *c, mp_digit * d) | 1967 mp_div_3 (mp_int * a, mp_int *c, mp_digit * d) |
1886 { | 1968 { |
1935 mp_clear(&q); | 2017 mp_clear(&q); |
1936 | 2018 |
1937 return res; | 2019 return res; |
1938 } | 2020 } |
1939 | 2021 |
2022 #endif | |
1940 | 2023 |
1941 /* End: bn_mp_div_3.c */ | 2024 /* End: bn_mp_div_3.c */ |
1942 | 2025 |
1943 /* Start: bn_mp_div_d.c */ | 2026 /* Start: bn_mp_div_d.c */ |
1944 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2027 #include <tommath.h> |
1945 * | 2028 #ifdef BN_MP_DIV_D_C |
1946 * LibTomMath is a library that provides multiple-precision | 2029 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
1947 * integer arithmetic as well as number theoretic functionality. | 2030 * |
1948 * | 2031 * LibTomMath is a library that provides multiple-precision |
1949 * The library was designed directly after the MPI library by | 2032 * integer arithmetic as well as number theoretic functionality. |
1950 * Michael Fromberger but has been written from scratch with | 2033 * |
1951 * additional optimizations in place. | 2034 * The library was designed directly after the MPI library by |
1952 * | 2035 * Michael Fromberger but has been written from scratch with |
1953 * The library is free for all purposes without any express | 2036 * additional optimizations in place. |
1954 * guarantee it works. | 2037 * |
1955 * | 2038 * The library is free for all purposes without any express |
1956 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2039 * guarantee it works. |
1957 */ | 2040 * |
1958 #include <tommath.h> | 2041 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2042 */ | |
1959 | 2043 |
1960 static int s_is_power_of_two(mp_digit b, int *p) | 2044 static int s_is_power_of_two(mp_digit b, int *p) |
1961 { | 2045 { |
1962 int x; | 2046 int x; |
1963 | 2047 |
1995 } | 2079 } |
1996 | 2080 |
1997 /* power of two ? */ | 2081 /* power of two ? */ |
1998 if (s_is_power_of_two(b, &ix) == 1) { | 2082 if (s_is_power_of_two(b, &ix) == 1) { |
1999 if (d != NULL) { | 2083 if (d != NULL) { |
2000 *d = a->dp[0] & ((1<<ix) - 1); | 2084 *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1); |
2001 } | 2085 } |
2002 if (c != NULL) { | 2086 if (c != NULL) { |
2003 return mp_div_2d(a, ix, c, NULL); | 2087 return mp_div_2d(a, ix, c, NULL); |
2004 } | 2088 } |
2005 return MP_OKAY; | 2089 return MP_OKAY; |
2006 } | 2090 } |
2007 | 2091 |
2092 #ifdef BN_MP_DIV_3_C | |
2008 /* three? */ | 2093 /* three? */ |
2009 if (b == 3) { | 2094 if (b == 3) { |
2010 return mp_div_3(a, c, d); | 2095 return mp_div_3(a, c, d); |
2011 } | 2096 } |
2097 #endif | |
2012 | 2098 |
2013 /* no easy answer [c'est la vie]. Just division */ | 2099 /* no easy answer [c'est la vie]. Just division */ |
2014 if ((res = mp_init_size(&q, a->used)) != MP_OKAY) { | 2100 if ((res = mp_init_size(&q, a->used)) != MP_OKAY) { |
2015 return res; | 2101 return res; |
2016 } | 2102 } |
2041 mp_clear(&q); | 2127 mp_clear(&q); |
2042 | 2128 |
2043 return res; | 2129 return res; |
2044 } | 2130 } |
2045 | 2131 |
2132 #endif | |
2046 | 2133 |
2047 /* End: bn_mp_div_d.c */ | 2134 /* End: bn_mp_div_d.c */ |
2048 | 2135 |
2049 /* Start: bn_mp_dr_is_modulus.c */ | 2136 /* Start: bn_mp_dr_is_modulus.c */ |
2050 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2137 #include <tommath.h> |
2051 * | 2138 #ifdef BN_MP_DR_IS_MODULUS_C |
2052 * LibTomMath is a library that provides multiple-precision | 2139 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2053 * integer arithmetic as well as number theoretic functionality. | 2140 * |
2054 * | 2141 * LibTomMath is a library that provides multiple-precision |
2055 * The library was designed directly after the MPI library by | 2142 * integer arithmetic as well as number theoretic functionality. |
2056 * Michael Fromberger but has been written from scratch with | 2143 * |
2057 * additional optimizations in place. | 2144 * The library was designed directly after the MPI library by |
2058 * | 2145 * Michael Fromberger but has been written from scratch with |
2059 * The library is free for all purposes without any express | 2146 * additional optimizations in place. |
2060 * guarantee it works. | 2147 * |
2061 * | 2148 * The library is free for all purposes without any express |
2062 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2149 * guarantee it works. |
2063 */ | 2150 * |
2064 #include <tommath.h> | 2151 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2152 */ | |
2065 | 2153 |
2066 /* determines if a number is a valid DR modulus */ | 2154 /* determines if a number is a valid DR modulus */ |
2067 int mp_dr_is_modulus(mp_int *a) | 2155 int mp_dr_is_modulus(mp_int *a) |
2068 { | 2156 { |
2069 int ix; | 2157 int ix; |
2082 } | 2170 } |
2083 } | 2171 } |
2084 return 1; | 2172 return 1; |
2085 } | 2173 } |
2086 | 2174 |
2175 #endif | |
2087 | 2176 |
2088 /* End: bn_mp_dr_is_modulus.c */ | 2177 /* End: bn_mp_dr_is_modulus.c */ |
2089 | 2178 |
2090 /* Start: bn_mp_dr_reduce.c */ | 2179 /* Start: bn_mp_dr_reduce.c */ |
2091 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2180 #include <tommath.h> |
2092 * | 2181 #ifdef BN_MP_DR_REDUCE_C |
2093 * LibTomMath is a library that provides multiple-precision | 2182 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2094 * integer arithmetic as well as number theoretic functionality. | 2183 * |
2095 * | 2184 * LibTomMath is a library that provides multiple-precision |
2096 * The library was designed directly after the MPI library by | 2185 * integer arithmetic as well as number theoretic functionality. |
2097 * Michael Fromberger but has been written from scratch with | 2186 * |
2098 * additional optimizations in place. | 2187 * The library was designed directly after the MPI library by |
2099 * | 2188 * Michael Fromberger but has been written from scratch with |
2100 * The library is free for all purposes without any express | 2189 * additional optimizations in place. |
2101 * guarantee it works. | 2190 * |
2102 * | 2191 * The library is free for all purposes without any express |
2103 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2192 * guarantee it works. |
2104 */ | 2193 * |
2105 #include <tommath.h> | 2194 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2195 */ | |
2106 | 2196 |
2107 /* reduce "x" in place modulo "n" using the Diminished Radix algorithm. | 2197 /* reduce "x" in place modulo "n" using the Diminished Radix algorithm. |
2108 * | 2198 * |
2109 * Based on algorithm from the paper | 2199 * Based on algorithm from the paper |
2110 * | 2200 * |
2174 s_mp_sub(x, n, x); | 2264 s_mp_sub(x, n, x); |
2175 goto top; | 2265 goto top; |
2176 } | 2266 } |
2177 return MP_OKAY; | 2267 return MP_OKAY; |
2178 } | 2268 } |
2269 #endif | |
2179 | 2270 |
2180 /* End: bn_mp_dr_reduce.c */ | 2271 /* End: bn_mp_dr_reduce.c */ |
2181 | 2272 |
2182 /* Start: bn_mp_dr_setup.c */ | 2273 /* Start: bn_mp_dr_setup.c */ |
2183 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2274 #include <tommath.h> |
2184 * | 2275 #ifdef BN_MP_DR_SETUP_C |
2185 * LibTomMath is a library that provides multiple-precision | 2276 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2186 * integer arithmetic as well as number theoretic functionality. | 2277 * |
2187 * | 2278 * LibTomMath is a library that provides multiple-precision |
2188 * The library was designed directly after the MPI library by | 2279 * integer arithmetic as well as number theoretic functionality. |
2189 * Michael Fromberger but has been written from scratch with | 2280 * |
2190 * additional optimizations in place. | 2281 * The library was designed directly after the MPI library by |
2191 * | 2282 * Michael Fromberger but has been written from scratch with |
2192 * The library is free for all purposes without any express | 2283 * additional optimizations in place. |
2193 * guarantee it works. | 2284 * |
2194 * | 2285 * The library is free for all purposes without any express |
2195 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2286 * guarantee it works. |
2196 */ | 2287 * |
2197 #include <tommath.h> | 2288 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2289 */ | |
2198 | 2290 |
2199 /* determines the setup value */ | 2291 /* determines the setup value */ |
2200 void mp_dr_setup(mp_int *a, mp_digit *d) | 2292 void mp_dr_setup(mp_int *a, mp_digit *d) |
2201 { | 2293 { |
2202 /* the casts are required if DIGIT_BIT is one less than | 2294 /* the casts are required if DIGIT_BIT is one less than |
2204 */ | 2296 */ |
2205 *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - | 2297 *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - |
2206 ((mp_word)a->dp[0])); | 2298 ((mp_word)a->dp[0])); |
2207 } | 2299 } |
2208 | 2300 |
2301 #endif | |
2209 | 2302 |
2210 /* End: bn_mp_dr_setup.c */ | 2303 /* End: bn_mp_dr_setup.c */ |
2211 | 2304 |
2212 /* Start: bn_mp_exch.c */ | 2305 /* Start: bn_mp_exch.c */ |
2213 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2306 #include <tommath.h> |
2214 * | 2307 #ifdef BN_MP_EXCH_C |
2215 * LibTomMath is a library that provides multiple-precision | 2308 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2216 * integer arithmetic as well as number theoretic functionality. | 2309 * |
2217 * | 2310 * LibTomMath is a library that provides multiple-precision |
2218 * The library was designed directly after the MPI library by | 2311 * integer arithmetic as well as number theoretic functionality. |
2219 * Michael Fromberger but has been written from scratch with | 2312 * |
2220 * additional optimizations in place. | 2313 * The library was designed directly after the MPI library by |
2221 * | 2314 * Michael Fromberger but has been written from scratch with |
2222 * The library is free for all purposes without any express | 2315 * additional optimizations in place. |
2223 * guarantee it works. | 2316 * |
2224 * | 2317 * The library is free for all purposes without any express |
2225 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2318 * guarantee it works. |
2226 */ | 2319 * |
2227 #include <tommath.h> | 2320 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2321 */ | |
2228 | 2322 |
2229 /* swap the elements of two integers, for cases where you can't simply swap the | 2323 /* swap the elements of two integers, for cases where you can't simply swap the |
2230 * mp_int pointers around | 2324 * mp_int pointers around |
2231 */ | 2325 */ |
2232 void | 2326 void |
2236 | 2330 |
2237 t = *a; | 2331 t = *a; |
2238 *a = *b; | 2332 *a = *b; |
2239 *b = t; | 2333 *b = t; |
2240 } | 2334 } |
2335 #endif | |
2241 | 2336 |
2242 /* End: bn_mp_exch.c */ | 2337 /* End: bn_mp_exch.c */ |
2243 | 2338 |
2244 /* Start: bn_mp_expt_d.c */ | 2339 /* Start: bn_mp_expt_d.c */ |
2245 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2340 #include <tommath.h> |
2246 * | 2341 #ifdef BN_MP_EXPT_D_C |
2247 * LibTomMath is a library that provides multiple-precision | 2342 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2248 * integer arithmetic as well as number theoretic functionality. | 2343 * |
2249 * | 2344 * LibTomMath is a library that provides multiple-precision |
2250 * The library was designed directly after the MPI library by | 2345 * integer arithmetic as well as number theoretic functionality. |
2251 * Michael Fromberger but has been written from scratch with | 2346 * |
2252 * additional optimizations in place. | 2347 * The library was designed directly after the MPI library by |
2253 * | 2348 * Michael Fromberger but has been written from scratch with |
2254 * The library is free for all purposes without any express | 2349 * additional optimizations in place. |
2255 * guarantee it works. | 2350 * |
2256 * | 2351 * The library is free for all purposes without any express |
2257 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2352 * guarantee it works. |
2258 */ | 2353 * |
2259 #include <tommath.h> | 2354 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2355 */ | |
2260 | 2356 |
2261 /* calculate c = a**b using a square-multiply algorithm */ | 2357 /* calculate c = a**b using a square-multiply algorithm */ |
2262 int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) | 2358 int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) |
2263 { | 2359 { |
2264 int res, x; | 2360 int res, x; |
2291 } | 2387 } |
2292 | 2388 |
2293 mp_clear (&g); | 2389 mp_clear (&g); |
2294 return MP_OKAY; | 2390 return MP_OKAY; |
2295 } | 2391 } |
2392 #endif | |
2296 | 2393 |
2297 /* End: bn_mp_expt_d.c */ | 2394 /* End: bn_mp_expt_d.c */ |
2298 | 2395 |
2299 /* Start: bn_mp_exptmod.c */ | 2396 /* Start: bn_mp_exptmod.c */ |
2300 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2397 #include <tommath.h> |
2301 * | 2398 #ifdef BN_MP_EXPTMOD_C |
2302 * LibTomMath is a library that provides multiple-precision | 2399 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2303 * integer arithmetic as well as number theoretic functionality. | 2400 * |
2304 * | 2401 * LibTomMath is a library that provides multiple-precision |
2305 * The library was designed directly after the MPI library by | 2402 * integer arithmetic as well as number theoretic functionality. |
2306 * Michael Fromberger but has been written from scratch with | 2403 * |
2307 * additional optimizations in place. | 2404 * The library was designed directly after the MPI library by |
2308 * | 2405 * Michael Fromberger but has been written from scratch with |
2309 * The library is free for all purposes without any express | 2406 * additional optimizations in place. |
2310 * guarantee it works. | 2407 * |
2311 * | 2408 * The library is free for all purposes without any express |
2312 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2409 * guarantee it works. |
2313 */ | 2410 * |
2314 #include <tommath.h> | 2411 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2412 */ | |
2315 | 2413 |
2316 | 2414 |
2317 /* this is a shell function that calls either the normal or Montgomery | 2415 /* this is a shell function that calls either the normal or Montgomery |
2318 * exptmod functions. Originally the call to the montgomery code was | 2416 * exptmod functions. Originally the call to the montgomery code was |
2319 * embedded in the normal function but that wasted alot of stack space | 2417 * embedded in the normal function but that wasted alot of stack space |
2328 return MP_VAL; | 2426 return MP_VAL; |
2329 } | 2427 } |
2330 | 2428 |
2331 /* if exponent X is negative we have to recurse */ | 2429 /* if exponent X is negative we have to recurse */ |
2332 if (X->sign == MP_NEG) { | 2430 if (X->sign == MP_NEG) { |
2431 #ifdef BN_MP_INVMOD_C | |
2333 mp_int tmpG, tmpX; | 2432 mp_int tmpG, tmpX; |
2334 int err; | 2433 int err; |
2335 | 2434 |
2336 /* first compute 1/G mod P */ | 2435 /* first compute 1/G mod P */ |
2337 if ((err = mp_init(&tmpG)) != MP_OKAY) { | 2436 if ((err = mp_init(&tmpG)) != MP_OKAY) { |
2354 | 2453 |
2355 /* and now compute (1/G)**|X| instead of G**X [X < 0] */ | 2454 /* and now compute (1/G)**|X| instead of G**X [X < 0] */ |
2356 err = mp_exptmod(&tmpG, &tmpX, P, Y); | 2455 err = mp_exptmod(&tmpG, &tmpX, P, Y); |
2357 mp_clear_multi(&tmpG, &tmpX, NULL); | 2456 mp_clear_multi(&tmpG, &tmpX, NULL); |
2358 return err; | 2457 return err; |
2359 } | 2458 #else |
2360 | 2459 /* no invmod */ |
2460 return MP_VAL | |
2461 #endif | |
2462 } | |
2463 | |
2464 #ifdef BN_MP_DR_IS_MODULUS_C | |
2361 /* is it a DR modulus? */ | 2465 /* is it a DR modulus? */ |
2362 dr = mp_dr_is_modulus(P); | 2466 dr = mp_dr_is_modulus(P); |
2363 | 2467 #else |
2468 dr = 0; | |
2469 #endif | |
2470 | |
2471 #ifdef BN_MP_REDUCE_IS_2K_C | |
2364 /* if not, is it a uDR modulus? */ | 2472 /* if not, is it a uDR modulus? */ |
2365 if (dr == 0) { | 2473 if (dr == 0) { |
2366 dr = mp_reduce_is_2k(P) << 1; | 2474 dr = mp_reduce_is_2k(P) << 1; |
2367 } | 2475 } |
2476 #endif | |
2368 | 2477 |
2369 /* if the modulus is odd or dr != 0 use the fast method */ | 2478 /* if the modulus is odd or dr != 0 use the fast method */ |
2479 #ifdef BN_MP_EXPTMOD_FAST_C | |
2370 if (mp_isodd (P) == 1 || dr != 0) { | 2480 if (mp_isodd (P) == 1 || dr != 0) { |
2371 return mp_exptmod_fast (G, X, P, Y, dr); | 2481 return mp_exptmod_fast (G, X, P, Y, dr); |
2372 } else { | 2482 } else { |
2483 #endif | |
2484 #ifdef BN_S_MP_EXPTMOD_C | |
2373 /* otherwise use the generic Barrett reduction technique */ | 2485 /* otherwise use the generic Barrett reduction technique */ |
2374 return s_mp_exptmod (G, X, P, Y); | 2486 return s_mp_exptmod (G, X, P, Y); |
2375 } | 2487 #else |
2376 } | 2488 /* no exptmod for evens */ |
2377 | 2489 return MP_VAL; |
2490 #endif | |
2491 #ifdef BN_MP_EXPTMOD_FAST_C | |
2492 } | |
2493 #endif | |
2494 } | |
2495 | |
2496 #endif | |
2378 | 2497 |
2379 /* End: bn_mp_exptmod.c */ | 2498 /* End: bn_mp_exptmod.c */ |
2380 | 2499 |
2381 /* Start: bn_mp_exptmod_fast.c */ | 2500 /* Start: bn_mp_exptmod_fast.c */ |
2382 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2501 #include <tommath.h> |
2383 * | 2502 #ifdef BN_MP_EXPTMOD_FAST_C |
2384 * LibTomMath is a library that provides multiple-precision | 2503 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2385 * integer arithmetic as well as number theoretic functionality. | 2504 * |
2386 * | 2505 * LibTomMath is a library that provides multiple-precision |
2387 * The library was designed directly after the MPI library by | 2506 * integer arithmetic as well as number theoretic functionality. |
2388 * Michael Fromberger but has been written from scratch with | 2507 * |
2389 * additional optimizations in place. | 2508 * The library was designed directly after the MPI library by |
2390 * | 2509 * Michael Fromberger but has been written from scratch with |
2391 * The library is free for all purposes without any express | 2510 * additional optimizations in place. |
2392 * guarantee it works. | 2511 * |
2393 * | 2512 * The library is free for all purposes without any express |
2394 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2513 * guarantee it works. |
2395 */ | 2514 * |
2396 #include <tommath.h> | 2515 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2516 */ | |
2397 | 2517 |
2398 /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 | 2518 /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 |
2399 * | 2519 * |
2400 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation. | 2520 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation. |
2401 * The value of k changes based on the size of the exponent. | 2521 * The value of k changes based on the size of the exponent. |
2463 } | 2583 } |
2464 } | 2584 } |
2465 | 2585 |
2466 /* determine and setup reduction code */ | 2586 /* determine and setup reduction code */ |
2467 if (redmode == 0) { | 2587 if (redmode == 0) { |
2588 #ifdef BN_MP_MONTGOMERY_SETUP_C | |
2468 /* now setup montgomery */ | 2589 /* now setup montgomery */ |
2469 if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) { | 2590 if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) { |
2470 goto __M; | 2591 goto __M; |
2471 } | 2592 } |
2593 #else | |
2594 err = MP_VAL; | |
2595 goto __M; | |
2596 #endif | |
2472 | 2597 |
2473 /* automatically pick the comba one if available (saves quite a few calls/ifs) */ | 2598 /* automatically pick the comba one if available (saves quite a few calls/ifs) */ |
2599 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C | |
2474 if (((P->used * 2 + 1) < MP_WARRAY) && | 2600 if (((P->used * 2 + 1) < MP_WARRAY) && |
2475 P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { | 2601 P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { |
2476 redux = fast_mp_montgomery_reduce; | 2602 redux = fast_mp_montgomery_reduce; |
2477 } else { | 2603 } else |
2604 #endif | |
2605 { | |
2606 #ifdef BN_MP_MONTGOMERY_REDUCE_C | |
2478 /* use slower baseline Montgomery method */ | 2607 /* use slower baseline Montgomery method */ |
2479 redux = mp_montgomery_reduce; | 2608 redux = mp_montgomery_reduce; |
2609 #else | |
2610 err = MP_VAL; | |
2611 goto __M; | |
2612 #endif | |
2480 } | 2613 } |
2481 } else if (redmode == 1) { | 2614 } else if (redmode == 1) { |
2615 #if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C) | |
2482 /* setup DR reduction for moduli of the form B**k - b */ | 2616 /* setup DR reduction for moduli of the form B**k - b */ |
2483 mp_dr_setup(P, &mp); | 2617 mp_dr_setup(P, &mp); |
2484 redux = mp_dr_reduce; | 2618 redux = mp_dr_reduce; |
2619 #else | |
2620 err = MP_VAL; | |
2621 goto __M; | |
2622 #endif | |
2485 } else { | 2623 } else { |
2624 #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C) | |
2486 /* setup DR reduction for moduli of the form 2**k - b */ | 2625 /* setup DR reduction for moduli of the form 2**k - b */ |
2487 if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) { | 2626 if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) { |
2488 goto __M; | 2627 goto __M; |
2489 } | 2628 } |
2490 redux = mp_reduce_2k; | 2629 redux = mp_reduce_2k; |
2630 #else | |
2631 err = MP_VAL; | |
2632 goto __M; | |
2633 #endif | |
2491 } | 2634 } |
2492 | 2635 |
2493 /* setup result */ | 2636 /* setup result */ |
2494 if ((err = mp_init (&res)) != MP_OKAY) { | 2637 if ((err = mp_init (&res)) != MP_OKAY) { |
2495 goto __M; | 2638 goto __M; |
2496 } | 2639 } |
2497 | 2640 |
2498 /* create M table | 2641 /* create M table |
2499 * | 2642 * |
2500 * The M table contains powers of the input base, e.g. M[x] = G^x mod P | 2643 |
2501 * | 2644 * |
2502 * The first half of the table is not computed though accept for M[0] and M[1] | 2645 * The first half of the table is not computed though accept for M[0] and M[1] |
2503 */ | 2646 */ |
2504 | 2647 |
2505 if (redmode == 0) { | 2648 if (redmode == 0) { |
2649 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C | |
2506 /* now we need R mod m */ | 2650 /* now we need R mod m */ |
2507 if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) { | 2651 if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) { |
2508 goto __RES; | 2652 goto __RES; |
2509 } | 2653 } |
2654 #else | |
2655 err = MP_VAL; | |
2656 goto __RES; | |
2657 #endif | |
2510 | 2658 |
2511 /* now set M[1] to G * R mod m */ | 2659 /* now set M[1] to G * R mod m */ |
2512 if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) { | 2660 if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) { |
2513 goto __RES; | 2661 goto __RES; |
2514 } | 2662 } |
2648 * recall that any value in a Montgomery system is | 2796 * recall that any value in a Montgomery system is |
2649 * actually multiplied by R mod n. So we have | 2797 * actually multiplied by R mod n. So we have |
2650 * to reduce one more time to cancel out the factor | 2798 * to reduce one more time to cancel out the factor |
2651 * of R. | 2799 * of R. |
2652 */ | 2800 */ |
2653 if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) { | 2801 if ((err = redux(&res, P, mp)) != MP_OKAY) { |
2654 goto __RES; | 2802 goto __RES; |
2655 } | 2803 } |
2656 } | 2804 } |
2657 | 2805 |
2658 /* swap res with Y */ | 2806 /* swap res with Y */ |
2664 for (x = 1<<(winsize-1); x < (1 << winsize); x++) { | 2812 for (x = 1<<(winsize-1); x < (1 << winsize); x++) { |
2665 mp_clear (&M[x]); | 2813 mp_clear (&M[x]); |
2666 } | 2814 } |
2667 return err; | 2815 return err; |
2668 } | 2816 } |
2817 #endif | |
2818 | |
2669 | 2819 |
2670 /* End: bn_mp_exptmod_fast.c */ | 2820 /* End: bn_mp_exptmod_fast.c */ |
2671 | 2821 |
2672 /* Start: bn_mp_exteuclid.c */ | 2822 /* Start: bn_mp_exteuclid.c */ |
2673 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2823 #include <tommath.h> |
2674 * | 2824 #ifdef BN_MP_EXTEUCLID_C |
2675 * LibTomMath is a library that provides multiple-precision | 2825 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2676 * integer arithmetic as well as number theoretic functionality. | 2826 * |
2677 * | 2827 * LibTomMath is a library that provides multiple-precision |
2678 * The library was designed directly after the MPI library by | 2828 * integer arithmetic as well as number theoretic functionality. |
2679 * Michael Fromberger but has been written from scratch with | 2829 * |
2680 * additional optimizations in place. | 2830 * The library was designed directly after the MPI library by |
2681 * | 2831 * Michael Fromberger but has been written from scratch with |
2682 * The library is free for all purposes without any express | 2832 * additional optimizations in place. |
2683 * guarantee it works. | 2833 * |
2684 * | 2834 * The library is free for all purposes without any express |
2685 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2835 * guarantee it works. |
2686 */ | 2836 * |
2687 #include <tommath.h> | 2837 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2838 */ | |
2688 | 2839 |
2689 /* Extended euclidean algorithm of (a, b) produces | 2840 /* Extended euclidean algorithm of (a, b) produces |
2690 a*u1 + b*u2 = u3 | 2841 a*u1 + b*u2 = u3 |
2691 */ | 2842 */ |
2692 int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) | 2843 int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) |
2737 | 2888 |
2738 err = MP_OKAY; | 2889 err = MP_OKAY; |
2739 _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); | 2890 _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); |
2740 return err; | 2891 return err; |
2741 } | 2892 } |
2893 #endif | |
2742 | 2894 |
2743 /* End: bn_mp_exteuclid.c */ | 2895 /* End: bn_mp_exteuclid.c */ |
2744 | 2896 |
2745 /* Start: bn_mp_fread.c */ | 2897 /* Start: bn_mp_fread.c */ |
2746 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2898 #include <tommath.h> |
2747 * | 2899 #ifdef BN_MP_FREAD_C |
2748 * LibTomMath is a library that provides multiple-precision | 2900 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2749 * integer arithmetic as well as number theoretic functionality. | 2901 * |
2750 * | 2902 * LibTomMath is a library that provides multiple-precision |
2751 * The library was designed directly after the MPI library by | 2903 * integer arithmetic as well as number theoretic functionality. |
2752 * Michael Fromberger but has been written from scratch with | 2904 * |
2753 * additional optimizations in place. | 2905 * The library was designed directly after the MPI library by |
2754 * | 2906 * Michael Fromberger but has been written from scratch with |
2755 * The library is free for all purposes without any express | 2907 * additional optimizations in place. |
2756 * guarantee it works. | 2908 * |
2757 * | 2909 * The library is free for all purposes without any express |
2758 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2910 * guarantee it works. |
2759 */ | 2911 * |
2760 #include <tommath.h> | 2912 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2913 */ | |
2761 | 2914 |
2762 /* read a bigint from a file stream in ASCII */ | 2915 /* read a bigint from a file stream in ASCII */ |
2763 int mp_fread(mp_int *a, int radix, FILE *stream) | 2916 int mp_fread(mp_int *a, int radix, FILE *stream) |
2764 { | 2917 { |
2765 int err, ch, neg, y; | 2918 int err, ch, neg, y; |
2802 } | 2955 } |
2803 | 2956 |
2804 return MP_OKAY; | 2957 return MP_OKAY; |
2805 } | 2958 } |
2806 | 2959 |
2960 #endif | |
2807 | 2961 |
2808 /* End: bn_mp_fread.c */ | 2962 /* End: bn_mp_fread.c */ |
2809 | 2963 |
2810 /* Start: bn_mp_fwrite.c */ | 2964 /* Start: bn_mp_fwrite.c */ |
2811 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 2965 #include <tommath.h> |
2812 * | 2966 #ifdef BN_MP_FWRITE_C |
2813 * LibTomMath is a library that provides multiple-precision | 2967 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2814 * integer arithmetic as well as number theoretic functionality. | 2968 * |
2815 * | 2969 * LibTomMath is a library that provides multiple-precision |
2816 * The library was designed directly after the MPI library by | 2970 * integer arithmetic as well as number theoretic functionality. |
2817 * Michael Fromberger but has been written from scratch with | 2971 * |
2818 * additional optimizations in place. | 2972 * The library was designed directly after the MPI library by |
2819 * | 2973 * Michael Fromberger but has been written from scratch with |
2820 * The library is free for all purposes without any express | 2974 * additional optimizations in place. |
2821 * guarantee it works. | 2975 * |
2822 * | 2976 * The library is free for all purposes without any express |
2823 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 2977 * guarantee it works. |
2824 */ | 2978 * |
2825 #include <tommath.h> | 2979 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
2980 */ | |
2826 | 2981 |
2827 int mp_fwrite(mp_int *a, int radix, FILE *stream) | 2982 int mp_fwrite(mp_int *a, int radix, FILE *stream) |
2828 { | 2983 { |
2829 char *buf; | 2984 char *buf; |
2830 int err, len, x; | 2985 int err, len, x; |
2852 | 3007 |
2853 XFREE (buf); | 3008 XFREE (buf); |
2854 return MP_OKAY; | 3009 return MP_OKAY; |
2855 } | 3010 } |
2856 | 3011 |
3012 #endif | |
2857 | 3013 |
2858 /* End: bn_mp_fwrite.c */ | 3014 /* End: bn_mp_fwrite.c */ |
2859 | 3015 |
2860 /* Start: bn_mp_gcd.c */ | 3016 /* Start: bn_mp_gcd.c */ |
2861 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3017 #include <tommath.h> |
2862 * | 3018 #ifdef BN_MP_GCD_C |
2863 * LibTomMath is a library that provides multiple-precision | 3019 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2864 * integer arithmetic as well as number theoretic functionality. | 3020 * |
2865 * | 3021 * LibTomMath is a library that provides multiple-precision |
2866 * The library was designed directly after the MPI library by | 3022 * integer arithmetic as well as number theoretic functionality. |
2867 * Michael Fromberger but has been written from scratch with | 3023 * |
2868 * additional optimizations in place. | 3024 * The library was designed directly after the MPI library by |
2869 * | 3025 * Michael Fromberger but has been written from scratch with |
2870 * The library is free for all purposes without any express | 3026 * additional optimizations in place. |
2871 * guarantee it works. | 3027 * |
2872 * | 3028 * The library is free for all purposes without any express |
2873 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3029 * guarantee it works. |
2874 */ | 3030 * |
2875 #include <tommath.h> | 3031 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3032 */ | |
2876 | 3033 |
2877 /* Greatest Common Divisor using the binary method */ | 3034 /* Greatest Common Divisor using the binary method */ |
2878 int mp_gcd (mp_int * a, mp_int * b, mp_int * c) | 3035 int mp_gcd (mp_int * a, mp_int * b, mp_int * c) |
2879 { | 3036 { |
2880 mp_int u, v; | 3037 mp_int u, v; |
2963 res = MP_OKAY; | 3120 res = MP_OKAY; |
2964 __V:mp_clear (&u); | 3121 __V:mp_clear (&u); |
2965 __U:mp_clear (&v); | 3122 __U:mp_clear (&v); |
2966 return res; | 3123 return res; |
2967 } | 3124 } |
3125 #endif | |
2968 | 3126 |
2969 /* End: bn_mp_gcd.c */ | 3127 /* End: bn_mp_gcd.c */ |
2970 | 3128 |
2971 /* Start: bn_mp_get_int.c */ | 3129 /* Start: bn_mp_get_int.c */ |
2972 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3130 #include <tommath.h> |
2973 * | 3131 #ifdef BN_MP_GET_INT_C |
2974 * LibTomMath is a library that provides multiple-precision | 3132 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
2975 * integer arithmetic as well as number theoretic functionality. | 3133 * |
2976 * | 3134 * LibTomMath is a library that provides multiple-precision |
2977 * The library was designed directly after the MPI library by | 3135 * integer arithmetic as well as number theoretic functionality. |
2978 * Michael Fromberger but has been written from scratch with | 3136 * |
2979 * additional optimizations in place. | 3137 * The library was designed directly after the MPI library by |
2980 * | 3138 * Michael Fromberger but has been written from scratch with |
2981 * The library is free for all purposes without any express | 3139 * additional optimizations in place. |
2982 * guarantee it works. | 3140 * |
2983 * | 3141 * The library is free for all purposes without any express |
2984 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3142 * guarantee it works. |
2985 */ | 3143 * |
2986 #include <tommath.h> | 3144 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3145 */ | |
2987 | 3146 |
2988 /* get the lower 32-bits of an mp_int */ | 3147 /* get the lower 32-bits of an mp_int */ |
2989 unsigned long mp_get_int(mp_int * a) | 3148 unsigned long mp_get_int(mp_int * a) |
2990 { | 3149 { |
2991 int i; | 3150 int i; |
3006 } | 3165 } |
3007 | 3166 |
3008 /* force result to 32-bits always so it is consistent on non 32-bit platforms */ | 3167 /* force result to 32-bits always so it is consistent on non 32-bit platforms */ |
3009 return res & 0xFFFFFFFFUL; | 3168 return res & 0xFFFFFFFFUL; |
3010 } | 3169 } |
3170 #endif | |
3011 | 3171 |
3012 /* End: bn_mp_get_int.c */ | 3172 /* End: bn_mp_get_int.c */ |
3013 | 3173 |
3014 /* Start: bn_mp_grow.c */ | 3174 /* Start: bn_mp_grow.c */ |
3015 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3175 #include <tommath.h> |
3016 * | 3176 #ifdef BN_MP_GROW_C |
3017 * LibTomMath is a library that provides multiple-precision | 3177 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3018 * integer arithmetic as well as number theoretic functionality. | 3178 * |
3019 * | 3179 * LibTomMath is a library that provides multiple-precision |
3020 * The library was designed directly after the MPI library by | 3180 * integer arithmetic as well as number theoretic functionality. |
3021 * Michael Fromberger but has been written from scratch with | 3181 * |
3022 * additional optimizations in place. | 3182 * The library was designed directly after the MPI library by |
3023 * | 3183 * Michael Fromberger but has been written from scratch with |
3024 * The library is free for all purposes without any express | 3184 * additional optimizations in place. |
3025 * guarantee it works. | 3185 * |
3026 * | 3186 * The library is free for all purposes without any express |
3027 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3187 * guarantee it works. |
3028 */ | 3188 * |
3029 #include <tommath.h> | 3189 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3190 */ | |
3030 | 3191 |
3031 /* grow as required */ | 3192 /* grow as required */ |
3032 int mp_grow (mp_int * a, int size) | 3193 int mp_grow (mp_int * a, int size) |
3033 { | 3194 { |
3034 int i; | 3195 int i; |
3061 a->dp[i] = 0; | 3222 a->dp[i] = 0; |
3062 } | 3223 } |
3063 } | 3224 } |
3064 return MP_OKAY; | 3225 return MP_OKAY; |
3065 } | 3226 } |
3227 #endif | |
3066 | 3228 |
3067 /* End: bn_mp_grow.c */ | 3229 /* End: bn_mp_grow.c */ |
3068 | 3230 |
3069 /* Start: bn_mp_init.c */ | 3231 /* Start: bn_mp_init.c */ |
3070 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3232 #include <tommath.h> |
3071 * | 3233 #ifdef BN_MP_INIT_C |
3072 * LibTomMath is a library that provides multiple-precision | 3234 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3073 * integer arithmetic as well as number theoretic functionality. | 3235 * |
3074 * | 3236 * LibTomMath is a library that provides multiple-precision |
3075 * The library was designed directly after the MPI library by | 3237 * integer arithmetic as well as number theoretic functionality. |
3076 * Michael Fromberger but has been written from scratch with | 3238 * |
3077 * additional optimizations in place. | 3239 * The library was designed directly after the MPI library by |
3078 * | 3240 * Michael Fromberger but has been written from scratch with |
3079 * The library is free for all purposes without any express | 3241 * additional optimizations in place. |
3080 * guarantee it works. | 3242 * |
3081 * | 3243 * The library is free for all purposes without any express |
3082 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3244 * guarantee it works. |
3083 */ | 3245 * |
3084 #include <tommath.h> | 3246 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3085 | 3247 */ |
3086 /* init a new bigint */ | 3248 |
3249 /* init a new mp_int */ | |
3087 int mp_init (mp_int * a) | 3250 int mp_init (mp_int * a) |
3088 { | 3251 { |
3252 int i; | |
3253 | |
3089 /* allocate memory required and clear it */ | 3254 /* allocate memory required and clear it */ |
3090 a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), MP_PREC); | 3255 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC); |
3091 if (a->dp == NULL) { | 3256 if (a->dp == NULL) { |
3092 return MP_MEM; | 3257 return MP_MEM; |
3258 } | |
3259 | |
3260 /* set the digits to zero */ | |
3261 for (i = 0; i < MP_PREC; i++) { | |
3262 a->dp[i] = 0; | |
3093 } | 3263 } |
3094 | 3264 |
3095 /* set the used to zero, allocated digits to the default precision | 3265 /* set the used to zero, allocated digits to the default precision |
3096 * and sign to positive */ | 3266 * and sign to positive */ |
3097 a->used = 0; | 3267 a->used = 0; |
3098 a->alloc = MP_PREC; | 3268 a->alloc = MP_PREC; |
3099 a->sign = MP_ZPOS; | 3269 a->sign = MP_ZPOS; |
3100 | 3270 |
3101 return MP_OKAY; | 3271 return MP_OKAY; |
3102 } | 3272 } |
3273 #endif | |
3103 | 3274 |
3104 /* End: bn_mp_init.c */ | 3275 /* End: bn_mp_init.c */ |
3105 | 3276 |
3106 /* Start: bn_mp_init_copy.c */ | 3277 /* Start: bn_mp_init_copy.c */ |
3107 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3278 #include <tommath.h> |
3108 * | 3279 #ifdef BN_MP_INIT_COPY_C |
3109 * LibTomMath is a library that provides multiple-precision | 3280 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3110 * integer arithmetic as well as number theoretic functionality. | 3281 * |
3111 * | 3282 * LibTomMath is a library that provides multiple-precision |
3112 * The library was designed directly after the MPI library by | 3283 * integer arithmetic as well as number theoretic functionality. |
3113 * Michael Fromberger but has been written from scratch with | 3284 * |
3114 * additional optimizations in place. | 3285 * The library was designed directly after the MPI library by |
3115 * | 3286 * Michael Fromberger but has been written from scratch with |
3116 * The library is free for all purposes without any express | 3287 * additional optimizations in place. |
3117 * guarantee it works. | 3288 * |
3118 * | 3289 * The library is free for all purposes without any express |
3119 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3290 * guarantee it works. |
3120 */ | 3291 * |
3121 #include <tommath.h> | 3292 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3293 */ | |
3122 | 3294 |
3123 /* creates "a" then copies b into it */ | 3295 /* creates "a" then copies b into it */ |
3124 int mp_init_copy (mp_int * a, mp_int * b) | 3296 int mp_init_copy (mp_int * a, mp_int * b) |
3125 { | 3297 { |
3126 int res; | 3298 int res; |
3128 if ((res = mp_init (a)) != MP_OKAY) { | 3300 if ((res = mp_init (a)) != MP_OKAY) { |
3129 return res; | 3301 return res; |
3130 } | 3302 } |
3131 return mp_copy (b, a); | 3303 return mp_copy (b, a); |
3132 } | 3304 } |
3305 #endif | |
3133 | 3306 |
3134 /* End: bn_mp_init_copy.c */ | 3307 /* End: bn_mp_init_copy.c */ |
3135 | 3308 |
3136 /* Start: bn_mp_init_multi.c */ | 3309 /* Start: bn_mp_init_multi.c */ |
3137 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3310 #include <tommath.h> |
3138 * | 3311 #ifdef BN_MP_INIT_MULTI_C |
3139 * LibTomMath is a library that provides multiple-precision | 3312 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3140 * integer arithmetic as well as number theoretic functionality. | 3313 * |
3141 * | 3314 * LibTomMath is a library that provides multiple-precision |
3142 * The library was designed directly after the MPI library by | 3315 * integer arithmetic as well as number theoretic functionality. |
3143 * Michael Fromberger but has been written from scratch with | 3316 * |
3144 * additional optimizations in place. | 3317 * The library was designed directly after the MPI library by |
3145 * | 3318 * Michael Fromberger but has been written from scratch with |
3146 * The library is free for all purposes without any express | 3319 * additional optimizations in place. |
3147 * guarantee it works. | 3320 * |
3148 * | 3321 * The library is free for all purposes without any express |
3149 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3322 * guarantee it works. |
3150 */ | 3323 * |
3151 #include <tommath.h> | 3324 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3325 */ | |
3152 #include <stdarg.h> | 3326 #include <stdarg.h> |
3153 | 3327 |
3154 int mp_init_multi(mp_int *mp, ...) | 3328 int mp_init_multi(mp_int *mp, ...) |
3155 { | 3329 { |
3156 mp_err res = MP_OKAY; /* Assume ok until proven otherwise */ | 3330 mp_err res = MP_OKAY; /* Assume ok until proven otherwise */ |
3185 } | 3359 } |
3186 va_end(args); | 3360 va_end(args); |
3187 return res; /* Assumed ok, if error flagged above. */ | 3361 return res; /* Assumed ok, if error flagged above. */ |
3188 } | 3362 } |
3189 | 3363 |
3364 #endif | |
3190 | 3365 |
3191 /* End: bn_mp_init_multi.c */ | 3366 /* End: bn_mp_init_multi.c */ |
3192 | 3367 |
3193 /* Start: bn_mp_init_set.c */ | 3368 /* Start: bn_mp_init_set.c */ |
3194 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3369 #include <tommath.h> |
3195 * | 3370 #ifdef BN_MP_INIT_SET_C |
3196 * LibTomMath is a library that provides multiple-precision | 3371 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3197 * integer arithmetic as well as number theoretic functionality. | 3372 * |
3198 * | 3373 * LibTomMath is a library that provides multiple-precision |
3199 * The library was designed directly after the MPI library by | 3374 * integer arithmetic as well as number theoretic functionality. |
3200 * Michael Fromberger but has been written from scratch with | 3375 * |
3201 * additional optimizations in place. | 3376 * The library was designed directly after the MPI library by |
3202 * | 3377 * Michael Fromberger but has been written from scratch with |
3203 * The library is free for all purposes without any express | 3378 * additional optimizations in place. |
3204 * guarantee it works. | 3379 * |
3205 * | 3380 * The library is free for all purposes without any express |
3206 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3381 * guarantee it works. |
3207 */ | 3382 * |
3208 #include <tommath.h> | 3383 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3384 */ | |
3209 | 3385 |
3210 /* initialize and set a digit */ | 3386 /* initialize and set a digit */ |
3211 int mp_init_set (mp_int * a, mp_digit b) | 3387 int mp_init_set (mp_int * a, mp_digit b) |
3212 { | 3388 { |
3213 int err; | 3389 int err; |
3215 return err; | 3391 return err; |
3216 } | 3392 } |
3217 mp_set(a, b); | 3393 mp_set(a, b); |
3218 return err; | 3394 return err; |
3219 } | 3395 } |
3396 #endif | |
3220 | 3397 |
3221 /* End: bn_mp_init_set.c */ | 3398 /* End: bn_mp_init_set.c */ |
3222 | 3399 |
3223 /* Start: bn_mp_init_set_int.c */ | 3400 /* Start: bn_mp_init_set_int.c */ |
3224 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3401 #include <tommath.h> |
3225 * | 3402 #ifdef BN_MP_INIT_SET_INT_C |
3226 * LibTomMath is a library that provides multiple-precision | 3403 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3227 * integer arithmetic as well as number theoretic functionality. | 3404 * |
3228 * | 3405 * LibTomMath is a library that provides multiple-precision |
3229 * The library was designed directly after the MPI library by | 3406 * integer arithmetic as well as number theoretic functionality. |
3230 * Michael Fromberger but has been written from scratch with | 3407 * |
3231 * additional optimizations in place. | 3408 * The library was designed directly after the MPI library by |
3232 * | 3409 * Michael Fromberger but has been written from scratch with |
3233 * The library is free for all purposes without any express | 3410 * additional optimizations in place. |
3234 * guarantee it works. | 3411 * |
3235 * | 3412 * The library is free for all purposes without any express |
3236 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3413 * guarantee it works. |
3237 */ | 3414 * |
3238 #include <tommath.h> | 3415 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3416 */ | |
3239 | 3417 |
3240 /* initialize and set a digit */ | 3418 /* initialize and set a digit */ |
3241 int mp_init_set_int (mp_int * a, unsigned long b) | 3419 int mp_init_set_int (mp_int * a, unsigned long b) |
3242 { | 3420 { |
3243 int err; | 3421 int err; |
3244 if ((err = mp_init(a)) != MP_OKAY) { | 3422 if ((err = mp_init(a)) != MP_OKAY) { |
3245 return err; | 3423 return err; |
3246 } | 3424 } |
3247 return mp_set_int(a, b); | 3425 return mp_set_int(a, b); |
3248 } | 3426 } |
3427 #endif | |
3249 | 3428 |
3250 /* End: bn_mp_init_set_int.c */ | 3429 /* End: bn_mp_init_set_int.c */ |
3251 | 3430 |
3252 /* Start: bn_mp_init_size.c */ | 3431 /* Start: bn_mp_init_size.c */ |
3253 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3432 #include <tommath.h> |
3254 * | 3433 #ifdef BN_MP_INIT_SIZE_C |
3255 * LibTomMath is a library that provides multiple-precision | 3434 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3256 * integer arithmetic as well as number theoretic functionality. | 3435 * |
3257 * | 3436 * LibTomMath is a library that provides multiple-precision |
3258 * The library was designed directly after the MPI library by | 3437 * integer arithmetic as well as number theoretic functionality. |
3259 * Michael Fromberger but has been written from scratch with | 3438 * |
3260 * additional optimizations in place. | 3439 * The library was designed directly after the MPI library by |
3261 * | 3440 * Michael Fromberger but has been written from scratch with |
3262 * The library is free for all purposes without any express | 3441 * additional optimizations in place. |
3263 * guarantee it works. | 3442 * |
3264 * | 3443 * The library is free for all purposes without any express |
3265 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3444 * guarantee it works. |
3266 */ | 3445 * |
3267 #include <tommath.h> | 3446 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3447 */ | |
3268 | 3448 |
3269 /* init an mp_init for a given size */ | 3449 /* init an mp_init for a given size */ |
3270 int mp_init_size (mp_int * a, int size) | 3450 int mp_init_size (mp_int * a, int size) |
3271 { | 3451 { |
3452 int x; | |
3453 | |
3272 /* pad size so there are always extra digits */ | 3454 /* pad size so there are always extra digits */ |
3273 size += (MP_PREC * 2) - (size % MP_PREC); | 3455 size += (MP_PREC * 2) - (size % MP_PREC); |
3274 | 3456 |
3275 /* alloc mem */ | 3457 /* alloc mem */ |
3276 a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), size); | 3458 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size); |
3277 if (a->dp == NULL) { | 3459 if (a->dp == NULL) { |
3278 return MP_MEM; | 3460 return MP_MEM; |
3279 } | 3461 } |
3462 | |
3463 /* set the members */ | |
3280 a->used = 0; | 3464 a->used = 0; |
3281 a->alloc = size; | 3465 a->alloc = size; |
3282 a->sign = MP_ZPOS; | 3466 a->sign = MP_ZPOS; |
3283 | 3467 |
3468 /* zero the digits */ | |
3469 for (x = 0; x < size; x++) { | |
3470 a->dp[x] = 0; | |
3471 } | |
3472 | |
3284 return MP_OKAY; | 3473 return MP_OKAY; |
3285 } | 3474 } |
3475 #endif | |
3286 | 3476 |
3287 /* End: bn_mp_init_size.c */ | 3477 /* End: bn_mp_init_size.c */ |
3288 | 3478 |
3289 /* Start: bn_mp_invmod.c */ | 3479 /* Start: bn_mp_invmod.c */ |
3290 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3480 #include <tommath.h> |
3291 * | 3481 #ifdef BN_MP_INVMOD_C |
3292 * LibTomMath is a library that provides multiple-precision | 3482 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3293 * integer arithmetic as well as number theoretic functionality. | 3483 * |
3294 * | 3484 * LibTomMath is a library that provides multiple-precision |
3295 * The library was designed directly after the MPI library by | 3485 * integer arithmetic as well as number theoretic functionality. |
3296 * Michael Fromberger but has been written from scratch with | 3486 * |
3297 * additional optimizations in place. | 3487 * The library was designed directly after the MPI library by |
3298 * | 3488 * Michael Fromberger but has been written from scratch with |
3299 * The library is free for all purposes without any express | 3489 * additional optimizations in place. |
3300 * guarantee it works. | 3490 * |
3301 * | 3491 * The library is free for all purposes without any express |
3302 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3492 * guarantee it works. |
3303 */ | 3493 * |
3304 #include <tommath.h> | 3494 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3495 */ | |
3305 | 3496 |
3306 /* hac 14.61, pp608 */ | 3497 /* hac 14.61, pp608 */ |
3307 int mp_invmod (mp_int * a, mp_int * b, mp_int * c) | 3498 int mp_invmod (mp_int * a, mp_int * b, mp_int * c) |
3308 { | 3499 { |
3309 mp_int x, y, u, v, A, B, C, D; | |
3310 int res; | |
3311 | |
3312 /* b cannot be negative */ | 3500 /* b cannot be negative */ |
3313 if (b->sign == MP_NEG || mp_iszero(b) == 1) { | 3501 if (b->sign == MP_NEG || mp_iszero(b) == 1) { |
3314 return MP_VAL; | 3502 return MP_VAL; |
3315 } | 3503 } |
3316 | 3504 |
3505 #ifdef BN_FAST_MP_INVMOD_C | |
3317 /* if the modulus is odd we can use a faster routine instead */ | 3506 /* if the modulus is odd we can use a faster routine instead */ |
3318 if (mp_isodd (b) == 1) { | 3507 if (mp_isodd (b) == 1) { |
3319 return fast_mp_invmod (a, b, c); | 3508 return fast_mp_invmod (a, b, c); |
3320 } | 3509 } |
3321 | 3510 #endif |
3511 | |
3512 #ifdef BN_MP_INVMOD_SLOW_C | |
3513 return mp_invmod_slow(a, b, c); | |
3514 #endif | |
3515 | |
3516 return MP_VAL; | |
3517 } | |
3518 #endif | |
3519 | |
3520 /* End: bn_mp_invmod.c */ | |
3521 | |
3522 /* Start: bn_mp_invmod_slow.c */ | |
3523 #include <tommath.h> | |
3524 #ifdef BN_MP_INVMOD_SLOW_C | |
3525 /* LibTomMath, multiple-precision integer library -- Tom St Denis | |
3526 * | |
3527 * LibTomMath is a library that provides multiple-precision | |
3528 * integer arithmetic as well as number theoretic functionality. | |
3529 * | |
3530 * The library was designed directly after the MPI library by | |
3531 * Michael Fromberger but has been written from scratch with | |
3532 * additional optimizations in place. | |
3533 * | |
3534 * The library is free for all purposes without any express | |
3535 * guarantee it works. | |
3536 * | |
3537 * Tom St Denis, [email protected], http://math.libtomcrypt.org | |
3538 */ | |
3539 | |
3540 /* hac 14.61, pp608 */ | |
3541 int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c) | |
3542 { | |
3543 mp_int x, y, u, v, A, B, C, D; | |
3544 int res; | |
3545 | |
3546 /* b cannot be negative */ | |
3547 if (b->sign == MP_NEG || mp_iszero(b) == 1) { | |
3548 return MP_VAL; | |
3549 } | |
3550 | |
3322 /* init temps */ | 3551 /* init temps */ |
3323 if ((res = mp_init_multi(&x, &y, &u, &v, | 3552 if ((res = mp_init_multi(&x, &y, &u, &v, |
3324 &A, &B, &C, &D, NULL)) != MP_OKAY) { | 3553 &A, &B, &C, &D, NULL)) != MP_OKAY) { |
3325 return res; | 3554 return res; |
3326 } | 3555 } |
3459 mp_exch (&C, c); | 3688 mp_exch (&C, c); |
3460 res = MP_OKAY; | 3689 res = MP_OKAY; |
3461 __ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); | 3690 __ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); |
3462 return res; | 3691 return res; |
3463 } | 3692 } |
3464 | 3693 #endif |
3465 /* End: bn_mp_invmod.c */ | 3694 |
3695 /* End: bn_mp_invmod_slow.c */ | |
3466 | 3696 |
3467 /* Start: bn_mp_is_square.c */ | 3697 /* Start: bn_mp_is_square.c */ |
3468 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3698 #include <tommath.h> |
3469 * | 3699 #ifdef BN_MP_IS_SQUARE_C |
3470 * LibTomMath is a library that provides multiple-precision | 3700 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3471 * integer arithmetic as well as number theoretic functionality. | 3701 * |
3472 * | 3702 * LibTomMath is a library that provides multiple-precision |
3473 * The library was designed directly after the MPI library by | 3703 * integer arithmetic as well as number theoretic functionality. |
3474 * Michael Fromberger but has been written from scratch with | 3704 * |
3475 * additional optimizations in place. | 3705 * The library was designed directly after the MPI library by |
3476 * | 3706 * Michael Fromberger but has been written from scratch with |
3477 * The library is free for all purposes without any express | 3707 * additional optimizations in place. |
3478 * guarantee it works. | 3708 * |
3479 * | 3709 * The library is free for all purposes without any express |
3480 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3710 * guarantee it works. |
3481 */ | 3711 * |
3482 #include <tommath.h> | 3712 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3713 */ | |
3483 | 3714 |
3484 /* Check if remainders are possible squares - fast exclude non-squares */ | 3715 /* Check if remainders are possible squares - fast exclude non-squares */ |
3485 static const char rem_128[128] = { | 3716 static const char rem_128[128] = { |
3486 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, | 3717 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, |
3487 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, | 3718 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, |
3534 } | 3765 } |
3535 if (rem_105[c] == 1) { | 3766 if (rem_105[c] == 1) { |
3536 return MP_OKAY; | 3767 return MP_OKAY; |
3537 } | 3768 } |
3538 | 3769 |
3539 /* product of primes less than 2^31 */ | 3770 |
3540 if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) { | 3771 if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) { |
3541 return res; | 3772 return res; |
3542 } | 3773 } |
3543 if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) { | 3774 if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) { |
3544 goto ERR; | 3775 goto ERR; |
3566 | 3797 |
3567 *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO; | 3798 *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO; |
3568 ERR:mp_clear(&t); | 3799 ERR:mp_clear(&t); |
3569 return res; | 3800 return res; |
3570 } | 3801 } |
3802 #endif | |
3571 | 3803 |
3572 /* End: bn_mp_is_square.c */ | 3804 /* End: bn_mp_is_square.c */ |
3573 | 3805 |
3574 /* Start: bn_mp_jacobi.c */ | 3806 /* Start: bn_mp_jacobi.c */ |
3575 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3807 #include <tommath.h> |
3576 * | 3808 #ifdef BN_MP_JACOBI_C |
3577 * LibTomMath is a library that provides multiple-precision | 3809 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3578 * integer arithmetic as well as number theoretic functionality. | 3810 * |
3579 * | 3811 * LibTomMath is a library that provides multiple-precision |
3580 * The library was designed directly after the MPI library by | 3812 * integer arithmetic as well as number theoretic functionality. |
3581 * Michael Fromberger but has been written from scratch with | 3813 * |
3582 * additional optimizations in place. | 3814 * The library was designed directly after the MPI library by |
3583 * | 3815 * Michael Fromberger but has been written from scratch with |
3584 * The library is free for all purposes without any express | 3816 * additional optimizations in place. |
3585 * guarantee it works. | 3817 * |
3586 * | 3818 * The library is free for all purposes without any express |
3587 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3819 * guarantee it works. |
3588 */ | 3820 * |
3589 #include <tommath.h> | 3821 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3822 */ | |
3590 | 3823 |
3591 /* computes the jacobi c = (a | n) (or Legendre if n is prime) | 3824 /* computes the jacobi c = (a | n) (or Legendre if n is prime) |
3592 * HAC pp. 73 Algorithm 2.149 | 3825 * HAC pp. 73 Algorithm 2.149 |
3593 */ | 3826 */ |
3594 int mp_jacobi (mp_int * a, mp_int * p, int *c) | 3827 int mp_jacobi (mp_int * a, mp_int * p, int *c) |
3669 res = MP_OKAY; | 3902 res = MP_OKAY; |
3670 __P1:mp_clear (&p1); | 3903 __P1:mp_clear (&p1); |
3671 __A1:mp_clear (&a1); | 3904 __A1:mp_clear (&a1); |
3672 return res; | 3905 return res; |
3673 } | 3906 } |
3907 #endif | |
3674 | 3908 |
3675 /* End: bn_mp_jacobi.c */ | 3909 /* End: bn_mp_jacobi.c */ |
3676 | 3910 |
3677 /* Start: bn_mp_karatsuba_mul.c */ | 3911 /* Start: bn_mp_karatsuba_mul.c */ |
3678 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 3912 #include <tommath.h> |
3679 * | 3913 #ifdef BN_MP_KARATSUBA_MUL_C |
3680 * LibTomMath is a library that provides multiple-precision | 3914 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3681 * integer arithmetic as well as number theoretic functionality. | 3915 * |
3682 * | 3916 * LibTomMath is a library that provides multiple-precision |
3683 * The library was designed directly after the MPI library by | 3917 * integer arithmetic as well as number theoretic functionality. |
3684 * Michael Fromberger but has been written from scratch with | 3918 * |
3685 * additional optimizations in place. | 3919 * The library was designed directly after the MPI library by |
3686 * | 3920 * Michael Fromberger but has been written from scratch with |
3687 * The library is free for all purposes without any express | 3921 * additional optimizations in place. |
3688 * guarantee it works. | 3922 * |
3689 * | 3923 * The library is free for all purposes without any express |
3690 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 3924 * guarantee it works. |
3691 */ | 3925 * |
3692 #include <tommath.h> | 3926 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
3927 */ | |
3693 | 3928 |
3694 /* c = |a| * |b| using Karatsuba Multiplication using | 3929 /* c = |a| * |b| using Karatsuba Multiplication using |
3695 * three half size multiplications | 3930 * three half size multiplications |
3696 * | 3931 * |
3697 * Let B represent the radix [e.g. 2**DIGIT_BIT] and | 3932 * Let B represent the radix [e.g. 2**DIGIT_BIT] and |
3751 goto T1; | 3986 goto T1; |
3752 if (mp_init_size (&x1y1, B * 2) != MP_OKAY) | 3987 if (mp_init_size (&x1y1, B * 2) != MP_OKAY) |
3753 goto X0Y0; | 3988 goto X0Y0; |
3754 | 3989 |
3755 /* now shift the digits */ | 3990 /* now shift the digits */ |
3756 x0.sign = x1.sign = a->sign; | |
3757 y0.sign = y1.sign = b->sign; | |
3758 | |
3759 x0.used = y0.used = B; | 3991 x0.used = y0.used = B; |
3760 x1.used = a->used - B; | 3992 x1.used = a->used - B; |
3761 y1.used = b->used - B; | 3993 y1.used = b->used - B; |
3762 | 3994 |
3763 { | 3995 { |
3837 X1:mp_clear (&x1); | 4069 X1:mp_clear (&x1); |
3838 X0:mp_clear (&x0); | 4070 X0:mp_clear (&x0); |
3839 ERR: | 4071 ERR: |
3840 return err; | 4072 return err; |
3841 } | 4073 } |
4074 #endif | |
3842 | 4075 |
3843 /* End: bn_mp_karatsuba_mul.c */ | 4076 /* End: bn_mp_karatsuba_mul.c */ |
3844 | 4077 |
3845 /* Start: bn_mp_karatsuba_sqr.c */ | 4078 /* Start: bn_mp_karatsuba_sqr.c */ |
3846 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4079 #include <tommath.h> |
3847 * | 4080 #ifdef BN_MP_KARATSUBA_SQR_C |
3848 * LibTomMath is a library that provides multiple-precision | 4081 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3849 * integer arithmetic as well as number theoretic functionality. | 4082 * |
3850 * | 4083 * LibTomMath is a library that provides multiple-precision |
3851 * The library was designed directly after the MPI library by | 4084 * integer arithmetic as well as number theoretic functionality. |
3852 * Michael Fromberger but has been written from scratch with | 4085 * |
3853 * additional optimizations in place. | 4086 * The library was designed directly after the MPI library by |
3854 * | 4087 * Michael Fromberger but has been written from scratch with |
3855 * The library is free for all purposes without any express | 4088 * additional optimizations in place. |
3856 * guarantee it works. | 4089 * |
3857 * | 4090 * The library is free for all purposes without any express |
3858 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4091 * guarantee it works. |
3859 */ | 4092 * |
3860 #include <tommath.h> | 4093 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4094 */ | |
3861 | 4095 |
3862 /* Karatsuba squaring, computes b = a*a using three | 4096 /* Karatsuba squaring, computes b = a*a using three |
3863 * half size squarings | 4097 * half size squarings |
3864 * | 4098 * |
3865 * See comments of mp_karatsuba_mul for details. It | 4099 * See comments of karatsuba_mul for details. It |
3866 * is essentially the same algorithm but merely | 4100 * is essentially the same algorithm but merely |
3867 * tuned to perform recursive squarings. | 4101 * tuned to perform recursive squarings. |
3868 */ | 4102 */ |
3869 int mp_karatsuba_sqr (mp_int * a, mp_int * b) | 4103 int mp_karatsuba_sqr (mp_int * a, mp_int * b) |
3870 { | 4104 { |
3956 X1:mp_clear (&x1); | 4190 X1:mp_clear (&x1); |
3957 X0:mp_clear (&x0); | 4191 X0:mp_clear (&x0); |
3958 ERR: | 4192 ERR: |
3959 return err; | 4193 return err; |
3960 } | 4194 } |
4195 #endif | |
3961 | 4196 |
3962 /* End: bn_mp_karatsuba_sqr.c */ | 4197 /* End: bn_mp_karatsuba_sqr.c */ |
3963 | 4198 |
3964 /* Start: bn_mp_lcm.c */ | 4199 /* Start: bn_mp_lcm.c */ |
3965 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4200 #include <tommath.h> |
3966 * | 4201 #ifdef BN_MP_LCM_C |
3967 * LibTomMath is a library that provides multiple-precision | 4202 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
3968 * integer arithmetic as well as number theoretic functionality. | 4203 * |
3969 * | 4204 * LibTomMath is a library that provides multiple-precision |
3970 * The library was designed directly after the MPI library by | 4205 * integer arithmetic as well as number theoretic functionality. |
3971 * Michael Fromberger but has been written from scratch with | 4206 * |
3972 * additional optimizations in place. | 4207 * The library was designed directly after the MPI library by |
3973 * | 4208 * Michael Fromberger but has been written from scratch with |
3974 * The library is free for all purposes without any express | 4209 * additional optimizations in place. |
3975 * guarantee it works. | 4210 * |
3976 * | 4211 * The library is free for all purposes without any express |
3977 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4212 * guarantee it works. |
3978 */ | 4213 * |
3979 #include <tommath.h> | 4214 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4215 */ | |
3980 | 4216 |
3981 /* computes least common multiple as |a*b|/(a, b) */ | 4217 /* computes least common multiple as |a*b|/(a, b) */ |
3982 int mp_lcm (mp_int * a, mp_int * b, mp_int * c) | 4218 int mp_lcm (mp_int * a, mp_int * b, mp_int * c) |
3983 { | 4219 { |
3984 int res; | 4220 int res; |
4014 | 4250 |
4015 __T: | 4251 __T: |
4016 mp_clear_multi (&t1, &t2, NULL); | 4252 mp_clear_multi (&t1, &t2, NULL); |
4017 return res; | 4253 return res; |
4018 } | 4254 } |
4255 #endif | |
4019 | 4256 |
4020 /* End: bn_mp_lcm.c */ | 4257 /* End: bn_mp_lcm.c */ |
4021 | 4258 |
4022 /* Start: bn_mp_lshd.c */ | 4259 /* Start: bn_mp_lshd.c */ |
4023 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4260 #include <tommath.h> |
4024 * | 4261 #ifdef BN_MP_LSHD_C |
4025 * LibTomMath is a library that provides multiple-precision | 4262 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4026 * integer arithmetic as well as number theoretic functionality. | 4263 * |
4027 * | 4264 * LibTomMath is a library that provides multiple-precision |
4028 * The library was designed directly after the MPI library by | 4265 * integer arithmetic as well as number theoretic functionality. |
4029 * Michael Fromberger but has been written from scratch with | 4266 * |
4030 * additional optimizations in place. | 4267 * The library was designed directly after the MPI library by |
4031 * | 4268 * Michael Fromberger but has been written from scratch with |
4032 * The library is free for all purposes without any express | 4269 * additional optimizations in place. |
4033 * guarantee it works. | 4270 * |
4034 * | 4271 * The library is free for all purposes without any express |
4035 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4272 * guarantee it works. |
4036 */ | 4273 * |
4037 #include <tommath.h> | 4274 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4275 */ | |
4038 | 4276 |
4039 /* shift left a certain amount of digits */ | 4277 /* shift left a certain amount of digits */ |
4040 int mp_lshd (mp_int * a, int b) | 4278 int mp_lshd (mp_int * a, int b) |
4041 { | 4279 { |
4042 int x, res; | 4280 int x, res; |
4079 *top++ = 0; | 4317 *top++ = 0; |
4080 } | 4318 } |
4081 } | 4319 } |
4082 return MP_OKAY; | 4320 return MP_OKAY; |
4083 } | 4321 } |
4322 #endif | |
4084 | 4323 |
4085 /* End: bn_mp_lshd.c */ | 4324 /* End: bn_mp_lshd.c */ |
4086 | 4325 |
4087 /* Start: bn_mp_mod.c */ | 4326 /* Start: bn_mp_mod.c */ |
4088 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4327 #include <tommath.h> |
4089 * | 4328 #ifdef BN_MP_MOD_C |
4090 * LibTomMath is a library that provides multiple-precision | 4329 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4091 * integer arithmetic as well as number theoretic functionality. | 4330 * |
4092 * | 4331 * LibTomMath is a library that provides multiple-precision |
4093 * The library was designed directly after the MPI library by | 4332 * integer arithmetic as well as number theoretic functionality. |
4094 * Michael Fromberger but has been written from scratch with | 4333 * |
4095 * additional optimizations in place. | 4334 * The library was designed directly after the MPI library by |
4096 * | 4335 * Michael Fromberger but has been written from scratch with |
4097 * The library is free for all purposes without any express | 4336 * additional optimizations in place. |
4098 * guarantee it works. | 4337 * |
4099 * | 4338 * The library is free for all purposes without any express |
4100 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4339 * guarantee it works. |
4101 */ | 4340 * |
4102 #include <tommath.h> | 4341 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4342 */ | |
4103 | 4343 |
4104 /* c = a mod b, 0 <= c < b */ | 4344 /* c = a mod b, 0 <= c < b */ |
4105 int | 4345 int |
4106 mp_mod (mp_int * a, mp_int * b, mp_int * c) | 4346 mp_mod (mp_int * a, mp_int * b, mp_int * c) |
4107 { | 4347 { |
4125 } | 4365 } |
4126 | 4366 |
4127 mp_clear (&t); | 4367 mp_clear (&t); |
4128 return res; | 4368 return res; |
4129 } | 4369 } |
4370 #endif | |
4130 | 4371 |
4131 /* End: bn_mp_mod.c */ | 4372 /* End: bn_mp_mod.c */ |
4132 | 4373 |
4133 /* Start: bn_mp_mod_2d.c */ | 4374 /* Start: bn_mp_mod_2d.c */ |
4134 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4375 #include <tommath.h> |
4135 * | 4376 #ifdef BN_MP_MOD_2D_C |
4136 * LibTomMath is a library that provides multiple-precision | 4377 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4137 * integer arithmetic as well as number theoretic functionality. | 4378 * |
4138 * | 4379 * LibTomMath is a library that provides multiple-precision |
4139 * The library was designed directly after the MPI library by | 4380 * integer arithmetic as well as number theoretic functionality. |
4140 * Michael Fromberger but has been written from scratch with | 4381 * |
4141 * additional optimizations in place. | 4382 * The library was designed directly after the MPI library by |
4142 * | 4383 * Michael Fromberger but has been written from scratch with |
4143 * The library is free for all purposes without any express | 4384 * additional optimizations in place. |
4144 * guarantee it works. | 4385 * |
4145 * | 4386 * The library is free for all purposes without any express |
4146 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4387 * guarantee it works. |
4147 */ | 4388 * |
4148 #include <tommath.h> | 4389 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4390 */ | |
4149 | 4391 |
4150 /* calc a value mod 2**b */ | 4392 /* calc a value mod 2**b */ |
4151 int | 4393 int |
4152 mp_mod_2d (mp_int * a, int b, mp_int * c) | 4394 mp_mod_2d (mp_int * a, int b, mp_int * c) |
4153 { | 4395 { |
4178 c->dp[b / DIGIT_BIT] &= | 4420 c->dp[b / DIGIT_BIT] &= |
4179 (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1)); | 4421 (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1)); |
4180 mp_clamp (c); | 4422 mp_clamp (c); |
4181 return MP_OKAY; | 4423 return MP_OKAY; |
4182 } | 4424 } |
4425 #endif | |
4183 | 4426 |
4184 /* End: bn_mp_mod_2d.c */ | 4427 /* End: bn_mp_mod_2d.c */ |
4185 | 4428 |
4186 /* Start: bn_mp_mod_d.c */ | 4429 /* Start: bn_mp_mod_d.c */ |
4187 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4430 #include <tommath.h> |
4188 * | 4431 #ifdef BN_MP_MOD_D_C |
4189 * LibTomMath is a library that provides multiple-precision | 4432 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4190 * integer arithmetic as well as number theoretic functionality. | 4433 * |
4191 * | 4434 * LibTomMath is a library that provides multiple-precision |
4192 * The library was designed directly after the MPI library by | 4435 * integer arithmetic as well as number theoretic functionality. |
4193 * Michael Fromberger but has been written from scratch with | 4436 * |
4194 * additional optimizations in place. | 4437 * The library was designed directly after the MPI library by |
4195 * | 4438 * Michael Fromberger but has been written from scratch with |
4196 * The library is free for all purposes without any express | 4439 * additional optimizations in place. |
4197 * guarantee it works. | 4440 * |
4198 * | 4441 * The library is free for all purposes without any express |
4199 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4442 * guarantee it works. |
4200 */ | 4443 * |
4201 #include <tommath.h> | 4444 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4445 */ | |
4202 | 4446 |
4203 int | 4447 int |
4204 mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) | 4448 mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) |
4205 { | 4449 { |
4206 return mp_div_d(a, b, NULL, c); | 4450 return mp_div_d(a, b, NULL, c); |
4207 } | 4451 } |
4452 #endif | |
4208 | 4453 |
4209 /* End: bn_mp_mod_d.c */ | 4454 /* End: bn_mp_mod_d.c */ |
4210 | 4455 |
4211 /* Start: bn_mp_montgomery_calc_normalization.c */ | 4456 /* Start: bn_mp_montgomery_calc_normalization.c */ |
4212 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4457 #include <tommath.h> |
4213 * | 4458 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C |
4214 * LibTomMath is a library that provides multiple-precision | 4459 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4215 * integer arithmetic as well as number theoretic functionality. | 4460 * |
4216 * | 4461 * LibTomMath is a library that provides multiple-precision |
4217 * The library was designed directly after the MPI library by | 4462 * integer arithmetic as well as number theoretic functionality. |
4218 * Michael Fromberger but has been written from scratch with | 4463 * |
4219 * additional optimizations in place. | 4464 * The library was designed directly after the MPI library by |
4220 * | 4465 * Michael Fromberger but has been written from scratch with |
4221 * The library is free for all purposes without any express | 4466 * additional optimizations in place. |
4222 * guarantee it works. | 4467 * |
4223 * | 4468 * The library is free for all purposes without any express |
4224 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4469 * guarantee it works. |
4225 */ | 4470 * |
4226 #include <tommath.h> | 4471 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4227 | 4472 */ |
4228 /* calculates a = B^n mod b for Montgomery reduction | 4473 |
4229 * Where B is the base [e.g. 2^DIGIT_BIT]. | 4474 /* |
4230 * B^n mod b is computed by first computing | |
4231 * A = B^(n-1) which doesn't require a reduction but a simple OR. | |
4232 * then C = A * B = B^n is computed by performing upto DIGIT_BIT | |
4233 * shifts with subtractions when the result is greater than b. | 4475 * shifts with subtractions when the result is greater than b. |
4234 * | 4476 * |
4235 * The method is slightly modified to shift B unconditionally upto just under | 4477 * The method is slightly modified to shift B unconditionally upto just under |
4236 * the leading bit of b. This saves alot of multiple precision shifting. | 4478 * the leading bit of b. This saves alot of multiple precision shifting. |
4237 */ | 4479 */ |
4238 int | 4480 int mp_montgomery_calc_normalization (mp_int * a, mp_int * b) |
4239 mp_montgomery_calc_normalization (mp_int * a, mp_int * b) | |
4240 { | 4481 { |
4241 int x, bits, res; | 4482 int x, bits, res; |
4242 | 4483 |
4243 /* how many bits of last digit does b use */ | 4484 /* how many bits of last digit does b use */ |
4244 bits = mp_count_bits (b) % DIGIT_BIT; | 4485 bits = mp_count_bits (b) % DIGIT_BIT; |
4245 | 4486 |
4246 /* compute A = B^(n-1) * 2^(bits-1) */ | 4487 |
4247 if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { | 4488 if (b->used > 1) { |
4248 return res; | 4489 if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { |
4249 } | 4490 return res; |
4491 } | |
4492 } else { | |
4493 mp_set(a, 1); | |
4494 bits = 1; | |
4495 } | |
4496 | |
4250 | 4497 |
4251 /* now compute C = A * B mod b */ | 4498 /* now compute C = A * B mod b */ |
4252 for (x = bits - 1; x < (int)DIGIT_BIT; x++) { | 4499 for (x = bits - 1; x < (int)DIGIT_BIT; x++) { |
4253 if ((res = mp_mul_2 (a, a)) != MP_OKAY) { | 4500 if ((res = mp_mul_2 (a, a)) != MP_OKAY) { |
4254 return res; | 4501 return res; |
4260 } | 4507 } |
4261 } | 4508 } |
4262 | 4509 |
4263 return MP_OKAY; | 4510 return MP_OKAY; |
4264 } | 4511 } |
4512 #endif | |
4265 | 4513 |
4266 /* End: bn_mp_montgomery_calc_normalization.c */ | 4514 /* End: bn_mp_montgomery_calc_normalization.c */ |
4267 | 4515 |
4268 /* Start: bn_mp_montgomery_reduce.c */ | 4516 /* Start: bn_mp_montgomery_reduce.c */ |
4269 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4517 #include <tommath.h> |
4270 * | 4518 #ifdef BN_MP_MONTGOMERY_REDUCE_C |
4271 * LibTomMath is a library that provides multiple-precision | 4519 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4272 * integer arithmetic as well as number theoretic functionality. | 4520 * |
4273 * | 4521 * LibTomMath is a library that provides multiple-precision |
4274 * The library was designed directly after the MPI library by | 4522 * integer arithmetic as well as number theoretic functionality. |
4275 * Michael Fromberger but has been written from scratch with | 4523 * |
4276 * additional optimizations in place. | 4524 * The library was designed directly after the MPI library by |
4277 * | 4525 * Michael Fromberger but has been written from scratch with |
4278 * The library is free for all purposes without any express | 4526 * additional optimizations in place. |
4279 * guarantee it works. | 4527 * |
4280 * | 4528 * The library is free for all purposes without any express |
4281 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4529 * guarantee it works. |
4282 */ | 4530 * |
4283 #include <tommath.h> | 4531 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4532 */ | |
4284 | 4533 |
4285 /* computes xR**-1 == x (mod N) via Montgomery Reduction */ | 4534 /* computes xR**-1 == x (mod N) via Montgomery Reduction */ |
4286 int | 4535 int |
4287 mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) | 4536 mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) |
4288 { | 4537 { |
4289 int ix, res, digs; | 4538 int ix, res, digs; |
4290 mp_digit mu; | 4539 mp_digit mu; |
4291 | 4540 |
4292 /* can the fast reduction [comba] method be used? | 4541 /* can the fast reduction [comba] method be used? |
4293 * | 4542 * |
4294 * Note that unlike in mp_mul you're safely allowed *less* | 4543 * Note that unlike in mul you're safely allowed *less* |
4295 * than the available columns [255 per default] since carries | 4544 * than the available columns [255 per default] since carries |
4296 * are fixed up in the inner loop. | 4545 * are fixed up in the inner loop. |
4297 */ | 4546 */ |
4298 digs = n->used * 2 + 1; | 4547 digs = n->used * 2 + 1; |
4299 if ((digs < MP_WARRAY) && | 4548 if ((digs < MP_WARRAY) && |
4312 | 4561 |
4313 for (ix = 0; ix < n->used; ix++) { | 4562 for (ix = 0; ix < n->used; ix++) { |
4314 /* mu = ai * rho mod b | 4563 /* mu = ai * rho mod b |
4315 * | 4564 * |
4316 * The value of rho must be precalculated via | 4565 * The value of rho must be precalculated via |
4317 * bn_mp_montgomery_setup() such that | 4566 * montgomery_setup() such that |
4318 * it equals -1/n0 mod b this allows the | 4567 * it equals -1/n0 mod b this allows the |
4319 * following inner loop to reduce the | 4568 * following inner loop to reduce the |
4320 * input one digit at a time | 4569 * input one digit at a time |
4321 */ | 4570 */ |
4322 mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK); | 4571 mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK); |
4376 return s_mp_sub (x, n, x); | 4625 return s_mp_sub (x, n, x); |
4377 } | 4626 } |
4378 | 4627 |
4379 return MP_OKAY; | 4628 return MP_OKAY; |
4380 } | 4629 } |
4630 #endif | |
4381 | 4631 |
4382 /* End: bn_mp_montgomery_reduce.c */ | 4632 /* End: bn_mp_montgomery_reduce.c */ |
4383 | 4633 |
4384 /* Start: bn_mp_montgomery_setup.c */ | 4634 /* Start: bn_mp_montgomery_setup.c */ |
4385 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4635 #include <tommath.h> |
4386 * | 4636 #ifdef BN_MP_MONTGOMERY_SETUP_C |
4387 * LibTomMath is a library that provides multiple-precision | 4637 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4388 * integer arithmetic as well as number theoretic functionality. | 4638 * |
4389 * | 4639 * LibTomMath is a library that provides multiple-precision |
4390 * The library was designed directly after the MPI library by | 4640 * integer arithmetic as well as number theoretic functionality. |
4391 * Michael Fromberger but has been written from scratch with | 4641 * |
4392 * additional optimizations in place. | 4642 * The library was designed directly after the MPI library by |
4393 * | 4643 * Michael Fromberger but has been written from scratch with |
4394 * The library is free for all purposes without any express | 4644 * additional optimizations in place. |
4395 * guarantee it works. | 4645 * |
4396 * | 4646 * The library is free for all purposes without any express |
4397 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4647 * guarantee it works. |
4398 */ | 4648 * |
4399 #include <tommath.h> | 4649 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4650 */ | |
4400 | 4651 |
4401 /* setups the montgomery reduction stuff */ | 4652 /* setups the montgomery reduction stuff */ |
4402 int | 4653 int |
4403 mp_montgomery_setup (mp_int * n, mp_digit * rho) | 4654 mp_montgomery_setup (mp_int * n, mp_digit * rho) |
4404 { | 4655 { |
4429 #ifdef MP_64BIT | 4680 #ifdef MP_64BIT |
4430 x *= 2 - b * x; /* here x*a==1 mod 2**64 */ | 4681 x *= 2 - b * x; /* here x*a==1 mod 2**64 */ |
4431 #endif | 4682 #endif |
4432 | 4683 |
4433 /* rho = -1/m mod b */ | 4684 /* rho = -1/m mod b */ |
4434 *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK; | 4685 *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; |
4435 | 4686 |
4436 return MP_OKAY; | 4687 return MP_OKAY; |
4437 } | 4688 } |
4689 #endif | |
4438 | 4690 |
4439 /* End: bn_mp_montgomery_setup.c */ | 4691 /* End: bn_mp_montgomery_setup.c */ |
4440 | 4692 |
4441 /* Start: bn_mp_mul.c */ | 4693 /* Start: bn_mp_mul.c */ |
4442 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4694 #include <tommath.h> |
4443 * | 4695 #ifdef BN_MP_MUL_C |
4444 * LibTomMath is a library that provides multiple-precision | 4696 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4445 * integer arithmetic as well as number theoretic functionality. | 4697 * |
4446 * | 4698 * LibTomMath is a library that provides multiple-precision |
4447 * The library was designed directly after the MPI library by | 4699 * integer arithmetic as well as number theoretic functionality. |
4448 * Michael Fromberger but has been written from scratch with | 4700 * |
4449 * additional optimizations in place. | 4701 * The library was designed directly after the MPI library by |
4450 * | 4702 * Michael Fromberger but has been written from scratch with |
4451 * The library is free for all purposes without any express | 4703 * additional optimizations in place. |
4452 * guarantee it works. | 4704 * |
4453 * | 4705 * The library is free for all purposes without any express |
4454 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4706 * guarantee it works. |
4455 */ | 4707 * |
4456 #include <tommath.h> | 4708 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4709 */ | |
4457 | 4710 |
4458 /* high level multiplication (handles sign) */ | 4711 /* high level multiplication (handles sign) */ |
4459 int mp_mul (mp_int * a, mp_int * b, mp_int * c) | 4712 int mp_mul (mp_int * a, mp_int * b, mp_int * c) |
4460 { | 4713 { |
4461 int res, neg; | 4714 int res, neg; |
4462 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; | 4715 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; |
4463 | 4716 |
4464 /* use Toom-Cook? */ | 4717 /* use Toom-Cook? */ |
4718 #ifdef BN_MP_TOOM_MUL_C | |
4465 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) { | 4719 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) { |
4466 res = mp_toom_mul(a, b, c); | 4720 res = mp_toom_mul(a, b, c); |
4721 } else | |
4722 #endif | |
4723 #ifdef BN_MP_KARATSUBA_MUL_C | |
4467 /* use Karatsuba? */ | 4724 /* use Karatsuba? */ |
4468 } else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) { | 4725 if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) { |
4469 res = mp_karatsuba_mul (a, b, c); | 4726 res = mp_karatsuba_mul (a, b, c); |
4470 } else { | 4727 } else |
4728 #endif | |
4729 { | |
4471 /* can we use the fast multiplier? | 4730 /* can we use the fast multiplier? |
4472 * | 4731 * |
4473 * The fast multiplier can be used if the output will | 4732 * The fast multiplier can be used if the output will |
4474 * have less than MP_WARRAY digits and the number of | 4733 * have less than MP_WARRAY digits and the number of |
4475 * digits won't affect carry propagation | 4734 * digits won't affect carry propagation |
4476 */ | 4735 */ |
4477 int digs = a->used + b->used + 1; | 4736 int digs = a->used + b->used + 1; |
4478 | 4737 |
4738 #ifdef BN_FAST_S_MP_MUL_DIGS_C | |
4479 if ((digs < MP_WARRAY) && | 4739 if ((digs < MP_WARRAY) && |
4480 MIN(a->used, b->used) <= | 4740 MIN(a->used, b->used) <= |
4481 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { | 4741 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { |
4482 res = fast_s_mp_mul_digs (a, b, c, digs); | 4742 res = fast_s_mp_mul_digs (a, b, c, digs); |
4483 } else { | 4743 } else |
4484 res = s_mp_mul (a, b, c); | 4744 #endif |
4485 } | 4745 #ifdef BN_S_MP_MUL_DIGS_C |
4486 } | 4746 res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */ |
4487 c->sign = neg; | 4747 #else |
4748 res = MP_VAL; | |
4749 #endif | |
4750 | |
4751 } | |
4752 c->sign = (c->used > 0) ? neg : MP_ZPOS; | |
4488 return res; | 4753 return res; |
4489 } | 4754 } |
4755 #endif | |
4490 | 4756 |
4491 /* End: bn_mp_mul.c */ | 4757 /* End: bn_mp_mul.c */ |
4492 | 4758 |
4493 /* Start: bn_mp_mul_2.c */ | 4759 /* Start: bn_mp_mul_2.c */ |
4494 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4760 #include <tommath.h> |
4495 * | 4761 #ifdef BN_MP_MUL_2_C |
4496 * LibTomMath is a library that provides multiple-precision | 4762 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4497 * integer arithmetic as well as number theoretic functionality. | 4763 * |
4498 * | 4764 * LibTomMath is a library that provides multiple-precision |
4499 * The library was designed directly after the MPI library by | 4765 * integer arithmetic as well as number theoretic functionality. |
4500 * Michael Fromberger but has been written from scratch with | 4766 * |
4501 * additional optimizations in place. | 4767 * The library was designed directly after the MPI library by |
4502 * | 4768 * Michael Fromberger but has been written from scratch with |
4503 * The library is free for all purposes without any express | 4769 * additional optimizations in place. |
4504 * guarantee it works. | 4770 * |
4505 * | 4771 * The library is free for all purposes without any express |
4506 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4772 * guarantee it works. |
4507 */ | 4773 * |
4508 #include <tommath.h> | 4774 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4775 */ | |
4509 | 4776 |
4510 /* b = a*2 */ | 4777 /* b = a*2 */ |
4511 int mp_mul_2(mp_int * a, mp_int * b) | 4778 int mp_mul_2(mp_int * a, mp_int * b) |
4512 { | 4779 { |
4513 int x, res, oldused; | 4780 int x, res, oldused; |
4565 } | 4832 } |
4566 } | 4833 } |
4567 b->sign = a->sign; | 4834 b->sign = a->sign; |
4568 return MP_OKAY; | 4835 return MP_OKAY; |
4569 } | 4836 } |
4837 #endif | |
4570 | 4838 |
4571 /* End: bn_mp_mul_2.c */ | 4839 /* End: bn_mp_mul_2.c */ |
4572 | 4840 |
4573 /* Start: bn_mp_mul_2d.c */ | 4841 /* Start: bn_mp_mul_2d.c */ |
4574 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4842 #include <tommath.h> |
4575 * | 4843 #ifdef BN_MP_MUL_2D_C |
4576 * LibTomMath is a library that provides multiple-precision | 4844 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4577 * integer arithmetic as well as number theoretic functionality. | 4845 * |
4578 * | 4846 * LibTomMath is a library that provides multiple-precision |
4579 * The library was designed directly after the MPI library by | 4847 * integer arithmetic as well as number theoretic functionality. |
4580 * Michael Fromberger but has been written from scratch with | 4848 * |
4581 * additional optimizations in place. | 4849 * The library was designed directly after the MPI library by |
4582 * | 4850 * Michael Fromberger but has been written from scratch with |
4583 * The library is free for all purposes without any express | 4851 * additional optimizations in place. |
4584 * guarantee it works. | 4852 * |
4585 * | 4853 * The library is free for all purposes without any express |
4586 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4854 * guarantee it works. |
4587 */ | 4855 * |
4588 #include <tommath.h> | 4856 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4857 */ | |
4589 | 4858 |
4590 /* shift left by a certain bit count */ | 4859 /* shift left by a certain bit count */ |
4591 int mp_mul_2d (mp_int * a, int b, mp_int * c) | 4860 int mp_mul_2d (mp_int * a, int b, mp_int * c) |
4592 { | 4861 { |
4593 mp_digit d; | 4862 mp_digit d; |
4648 } | 4917 } |
4649 } | 4918 } |
4650 mp_clamp (c); | 4919 mp_clamp (c); |
4651 return MP_OKAY; | 4920 return MP_OKAY; |
4652 } | 4921 } |
4922 #endif | |
4653 | 4923 |
4654 /* End: bn_mp_mul_2d.c */ | 4924 /* End: bn_mp_mul_2d.c */ |
4655 | 4925 |
4656 /* Start: bn_mp_mul_d.c */ | 4926 /* Start: bn_mp_mul_d.c */ |
4657 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 4927 #include <tommath.h> |
4658 * | 4928 #ifdef BN_MP_MUL_D_C |
4659 * LibTomMath is a library that provides multiple-precision | 4929 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4660 * integer arithmetic as well as number theoretic functionality. | 4930 * |
4661 * | 4931 * LibTomMath is a library that provides multiple-precision |
4662 * The library was designed directly after the MPI library by | 4932 * integer arithmetic as well as number theoretic functionality. |
4663 * Michael Fromberger but has been written from scratch with | 4933 * |
4664 * additional optimizations in place. | 4934 * The library was designed directly after the MPI library by |
4665 * | 4935 * Michael Fromberger but has been written from scratch with |
4666 * The library is free for all purposes without any express | 4936 * additional optimizations in place. |
4667 * guarantee it works. | 4937 * |
4668 * | 4938 * The library is free for all purposes without any express |
4669 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 4939 * guarantee it works. |
4670 */ | 4940 * |
4671 #include <tommath.h> | 4941 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
4942 */ | |
4672 | 4943 |
4673 /* multiply by a digit */ | 4944 /* multiply by a digit */ |
4674 int | 4945 int |
4675 mp_mul_d (mp_int * a, mp_digit b, mp_int * c) | 4946 mp_mul_d (mp_int * a, mp_digit b, mp_int * c) |
4676 { | 4947 { |
4724 c->used = a->used + 1; | 4995 c->used = a->used + 1; |
4725 mp_clamp(c); | 4996 mp_clamp(c); |
4726 | 4997 |
4727 return MP_OKAY; | 4998 return MP_OKAY; |
4728 } | 4999 } |
5000 #endif | |
4729 | 5001 |
4730 /* End: bn_mp_mul_d.c */ | 5002 /* End: bn_mp_mul_d.c */ |
4731 | 5003 |
4732 /* Start: bn_mp_mulmod.c */ | 5004 /* Start: bn_mp_mulmod.c */ |
4733 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5005 #include <tommath.h> |
4734 * | 5006 #ifdef BN_MP_MULMOD_C |
4735 * LibTomMath is a library that provides multiple-precision | 5007 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4736 * integer arithmetic as well as number theoretic functionality. | 5008 * |
4737 * | 5009 * LibTomMath is a library that provides multiple-precision |
4738 * The library was designed directly after the MPI library by | 5010 * integer arithmetic as well as number theoretic functionality. |
4739 * Michael Fromberger but has been written from scratch with | 5011 * |
4740 * additional optimizations in place. | 5012 * The library was designed directly after the MPI library by |
4741 * | 5013 * Michael Fromberger but has been written from scratch with |
4742 * The library is free for all purposes without any express | 5014 * additional optimizations in place. |
4743 * guarantee it works. | 5015 * |
4744 * | 5016 * The library is free for all purposes without any express |
4745 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5017 * guarantee it works. |
4746 */ | 5018 * |
4747 #include <tommath.h> | 5019 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5020 */ | |
4748 | 5021 |
4749 /* d = a * b (mod c) */ | 5022 /* d = a * b (mod c) */ |
4750 int | 5023 int |
4751 mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) | 5024 mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) |
4752 { | 5025 { |
4763 } | 5036 } |
4764 res = mp_mod (&t, c, d); | 5037 res = mp_mod (&t, c, d); |
4765 mp_clear (&t); | 5038 mp_clear (&t); |
4766 return res; | 5039 return res; |
4767 } | 5040 } |
5041 #endif | |
4768 | 5042 |
4769 /* End: bn_mp_mulmod.c */ | 5043 /* End: bn_mp_mulmod.c */ |
4770 | 5044 |
4771 /* Start: bn_mp_n_root.c */ | 5045 /* Start: bn_mp_n_root.c */ |
4772 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5046 #include <tommath.h> |
4773 * | 5047 #ifdef BN_MP_N_ROOT_C |
4774 * LibTomMath is a library that provides multiple-precision | 5048 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4775 * integer arithmetic as well as number theoretic functionality. | 5049 * |
4776 * | 5050 * LibTomMath is a library that provides multiple-precision |
4777 * The library was designed directly after the MPI library by | 5051 * integer arithmetic as well as number theoretic functionality. |
4778 * Michael Fromberger but has been written from scratch with | 5052 * |
4779 * additional optimizations in place. | 5053 * The library was designed directly after the MPI library by |
4780 * | 5054 * Michael Fromberger but has been written from scratch with |
4781 * The library is free for all purposes without any express | 5055 * additional optimizations in place. |
4782 * guarantee it works. | 5056 * |
4783 * | 5057 * The library is free for all purposes without any express |
4784 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5058 * guarantee it works. |
4785 */ | 5059 * |
4786 #include <tommath.h> | 5060 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5061 */ | |
4787 | 5062 |
4788 /* find the n'th root of an integer | 5063 /* find the n'th root of an integer |
4789 * | 5064 * |
4790 * Result found such that (c)**b <= a and (c+1)**b > a | 5065 * Result found such that (c)**b <= a and (c+1)**b > a |
4791 * | 5066 * |
4893 __T3:mp_clear (&t3); | 5168 __T3:mp_clear (&t3); |
4894 __T2:mp_clear (&t2); | 5169 __T2:mp_clear (&t2); |
4895 __T1:mp_clear (&t1); | 5170 __T1:mp_clear (&t1); |
4896 return res; | 5171 return res; |
4897 } | 5172 } |
5173 #endif | |
4898 | 5174 |
4899 /* End: bn_mp_n_root.c */ | 5175 /* End: bn_mp_n_root.c */ |
4900 | 5176 |
4901 /* Start: bn_mp_neg.c */ | 5177 /* Start: bn_mp_neg.c */ |
4902 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5178 #include <tommath.h> |
4903 * | 5179 #ifdef BN_MP_NEG_C |
4904 * LibTomMath is a library that provides multiple-precision | 5180 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4905 * integer arithmetic as well as number theoretic functionality. | 5181 * |
4906 * | 5182 * LibTomMath is a library that provides multiple-precision |
4907 * The library was designed directly after the MPI library by | 5183 * integer arithmetic as well as number theoretic functionality. |
4908 * Michael Fromberger but has been written from scratch with | 5184 * |
4909 * additional optimizations in place. | 5185 * The library was designed directly after the MPI library by |
4910 * | 5186 * Michael Fromberger but has been written from scratch with |
4911 * The library is free for all purposes without any express | 5187 * additional optimizations in place. |
4912 * guarantee it works. | 5188 * |
4913 * | 5189 * The library is free for all purposes without any express |
4914 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5190 * guarantee it works. |
4915 */ | 5191 * |
4916 #include <tommath.h> | 5192 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5193 */ | |
4917 | 5194 |
4918 /* b = -a */ | 5195 /* b = -a */ |
4919 int mp_neg (mp_int * a, mp_int * b) | 5196 int mp_neg (mp_int * a, mp_int * b) |
4920 { | 5197 { |
4921 int res; | 5198 int res; |
4925 if (mp_iszero(b) != MP_YES) { | 5202 if (mp_iszero(b) != MP_YES) { |
4926 b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; | 5203 b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; |
4927 } | 5204 } |
4928 return MP_OKAY; | 5205 return MP_OKAY; |
4929 } | 5206 } |
5207 #endif | |
4930 | 5208 |
4931 /* End: bn_mp_neg.c */ | 5209 /* End: bn_mp_neg.c */ |
4932 | 5210 |
4933 /* Start: bn_mp_or.c */ | 5211 /* Start: bn_mp_or.c */ |
4934 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5212 #include <tommath.h> |
4935 * | 5213 #ifdef BN_MP_OR_C |
4936 * LibTomMath is a library that provides multiple-precision | 5214 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4937 * integer arithmetic as well as number theoretic functionality. | 5215 * |
4938 * | 5216 * LibTomMath is a library that provides multiple-precision |
4939 * The library was designed directly after the MPI library by | 5217 * integer arithmetic as well as number theoretic functionality. |
4940 * Michael Fromberger but has been written from scratch with | 5218 * |
4941 * additional optimizations in place. | 5219 * The library was designed directly after the MPI library by |
4942 * | 5220 * Michael Fromberger but has been written from scratch with |
4943 * The library is free for all purposes without any express | 5221 * additional optimizations in place. |
4944 * guarantee it works. | 5222 * |
4945 * | 5223 * The library is free for all purposes without any express |
4946 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5224 * guarantee it works. |
4947 */ | 5225 * |
4948 #include <tommath.h> | 5226 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5227 */ | |
4949 | 5228 |
4950 /* OR two ints together */ | 5229 /* OR two ints together */ |
4951 int mp_or (mp_int * a, mp_int * b, mp_int * c) | 5230 int mp_or (mp_int * a, mp_int * b, mp_int * c) |
4952 { | 5231 { |
4953 int res, ix, px; | 5232 int res, ix, px; |
4973 mp_clamp (&t); | 5252 mp_clamp (&t); |
4974 mp_exch (c, &t); | 5253 mp_exch (c, &t); |
4975 mp_clear (&t); | 5254 mp_clear (&t); |
4976 return MP_OKAY; | 5255 return MP_OKAY; |
4977 } | 5256 } |
5257 #endif | |
4978 | 5258 |
4979 /* End: bn_mp_or.c */ | 5259 /* End: bn_mp_or.c */ |
4980 | 5260 |
4981 /* Start: bn_mp_prime_fermat.c */ | 5261 /* Start: bn_mp_prime_fermat.c */ |
4982 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5262 #include <tommath.h> |
4983 * | 5263 #ifdef BN_MP_PRIME_FERMAT_C |
4984 * LibTomMath is a library that provides multiple-precision | 5264 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
4985 * integer arithmetic as well as number theoretic functionality. | 5265 * |
4986 * | 5266 * LibTomMath is a library that provides multiple-precision |
4987 * The library was designed directly after the MPI library by | 5267 * integer arithmetic as well as number theoretic functionality. |
4988 * Michael Fromberger but has been written from scratch with | 5268 * |
4989 * additional optimizations in place. | 5269 * The library was designed directly after the MPI library by |
4990 * | 5270 * Michael Fromberger but has been written from scratch with |
4991 * The library is free for all purposes without any express | 5271 * additional optimizations in place. |
4992 * guarantee it works. | 5272 * |
4993 * | 5273 * The library is free for all purposes without any express |
4994 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5274 * guarantee it works. |
4995 */ | 5275 * |
4996 #include <tommath.h> | 5276 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5277 */ | |
4997 | 5278 |
4998 /* performs one Fermat test. | 5279 /* performs one Fermat test. |
4999 * | 5280 * |
5000 * If "a" were prime then b**a == b (mod a) since the order of | 5281 * If "a" were prime then b**a == b (mod a) since the order of |
5001 * the multiplicative sub-group would be phi(a) = a-1. That means | 5282 * the multiplicative sub-group would be phi(a) = a-1. That means |
5033 | 5314 |
5034 err = MP_OKAY; | 5315 err = MP_OKAY; |
5035 __T:mp_clear (&t); | 5316 __T:mp_clear (&t); |
5036 return err; | 5317 return err; |
5037 } | 5318 } |
5319 #endif | |
5038 | 5320 |
5039 /* End: bn_mp_prime_fermat.c */ | 5321 /* End: bn_mp_prime_fermat.c */ |
5040 | 5322 |
5041 /* Start: bn_mp_prime_is_divisible.c */ | 5323 /* Start: bn_mp_prime_is_divisible.c */ |
5042 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5324 #include <tommath.h> |
5043 * | 5325 #ifdef BN_MP_PRIME_IS_DIVISIBLE_C |
5044 * LibTomMath is a library that provides multiple-precision | 5326 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5045 * integer arithmetic as well as number theoretic functionality. | 5327 * |
5046 * | 5328 * LibTomMath is a library that provides multiple-precision |
5047 * The library was designed directly after the MPI library by | 5329 * integer arithmetic as well as number theoretic functionality. |
5048 * Michael Fromberger but has been written from scratch with | 5330 * |
5049 * additional optimizations in place. | 5331 * The library was designed directly after the MPI library by |
5050 * | 5332 * Michael Fromberger but has been written from scratch with |
5051 * The library is free for all purposes without any express | 5333 * additional optimizations in place. |
5052 * guarantee it works. | 5334 * |
5053 * | 5335 * The library is free for all purposes without any express |
5054 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5336 * guarantee it works. |
5055 */ | 5337 * |
5056 #include <tommath.h> | 5338 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5339 */ | |
5057 | 5340 |
5058 /* determines if an integers is divisible by one | 5341 /* determines if an integers is divisible by one |
5059 * of the first PRIME_SIZE primes or not | 5342 * of the first PRIME_SIZE primes or not |
5060 * | 5343 * |
5061 * sets result to 0 if not, 1 if yes | 5344 * sets result to 0 if not, 1 if yes |
5081 } | 5364 } |
5082 } | 5365 } |
5083 | 5366 |
5084 return MP_OKAY; | 5367 return MP_OKAY; |
5085 } | 5368 } |
5369 #endif | |
5086 | 5370 |
5087 /* End: bn_mp_prime_is_divisible.c */ | 5371 /* End: bn_mp_prime_is_divisible.c */ |
5088 | 5372 |
5089 /* Start: bn_mp_prime_is_prime.c */ | 5373 /* Start: bn_mp_prime_is_prime.c */ |
5090 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5374 #include <tommath.h> |
5091 * | 5375 #ifdef BN_MP_PRIME_IS_PRIME_C |
5092 * LibTomMath is a library that provides multiple-precision | 5376 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5093 * integer arithmetic as well as number theoretic functionality. | 5377 * |
5094 * | 5378 * LibTomMath is a library that provides multiple-precision |
5095 * The library was designed directly after the MPI library by | 5379 * integer arithmetic as well as number theoretic functionality. |
5096 * Michael Fromberger but has been written from scratch with | 5380 * |
5097 * additional optimizations in place. | 5381 * The library was designed directly after the MPI library by |
5098 * | 5382 * Michael Fromberger but has been written from scratch with |
5099 * The library is free for all purposes without any express | 5383 * additional optimizations in place. |
5100 * guarantee it works. | 5384 * |
5101 * | 5385 * The library is free for all purposes without any express |
5102 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5386 * guarantee it works. |
5103 */ | 5387 * |
5104 #include <tommath.h> | 5388 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5389 */ | |
5105 | 5390 |
5106 /* performs a variable number of rounds of Miller-Rabin | 5391 /* performs a variable number of rounds of Miller-Rabin |
5107 * | 5392 * |
5108 * Probability of error after t rounds is no more than | 5393 * Probability of error after t rounds is no more than |
5109 * (1/4)^t when 1 <= t <= PRIME_SIZE | 5394 |
5110 * | 5395 * |
5111 * Sets result to 1 if probably prime, 0 otherwise | 5396 * Sets result to 1 if probably prime, 0 otherwise |
5112 */ | 5397 */ |
5113 int mp_prime_is_prime (mp_int * a, int t, int *result) | 5398 int mp_prime_is_prime (mp_int * a, int t, int *result) |
5114 { | 5399 { |
5162 /* passed the test */ | 5447 /* passed the test */ |
5163 *result = MP_YES; | 5448 *result = MP_YES; |
5164 __B:mp_clear (&b); | 5449 __B:mp_clear (&b); |
5165 return err; | 5450 return err; |
5166 } | 5451 } |
5452 #endif | |
5167 | 5453 |
5168 /* End: bn_mp_prime_is_prime.c */ | 5454 /* End: bn_mp_prime_is_prime.c */ |
5169 | 5455 |
5170 /* Start: bn_mp_prime_miller_rabin.c */ | 5456 /* Start: bn_mp_prime_miller_rabin.c */ |
5171 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5457 #include <tommath.h> |
5172 * | 5458 #ifdef BN_MP_PRIME_MILLER_RABIN_C |
5173 * LibTomMath is a library that provides multiple-precision | 5459 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5174 * integer arithmetic as well as number theoretic functionality. | 5460 * |
5175 * | 5461 * LibTomMath is a library that provides multiple-precision |
5176 * The library was designed directly after the MPI library by | 5462 * integer arithmetic as well as number theoretic functionality. |
5177 * Michael Fromberger but has been written from scratch with | 5463 * |
5178 * additional optimizations in place. | 5464 * The library was designed directly after the MPI library by |
5179 * | 5465 * Michael Fromberger but has been written from scratch with |
5180 * The library is free for all purposes without any express | 5466 * additional optimizations in place. |
5181 * guarantee it works. | 5467 * |
5182 * | 5468 * The library is free for all purposes without any express |
5183 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5469 * guarantee it works. |
5184 */ | 5470 * |
5185 #include <tommath.h> | 5471 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5472 */ | |
5186 | 5473 |
5187 /* Miller-Rabin test of "a" to the base of "b" as described in | 5474 /* Miller-Rabin test of "a" to the base of "b" as described in |
5188 * HAC pp. 139 Algorithm 4.24 | 5475 * HAC pp. 139 Algorithm 4.24 |
5189 * | 5476 * |
5190 * Sets result to 0 if definitely composite or 1 if probably prime. | 5477 * Sets result to 0 if definitely composite or 1 if probably prime. |
5263 __Y:mp_clear (&y); | 5550 __Y:mp_clear (&y); |
5264 __R:mp_clear (&r); | 5551 __R:mp_clear (&r); |
5265 __N1:mp_clear (&n1); | 5552 __N1:mp_clear (&n1); |
5266 return err; | 5553 return err; |
5267 } | 5554 } |
5555 #endif | |
5268 | 5556 |
5269 /* End: bn_mp_prime_miller_rabin.c */ | 5557 /* End: bn_mp_prime_miller_rabin.c */ |
5270 | 5558 |
5271 /* Start: bn_mp_prime_next_prime.c */ | 5559 /* Start: bn_mp_prime_next_prime.c */ |
5272 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5560 #include <tommath.h> |
5273 * | 5561 #ifdef BN_MP_PRIME_NEXT_PRIME_C |
5274 * LibTomMath is a library that provides multiple-precision | 5562 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5275 * integer arithmetic as well as number theoretic functionality. | 5563 * |
5276 * | 5564 * LibTomMath is a library that provides multiple-precision |
5277 * The library was designed directly after the MPI library by | 5565 * integer arithmetic as well as number theoretic functionality. |
5278 * Michael Fromberger but has been written from scratch with | 5566 * |
5279 * additional optimizations in place. | 5567 * The library was designed directly after the MPI library by |
5280 * | 5568 * Michael Fromberger but has been written from scratch with |
5281 * The library is free for all purposes without any express | 5569 * additional optimizations in place. |
5282 * guarantee it works. | 5570 * |
5283 * | 5571 * The library is free for all purposes without any express |
5284 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5572 * guarantee it works. |
5285 */ | 5573 * |
5286 #include <tommath.h> | 5574 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5575 */ | |
5287 | 5576 |
5288 /* finds the next prime after the number "a" using "t" trials | 5577 /* finds the next prime after the number "a" using "t" trials |
5289 * of Miller-Rabin. | 5578 * of Miller-Rabin. |
5290 * | 5579 * |
5291 * bbs_style = 1 means the prime must be congruent to 3 mod 4 | 5580 * bbs_style = 1 means the prime must be congruent to 3 mod 4 |
5431 __ERR: | 5720 __ERR: |
5432 mp_clear(&b); | 5721 mp_clear(&b); |
5433 return err; | 5722 return err; |
5434 } | 5723 } |
5435 | 5724 |
5725 #endif | |
5436 | 5726 |
5437 /* End: bn_mp_prime_next_prime.c */ | 5727 /* End: bn_mp_prime_next_prime.c */ |
5438 | 5728 |
5729 /* Start: bn_mp_prime_rabin_miller_trials.c */ | |
5730 #include <tommath.h> | |
5731 #ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C | |
5732 /* LibTomMath, multiple-precision integer library -- Tom St Denis | |
5733 * | |
5734 * LibTomMath is a library that provides multiple-precision | |
5735 * integer arithmetic as well as number theoretic functionality. | |
5736 * | |
5737 * The library was designed directly after the MPI library by | |
5738 * Michael Fromberger but has been written from scratch with | |
5739 * additional optimizations in place. | |
5740 * | |
5741 * The library is free for all purposes without any express | |
5742 * guarantee it works. | |
5743 * | |
5744 * Tom St Denis, [email protected], http://math.libtomcrypt.org | |
5745 */ | |
5746 | |
5747 | |
5748 static const struct { | |
5749 int k, t; | |
5750 } sizes[] = { | |
5751 { 128, 28 }, | |
5752 { 256, 16 }, | |
5753 { 384, 10 }, | |
5754 { 512, 7 }, | |
5755 { 640, 6 }, | |
5756 { 768, 5 }, | |
5757 { 896, 4 }, | |
5758 { 1024, 4 } | |
5759 }; | |
5760 | |
5761 /* returns # of RM trials required for a given bit size */ | |
5762 int mp_prime_rabin_miller_trials(int size) | |
5763 { | |
5764 int x; | |
5765 | |
5766 for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) { | |
5767 if (sizes[x].k == size) { | |
5768 return sizes[x].t; | |
5769 } else if (sizes[x].k > size) { | |
5770 return (x == 0) ? sizes[0].t : sizes[x - 1].t; | |
5771 } | |
5772 } | |
5773 return sizes[x-1].t + 1; | |
5774 } | |
5775 | |
5776 | |
5777 #endif | |
5778 | |
5779 /* End: bn_mp_prime_rabin_miller_trials.c */ | |
5780 | |
5439 /* Start: bn_mp_prime_random_ex.c */ | 5781 /* Start: bn_mp_prime_random_ex.c */ |
5440 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5782 #include <tommath.h> |
5441 * | 5783 #ifdef BN_MP_PRIME_RANDOM_EX_C |
5442 * LibTomMath is a library that provides multiple-precision | 5784 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5443 * integer arithmetic as well as number theoretic functionality. | 5785 * |
5444 * | 5786 * LibTomMath is a library that provides multiple-precision |
5445 * The library was designed directly after the MPI library by | 5787 * integer arithmetic as well as number theoretic functionality. |
5446 * Michael Fromberger but has been written from scratch with | 5788 * |
5447 * additional optimizations in place. | 5789 * The library was designed directly after the MPI library by |
5448 * | 5790 * Michael Fromberger but has been written from scratch with |
5449 * The library is free for all purposes without any express | 5791 * additional optimizations in place. |
5450 * guarantee it works. | 5792 * |
5451 * | 5793 * The library is free for all purposes without any express |
5452 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5794 * guarantee it works. |
5453 */ | 5795 * |
5454 #include <tommath.h> | 5796 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5797 */ | |
5455 | 5798 |
5456 /* makes a truly random prime of a given size (bits), | 5799 /* makes a truly random prime of a given size (bits), |
5457 * | 5800 * |
5458 * Flags are as follows: | 5801 * Flags are as follows: |
5459 * | 5802 * |
5529 /* read it in */ | 5872 /* read it in */ |
5530 if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY) { goto error; } | 5873 if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY) { goto error; } |
5531 | 5874 |
5532 /* is it prime? */ | 5875 /* is it prime? */ |
5533 if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; } | 5876 if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; } |
5877 if (res == MP_NO) { | |
5878 continue; | |
5879 } | |
5534 | 5880 |
5535 if (flags & LTM_PRIME_SAFE) { | 5881 if (flags & LTM_PRIME_SAFE) { |
5536 /* see if (a-1)/2 is prime */ | 5882 /* see if (a-1)/2 is prime */ |
5537 if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { goto error; } | 5883 if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { goto error; } |
5538 if ((err = mp_div_2(a, a)) != MP_OKAY) { goto error; } | 5884 if ((err = mp_div_2(a, a)) != MP_OKAY) { goto error; } |
5553 XFREE(tmp); | 5899 XFREE(tmp); |
5554 return err; | 5900 return err; |
5555 } | 5901 } |
5556 | 5902 |
5557 | 5903 |
5904 #endif | |
5558 | 5905 |
5559 /* End: bn_mp_prime_random_ex.c */ | 5906 /* End: bn_mp_prime_random_ex.c */ |
5560 | 5907 |
5561 /* Start: bn_mp_radix_size.c */ | 5908 /* Start: bn_mp_radix_size.c */ |
5562 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5909 #include <tommath.h> |
5563 * | 5910 #ifdef BN_MP_RADIX_SIZE_C |
5564 * LibTomMath is a library that provides multiple-precision | 5911 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5565 * integer arithmetic as well as number theoretic functionality. | 5912 * |
5566 * | 5913 * LibTomMath is a library that provides multiple-precision |
5567 * The library was designed directly after the MPI library by | 5914 * integer arithmetic as well as number theoretic functionality. |
5568 * Michael Fromberger but has been written from scratch with | 5915 * |
5569 * additional optimizations in place. | 5916 * The library was designed directly after the MPI library by |
5570 * | 5917 * Michael Fromberger but has been written from scratch with |
5571 * The library is free for all purposes without any express | 5918 * additional optimizations in place. |
5572 * guarantee it works. | 5919 * |
5573 * | 5920 * The library is free for all purposes without any express |
5574 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5921 * guarantee it works. |
5575 */ | 5922 * |
5576 #include <tommath.h> | 5923 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5924 */ | |
5577 | 5925 |
5578 /* returns size of ASCII reprensentation */ | 5926 /* returns size of ASCII reprensentation */ |
5579 int mp_radix_size (mp_int * a, int radix, int *size) | 5927 int mp_radix_size (mp_int * a, int radix, int *size) |
5580 { | 5928 { |
5581 int res, digs; | 5929 int res, digs; |
5622 /* return digs + 1, the 1 is for the NULL byte that would be required. */ | 5970 /* return digs + 1, the 1 is for the NULL byte that would be required. */ |
5623 *size = digs + 1; | 5971 *size = digs + 1; |
5624 return MP_OKAY; | 5972 return MP_OKAY; |
5625 } | 5973 } |
5626 | 5974 |
5975 #endif | |
5627 | 5976 |
5628 /* End: bn_mp_radix_size.c */ | 5977 /* End: bn_mp_radix_size.c */ |
5629 | 5978 |
5630 /* Start: bn_mp_radix_smap.c */ | 5979 /* Start: bn_mp_radix_smap.c */ |
5631 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 5980 #include <tommath.h> |
5632 * | 5981 #ifdef BN_MP_RADIX_SMAP_C |
5633 * LibTomMath is a library that provides multiple-precision | 5982 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5634 * integer arithmetic as well as number theoretic functionality. | 5983 * |
5635 * | 5984 * LibTomMath is a library that provides multiple-precision |
5636 * The library was designed directly after the MPI library by | 5985 * integer arithmetic as well as number theoretic functionality. |
5637 * Michael Fromberger but has been written from scratch with | 5986 * |
5638 * additional optimizations in place. | 5987 * The library was designed directly after the MPI library by |
5639 * | 5988 * Michael Fromberger but has been written from scratch with |
5640 * The library is free for all purposes without any express | 5989 * additional optimizations in place. |
5641 * guarantee it works. | 5990 * |
5642 * | 5991 * The library is free for all purposes without any express |
5643 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 5992 * guarantee it works. |
5644 */ | 5993 * |
5645 #include <tommath.h> | 5994 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
5995 */ | |
5646 | 5996 |
5647 /* chars used in radix conversions */ | 5997 /* chars used in radix conversions */ |
5648 const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; | 5998 const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; |
5999 #endif | |
5649 | 6000 |
5650 /* End: bn_mp_radix_smap.c */ | 6001 /* End: bn_mp_radix_smap.c */ |
5651 | 6002 |
5652 /* Start: bn_mp_rand.c */ | 6003 /* Start: bn_mp_rand.c */ |
5653 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6004 #include <tommath.h> |
5654 * | 6005 #ifdef BN_MP_RAND_C |
5655 * LibTomMath is a library that provides multiple-precision | 6006 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5656 * integer arithmetic as well as number theoretic functionality. | 6007 * |
5657 * | 6008 * LibTomMath is a library that provides multiple-precision |
5658 * The library was designed directly after the MPI library by | 6009 * integer arithmetic as well as number theoretic functionality. |
5659 * Michael Fromberger but has been written from scratch with | 6010 * |
5660 * additional optimizations in place. | 6011 * The library was designed directly after the MPI library by |
5661 * | 6012 * Michael Fromberger but has been written from scratch with |
5662 * The library is free for all purposes without any express | 6013 * additional optimizations in place. |
5663 * guarantee it works. | 6014 * |
5664 * | 6015 * The library is free for all purposes without any express |
5665 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6016 * guarantee it works. |
5666 */ | 6017 * |
5667 #include <tommath.h> | 6018 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6019 */ | |
5668 | 6020 |
5669 /* makes a pseudo-random int of a given size */ | 6021 /* makes a pseudo-random int of a given size */ |
5670 int | 6022 int |
5671 mp_rand (mp_int * a, int digits) | 6023 mp_rand (mp_int * a, int digits) |
5672 { | 6024 { |
5697 } | 6049 } |
5698 } | 6050 } |
5699 | 6051 |
5700 return MP_OKAY; | 6052 return MP_OKAY; |
5701 } | 6053 } |
6054 #endif | |
5702 | 6055 |
5703 /* End: bn_mp_rand.c */ | 6056 /* End: bn_mp_rand.c */ |
5704 | 6057 |
5705 /* Start: bn_mp_read_radix.c */ | 6058 /* Start: bn_mp_read_radix.c */ |
5706 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6059 #include <tommath.h> |
5707 * | 6060 #ifdef BN_MP_READ_RADIX_C |
5708 * LibTomMath is a library that provides multiple-precision | 6061 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5709 * integer arithmetic as well as number theoretic functionality. | 6062 * |
5710 * | 6063 * LibTomMath is a library that provides multiple-precision |
5711 * The library was designed directly after the MPI library by | 6064 * integer arithmetic as well as number theoretic functionality. |
5712 * Michael Fromberger but has been written from scratch with | 6065 * |
5713 * additional optimizations in place. | 6066 * The library was designed directly after the MPI library by |
5714 * | 6067 * Michael Fromberger but has been written from scratch with |
5715 * The library is free for all purposes without any express | 6068 * additional optimizations in place. |
5716 * guarantee it works. | 6069 * |
5717 * | 6070 * The library is free for all purposes without any express |
5718 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6071 * guarantee it works. |
5719 */ | 6072 * |
5720 #include <tommath.h> | 6073 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6074 */ | |
5721 | 6075 |
5722 /* read a string [ASCII] in a given radix */ | 6076 /* read a string [ASCII] in a given radix */ |
5723 int mp_read_radix (mp_int * a, char *str, int radix) | 6077 int mp_read_radix (mp_int * a, char *str, int radix) |
5724 { | 6078 { |
5725 int y, res, neg; | 6079 int y, res, neg; |
5777 if (mp_iszero(a) != 1) { | 6131 if (mp_iszero(a) != 1) { |
5778 a->sign = neg; | 6132 a->sign = neg; |
5779 } | 6133 } |
5780 return MP_OKAY; | 6134 return MP_OKAY; |
5781 } | 6135 } |
6136 #endif | |
5782 | 6137 |
5783 /* End: bn_mp_read_radix.c */ | 6138 /* End: bn_mp_read_radix.c */ |
5784 | 6139 |
5785 /* Start: bn_mp_read_signed_bin.c */ | 6140 /* Start: bn_mp_read_signed_bin.c */ |
5786 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6141 #include <tommath.h> |
5787 * | 6142 #ifdef BN_MP_READ_SIGNED_BIN_C |
5788 * LibTomMath is a library that provides multiple-precision | 6143 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5789 * integer arithmetic as well as number theoretic functionality. | 6144 * |
5790 * | 6145 * LibTomMath is a library that provides multiple-precision |
5791 * The library was designed directly after the MPI library by | 6146 * integer arithmetic as well as number theoretic functionality. |
5792 * Michael Fromberger but has been written from scratch with | 6147 * |
5793 * additional optimizations in place. | 6148 * The library was designed directly after the MPI library by |
5794 * | 6149 * Michael Fromberger but has been written from scratch with |
5795 * The library is free for all purposes without any express | 6150 * additional optimizations in place. |
5796 * guarantee it works. | 6151 * |
5797 * | 6152 * The library is free for all purposes without any express |
5798 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6153 * guarantee it works. |
5799 */ | 6154 * |
5800 #include <tommath.h> | 6155 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6156 */ | |
5801 | 6157 |
5802 /* read signed bin, big endian, first byte is 0==positive or 1==negative */ | 6158 /* read signed bin, big endian, first byte is 0==positive or 1==negative */ |
5803 int | 6159 int |
5804 mp_read_signed_bin (mp_int * a, unsigned char *b, int c) | 6160 mp_read_signed_bin (mp_int * a, unsigned char *b, int c) |
5805 { | 6161 { |
5817 a->sign = MP_NEG; | 6173 a->sign = MP_NEG; |
5818 } | 6174 } |
5819 | 6175 |
5820 return MP_OKAY; | 6176 return MP_OKAY; |
5821 } | 6177 } |
6178 #endif | |
5822 | 6179 |
5823 /* End: bn_mp_read_signed_bin.c */ | 6180 /* End: bn_mp_read_signed_bin.c */ |
5824 | 6181 |
5825 /* Start: bn_mp_read_unsigned_bin.c */ | 6182 /* Start: bn_mp_read_unsigned_bin.c */ |
5826 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6183 #include <tommath.h> |
5827 * | 6184 #ifdef BN_MP_READ_UNSIGNED_BIN_C |
5828 * LibTomMath is a library that provides multiple-precision | 6185 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5829 * integer arithmetic as well as number theoretic functionality. | 6186 * |
5830 * | 6187 * LibTomMath is a library that provides multiple-precision |
5831 * The library was designed directly after the MPI library by | 6188 * integer arithmetic as well as number theoretic functionality. |
5832 * Michael Fromberger but has been written from scratch with | 6189 * |
5833 * additional optimizations in place. | 6190 * The library was designed directly after the MPI library by |
5834 * | 6191 * Michael Fromberger but has been written from scratch with |
5835 * The library is free for all purposes without any express | 6192 * additional optimizations in place. |
5836 * guarantee it works. | 6193 * |
5837 * | 6194 * The library is free for all purposes without any express |
5838 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6195 * guarantee it works. |
5839 */ | 6196 * |
5840 #include <tommath.h> | 6197 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6198 */ | |
5841 | 6199 |
5842 /* reads a unsigned char array, assumes the msb is stored first [big endian] */ | 6200 /* reads a unsigned char array, assumes the msb is stored first [big endian] */ |
5843 int | 6201 int |
5844 mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c) | 6202 mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c) |
5845 { | 6203 { |
5871 #endif | 6229 #endif |
5872 } | 6230 } |
5873 mp_clamp (a); | 6231 mp_clamp (a); |
5874 return MP_OKAY; | 6232 return MP_OKAY; |
5875 } | 6233 } |
6234 #endif | |
5876 | 6235 |
5877 /* End: bn_mp_read_unsigned_bin.c */ | 6236 /* End: bn_mp_read_unsigned_bin.c */ |
5878 | 6237 |
5879 /* Start: bn_mp_reduce.c */ | 6238 /* Start: bn_mp_reduce.c */ |
5880 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6239 #include <tommath.h> |
5881 * | 6240 #ifdef BN_MP_REDUCE_C |
5882 * LibTomMath is a library that provides multiple-precision | 6241 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5883 * integer arithmetic as well as number theoretic functionality. | 6242 * |
5884 * | 6243 * LibTomMath is a library that provides multiple-precision |
5885 * The library was designed directly after the MPI library by | 6244 * integer arithmetic as well as number theoretic functionality. |
5886 * Michael Fromberger but has been written from scratch with | 6245 * |
5887 * additional optimizations in place. | 6246 * The library was designed directly after the MPI library by |
5888 * | 6247 * Michael Fromberger but has been written from scratch with |
5889 * The library is free for all purposes without any express | 6248 * additional optimizations in place. |
5890 * guarantee it works. | 6249 * |
5891 * | 6250 * The library is free for all purposes without any express |
5892 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6251 * guarantee it works. |
5893 */ | 6252 * |
5894 #include <tommath.h> | 6253 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6254 */ | |
5895 | 6255 |
5896 /* reduces x mod m, assumes 0 < x < m**2, mu is | 6256 /* reduces x mod m, assumes 0 < x < m**2, mu is |
5897 * precomputed via mp_reduce_setup. | 6257 * precomputed via mp_reduce_setup. |
5898 * From HAC pp.604 Algorithm 14.42 | 6258 * From HAC pp.604 Algorithm 14.42 |
5899 */ | 6259 */ |
5915 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) { | 6275 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) { |
5916 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) { | 6276 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) { |
5917 goto CLEANUP; | 6277 goto CLEANUP; |
5918 } | 6278 } |
5919 } else { | 6279 } else { |
6280 #ifdef BN_S_MP_MUL_HIGH_DIGS_C | |
5920 if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { | 6281 if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { |
5921 goto CLEANUP; | 6282 goto CLEANUP; |
5922 } | 6283 } |
6284 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) | |
6285 if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { | |
6286 goto CLEANUP; | |
6287 } | |
6288 #else | |
6289 { | |
6290 res = MP_VAL; | |
6291 goto CLEANUP; | |
6292 } | |
6293 #endif | |
5923 } | 6294 } |
5924 | 6295 |
5925 /* q3 = q2 / b**(k+1) */ | 6296 /* q3 = q2 / b**(k+1) */ |
5926 mp_rshd (&q, um + 1); | 6297 mp_rshd (&q, um + 1); |
5927 | 6298 |
5959 CLEANUP: | 6330 CLEANUP: |
5960 mp_clear (&q); | 6331 mp_clear (&q); |
5961 | 6332 |
5962 return res; | 6333 return res; |
5963 } | 6334 } |
6335 #endif | |
5964 | 6336 |
5965 /* End: bn_mp_reduce.c */ | 6337 /* End: bn_mp_reduce.c */ |
5966 | 6338 |
5967 /* Start: bn_mp_reduce_2k.c */ | 6339 /* Start: bn_mp_reduce_2k.c */ |
5968 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6340 #include <tommath.h> |
5969 * | 6341 #ifdef BN_MP_REDUCE_2K_C |
5970 * LibTomMath is a library that provides multiple-precision | 6342 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
5971 * integer arithmetic as well as number theoretic functionality. | 6343 * |
5972 * | 6344 * LibTomMath is a library that provides multiple-precision |
5973 * The library was designed directly after the MPI library by | 6345 * integer arithmetic as well as number theoretic functionality. |
5974 * Michael Fromberger but has been written from scratch with | 6346 * |
5975 * additional optimizations in place. | 6347 * The library was designed directly after the MPI library by |
5976 * | 6348 * Michael Fromberger but has been written from scratch with |
5977 * The library is free for all purposes without any express | 6349 * additional optimizations in place. |
5978 * guarantee it works. | 6350 * |
5979 * | 6351 * The library is free for all purposes without any express |
5980 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6352 * guarantee it works. |
5981 */ | 6353 * |
5982 #include <tommath.h> | 6354 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6355 */ | |
5983 | 6356 |
5984 /* reduces a modulo n where n is of the form 2**p - d */ | 6357 /* reduces a modulo n where n is of the form 2**p - d */ |
5985 int | 6358 int |
5986 mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d) | 6359 mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d) |
5987 { | 6360 { |
6019 ERR: | 6392 ERR: |
6020 mp_clear(&q); | 6393 mp_clear(&q); |
6021 return res; | 6394 return res; |
6022 } | 6395 } |
6023 | 6396 |
6397 #endif | |
6024 | 6398 |
6025 /* End: bn_mp_reduce_2k.c */ | 6399 /* End: bn_mp_reduce_2k.c */ |
6026 | 6400 |
6027 /* Start: bn_mp_reduce_2k_setup.c */ | 6401 /* Start: bn_mp_reduce_2k_setup.c */ |
6028 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6402 #include <tommath.h> |
6029 * | 6403 #ifdef BN_MP_REDUCE_2K_SETUP_C |
6030 * LibTomMath is a library that provides multiple-precision | 6404 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6031 * integer arithmetic as well as number theoretic functionality. | 6405 * |
6032 * | 6406 * LibTomMath is a library that provides multiple-precision |
6033 * The library was designed directly after the MPI library by | 6407 * integer arithmetic as well as number theoretic functionality. |
6034 * Michael Fromberger but has been written from scratch with | 6408 * |
6035 * additional optimizations in place. | 6409 * The library was designed directly after the MPI library by |
6036 * | 6410 * Michael Fromberger but has been written from scratch with |
6037 * The library is free for all purposes without any express | 6411 * additional optimizations in place. |
6038 * guarantee it works. | 6412 * |
6039 * | 6413 * The library is free for all purposes without any express |
6040 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6414 * guarantee it works. |
6041 */ | 6415 * |
6042 #include <tommath.h> | 6416 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6417 */ | |
6043 | 6418 |
6044 /* determines the setup value */ | 6419 /* determines the setup value */ |
6045 int | 6420 int |
6046 mp_reduce_2k_setup(mp_int *a, mp_digit *d) | 6421 mp_reduce_2k_setup(mp_int *a, mp_digit *d) |
6047 { | 6422 { |
6065 | 6440 |
6066 *d = tmp.dp[0]; | 6441 *d = tmp.dp[0]; |
6067 mp_clear(&tmp); | 6442 mp_clear(&tmp); |
6068 return MP_OKAY; | 6443 return MP_OKAY; |
6069 } | 6444 } |
6445 #endif | |
6070 | 6446 |
6071 /* End: bn_mp_reduce_2k_setup.c */ | 6447 /* End: bn_mp_reduce_2k_setup.c */ |
6072 | 6448 |
6073 /* Start: bn_mp_reduce_is_2k.c */ | 6449 /* Start: bn_mp_reduce_is_2k.c */ |
6074 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6450 #include <tommath.h> |
6075 * | 6451 #ifdef BN_MP_REDUCE_IS_2K_C |
6076 * LibTomMath is a library that provides multiple-precision | 6452 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6077 * integer arithmetic as well as number theoretic functionality. | 6453 * |
6078 * | 6454 * LibTomMath is a library that provides multiple-precision |
6079 * The library was designed directly after the MPI library by | 6455 * integer arithmetic as well as number theoretic functionality. |
6080 * Michael Fromberger but has been written from scratch with | 6456 * |
6081 * additional optimizations in place. | 6457 * The library was designed directly after the MPI library by |
6082 * | 6458 * Michael Fromberger but has been written from scratch with |
6083 * The library is free for all purposes without any express | 6459 * additional optimizations in place. |
6084 * guarantee it works. | 6460 * |
6085 * | 6461 * The library is free for all purposes without any express |
6086 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6462 * guarantee it works. |
6087 */ | 6463 * |
6088 #include <tommath.h> | 6464 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6465 */ | |
6089 | 6466 |
6090 /* determines if mp_reduce_2k can be used */ | 6467 /* determines if mp_reduce_2k can be used */ |
6091 int mp_reduce_is_2k(mp_int *a) | 6468 int mp_reduce_is_2k(mp_int *a) |
6092 { | 6469 { |
6093 int ix, iy, iz, iw; | 6470 int ix, iy, iw; |
6471 mp_digit iz; | |
6094 | 6472 |
6095 if (a->used == 0) { | 6473 if (a->used == 0) { |
6096 return 0; | 6474 return 0; |
6097 } else if (a->used == 1) { | 6475 } else if (a->used == 1) { |
6098 return 1; | 6476 return 1; |
6105 for (ix = DIGIT_BIT; ix < iy; ix++) { | 6483 for (ix = DIGIT_BIT; ix < iy; ix++) { |
6106 if ((a->dp[iw] & iz) == 0) { | 6484 if ((a->dp[iw] & iz) == 0) { |
6107 return 0; | 6485 return 0; |
6108 } | 6486 } |
6109 iz <<= 1; | 6487 iz <<= 1; |
6110 if (iz > (int)MP_MASK) { | 6488 if (iz > (mp_digit)MP_MASK) { |
6111 ++iw; | 6489 ++iw; |
6112 iz = 1; | 6490 iz = 1; |
6113 } | 6491 } |
6114 } | 6492 } |
6115 } | 6493 } |
6116 return 1; | 6494 return 1; |
6117 } | 6495 } |
6118 | 6496 |
6497 #endif | |
6119 | 6498 |
6120 /* End: bn_mp_reduce_is_2k.c */ | 6499 /* End: bn_mp_reduce_is_2k.c */ |
6121 | 6500 |
6122 /* Start: bn_mp_reduce_setup.c */ | 6501 /* Start: bn_mp_reduce_setup.c */ |
6123 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6502 #include <tommath.h> |
6124 * | 6503 #ifdef BN_MP_REDUCE_SETUP_C |
6125 * LibTomMath is a library that provides multiple-precision | 6504 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6126 * integer arithmetic as well as number theoretic functionality. | 6505 * |
6127 * | 6506 * LibTomMath is a library that provides multiple-precision |
6128 * The library was designed directly after the MPI library by | 6507 * integer arithmetic as well as number theoretic functionality. |
6129 * Michael Fromberger but has been written from scratch with | 6508 * |
6130 * additional optimizations in place. | 6509 * The library was designed directly after the MPI library by |
6131 * | 6510 * Michael Fromberger but has been written from scratch with |
6132 * The library is free for all purposes without any express | 6511 * additional optimizations in place. |
6133 * guarantee it works. | 6512 * |
6134 * | 6513 * The library is free for all purposes without any express |
6135 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6514 * guarantee it works. |
6136 */ | 6515 * |
6137 #include <tommath.h> | 6516 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6517 */ | |
6138 | 6518 |
6139 /* pre-calculate the value required for Barrett reduction | 6519 /* pre-calculate the value required for Barrett reduction |
6140 * For a given modulus "b" it calulates the value required in "a" | 6520 * For a given modulus "b" it calulates the value required in "a" |
6141 */ | 6521 */ |
6142 int | 6522 int mp_reduce_setup (mp_int * a, mp_int * b) |
6143 mp_reduce_setup (mp_int * a, mp_int * b) | |
6144 { | 6523 { |
6145 int res; | 6524 int res; |
6146 | 6525 |
6147 if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) { | 6526 if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) { |
6148 return res; | 6527 return res; |
6149 } | 6528 } |
6150 return mp_div (a, b, a, NULL); | 6529 return mp_div (a, b, a, NULL); |
6151 } | 6530 } |
6531 #endif | |
6152 | 6532 |
6153 /* End: bn_mp_reduce_setup.c */ | 6533 /* End: bn_mp_reduce_setup.c */ |
6154 | 6534 |
6155 /* Start: bn_mp_rshd.c */ | 6535 /* Start: bn_mp_rshd.c */ |
6156 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6536 #include <tommath.h> |
6157 * | 6537 #ifdef BN_MP_RSHD_C |
6158 * LibTomMath is a library that provides multiple-precision | 6538 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6159 * integer arithmetic as well as number theoretic functionality. | 6539 * |
6160 * | 6540 * LibTomMath is a library that provides multiple-precision |
6161 * The library was designed directly after the MPI library by | 6541 * integer arithmetic as well as number theoretic functionality. |
6162 * Michael Fromberger but has been written from scratch with | 6542 * |
6163 * additional optimizations in place. | 6543 * The library was designed directly after the MPI library by |
6164 * | 6544 * Michael Fromberger but has been written from scratch with |
6165 * The library is free for all purposes without any express | 6545 * additional optimizations in place. |
6166 * guarantee it works. | 6546 * |
6167 * | 6547 * The library is free for all purposes without any express |
6168 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6548 * guarantee it works. |
6169 */ | 6549 * |
6170 #include <tommath.h> | 6550 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6551 */ | |
6171 | 6552 |
6172 /* shift right a certain amount of digits */ | 6553 /* shift right a certain amount of digits */ |
6173 void mp_rshd (mp_int * a, int b) | 6554 void mp_rshd (mp_int * a, int b) |
6174 { | 6555 { |
6175 int x; | 6556 int x; |
6217 } | 6598 } |
6218 | 6599 |
6219 /* remove excess digits */ | 6600 /* remove excess digits */ |
6220 a->used -= b; | 6601 a->used -= b; |
6221 } | 6602 } |
6603 #endif | |
6222 | 6604 |
6223 /* End: bn_mp_rshd.c */ | 6605 /* End: bn_mp_rshd.c */ |
6224 | 6606 |
6225 /* Start: bn_mp_set.c */ | 6607 /* Start: bn_mp_set.c */ |
6226 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6608 #include <tommath.h> |
6227 * | 6609 #ifdef BN_MP_SET_C |
6228 * LibTomMath is a library that provides multiple-precision | 6610 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6229 * integer arithmetic as well as number theoretic functionality. | 6611 * |
6230 * | 6612 * LibTomMath is a library that provides multiple-precision |
6231 * The library was designed directly after the MPI library by | 6613 * integer arithmetic as well as number theoretic functionality. |
6232 * Michael Fromberger but has been written from scratch with | 6614 * |
6233 * additional optimizations in place. | 6615 * The library was designed directly after the MPI library by |
6234 * | 6616 * Michael Fromberger but has been written from scratch with |
6235 * The library is free for all purposes without any express | 6617 * additional optimizations in place. |
6236 * guarantee it works. | 6618 * |
6237 * | 6619 * The library is free for all purposes without any express |
6238 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6620 * guarantee it works. |
6239 */ | 6621 * |
6240 #include <tommath.h> | 6622 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6623 */ | |
6241 | 6624 |
6242 /* set to a digit */ | 6625 /* set to a digit */ |
6243 void mp_set (mp_int * a, mp_digit b) | 6626 void mp_set (mp_int * a, mp_digit b) |
6244 { | 6627 { |
6245 mp_zero (a); | 6628 mp_zero (a); |
6246 a->dp[0] = b & MP_MASK; | 6629 a->dp[0] = b & MP_MASK; |
6247 a->used = (a->dp[0] != 0) ? 1 : 0; | 6630 a->used = (a->dp[0] != 0) ? 1 : 0; |
6248 } | 6631 } |
6632 #endif | |
6249 | 6633 |
6250 /* End: bn_mp_set.c */ | 6634 /* End: bn_mp_set.c */ |
6251 | 6635 |
6252 /* Start: bn_mp_set_int.c */ | 6636 /* Start: bn_mp_set_int.c */ |
6253 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6637 #include <tommath.h> |
6254 * | 6638 #ifdef BN_MP_SET_INT_C |
6255 * LibTomMath is a library that provides multiple-precision | 6639 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6256 * integer arithmetic as well as number theoretic functionality. | 6640 * |
6257 * | 6641 * LibTomMath is a library that provides multiple-precision |
6258 * The library was designed directly after the MPI library by | 6642 * integer arithmetic as well as number theoretic functionality. |
6259 * Michael Fromberger but has been written from scratch with | 6643 * |
6260 * additional optimizations in place. | 6644 * The library was designed directly after the MPI library by |
6261 * | 6645 * Michael Fromberger but has been written from scratch with |
6262 * The library is free for all purposes without any express | 6646 * additional optimizations in place. |
6263 * guarantee it works. | 6647 * |
6264 * | 6648 * The library is free for all purposes without any express |
6265 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6649 * guarantee it works. |
6266 */ | 6650 * |
6267 #include <tommath.h> | 6651 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6652 */ | |
6268 | 6653 |
6269 /* set a 32-bit const */ | 6654 /* set a 32-bit const */ |
6270 int mp_set_int (mp_int * a, unsigned long b) | 6655 int mp_set_int (mp_int * a, unsigned long b) |
6271 { | 6656 { |
6272 int x, res; | 6657 int x, res; |
6290 a->used += 1; | 6675 a->used += 1; |
6291 } | 6676 } |
6292 mp_clamp (a); | 6677 mp_clamp (a); |
6293 return MP_OKAY; | 6678 return MP_OKAY; |
6294 } | 6679 } |
6680 #endif | |
6295 | 6681 |
6296 /* End: bn_mp_set_int.c */ | 6682 /* End: bn_mp_set_int.c */ |
6297 | 6683 |
6298 /* Start: bn_mp_shrink.c */ | 6684 /* Start: bn_mp_shrink.c */ |
6299 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6685 #include <tommath.h> |
6300 * | 6686 #ifdef BN_MP_SHRINK_C |
6301 * LibTomMath is a library that provides multiple-precision | 6687 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6302 * integer arithmetic as well as number theoretic functionality. | 6688 * |
6303 * | 6689 * LibTomMath is a library that provides multiple-precision |
6304 * The library was designed directly after the MPI library by | 6690 * integer arithmetic as well as number theoretic functionality. |
6305 * Michael Fromberger but has been written from scratch with | 6691 * |
6306 * additional optimizations in place. | 6692 * The library was designed directly after the MPI library by |
6307 * | 6693 * Michael Fromberger but has been written from scratch with |
6308 * The library is free for all purposes without any express | 6694 * additional optimizations in place. |
6309 * guarantee it works. | 6695 * |
6310 * | 6696 * The library is free for all purposes without any express |
6311 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6697 * guarantee it works. |
6312 */ | 6698 * |
6313 #include <tommath.h> | 6699 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6700 */ | |
6314 | 6701 |
6315 /* shrink a bignum */ | 6702 /* shrink a bignum */ |
6316 int mp_shrink (mp_int * a) | 6703 int mp_shrink (mp_int * a) |
6317 { | 6704 { |
6318 mp_digit *tmp; | 6705 mp_digit *tmp; |
6323 a->dp = tmp; | 6710 a->dp = tmp; |
6324 a->alloc = a->used; | 6711 a->alloc = a->used; |
6325 } | 6712 } |
6326 return MP_OKAY; | 6713 return MP_OKAY; |
6327 } | 6714 } |
6715 #endif | |
6328 | 6716 |
6329 /* End: bn_mp_shrink.c */ | 6717 /* End: bn_mp_shrink.c */ |
6330 | 6718 |
6331 /* Start: bn_mp_signed_bin_size.c */ | 6719 /* Start: bn_mp_signed_bin_size.c */ |
6332 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6720 #include <tommath.h> |
6333 * | 6721 #ifdef BN_MP_SIGNED_BIN_SIZE_C |
6334 * LibTomMath is a library that provides multiple-precision | 6722 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6335 * integer arithmetic as well as number theoretic functionality. | 6723 * |
6336 * | 6724 * LibTomMath is a library that provides multiple-precision |
6337 * The library was designed directly after the MPI library by | 6725 * integer arithmetic as well as number theoretic functionality. |
6338 * Michael Fromberger but has been written from scratch with | 6726 * |
6339 * additional optimizations in place. | 6727 * The library was designed directly after the MPI library by |
6340 * | 6728 * Michael Fromberger but has been written from scratch with |
6341 * The library is free for all purposes without any express | 6729 * additional optimizations in place. |
6342 * guarantee it works. | 6730 * |
6343 * | 6731 * The library is free for all purposes without any express |
6344 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6732 * guarantee it works. |
6345 */ | 6733 * |
6346 #include <tommath.h> | 6734 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6735 */ | |
6347 | 6736 |
6348 /* get the size for an signed equivalent */ | 6737 /* get the size for an signed equivalent */ |
6349 int mp_signed_bin_size (mp_int * a) | 6738 int mp_signed_bin_size (mp_int * a) |
6350 { | 6739 { |
6351 return 1 + mp_unsigned_bin_size (a); | 6740 return 1 + mp_unsigned_bin_size (a); |
6352 } | 6741 } |
6742 #endif | |
6353 | 6743 |
6354 /* End: bn_mp_signed_bin_size.c */ | 6744 /* End: bn_mp_signed_bin_size.c */ |
6355 | 6745 |
6356 /* Start: bn_mp_sqr.c */ | 6746 /* Start: bn_mp_sqr.c */ |
6357 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6747 #include <tommath.h> |
6358 * | 6748 #ifdef BN_MP_SQR_C |
6359 * LibTomMath is a library that provides multiple-precision | 6749 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6360 * integer arithmetic as well as number theoretic functionality. | 6750 * |
6361 * | 6751 * LibTomMath is a library that provides multiple-precision |
6362 * The library was designed directly after the MPI library by | 6752 * integer arithmetic as well as number theoretic functionality. |
6363 * Michael Fromberger but has been written from scratch with | 6753 * |
6364 * additional optimizations in place. | 6754 * The library was designed directly after the MPI library by |
6365 * | 6755 * Michael Fromberger but has been written from scratch with |
6366 * The library is free for all purposes without any express | 6756 * additional optimizations in place. |
6367 * guarantee it works. | 6757 * |
6368 * | 6758 * The library is free for all purposes without any express |
6369 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6759 * guarantee it works. |
6370 */ | 6760 * |
6371 #include <tommath.h> | 6761 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6762 */ | |
6372 | 6763 |
6373 /* computes b = a*a */ | 6764 /* computes b = a*a */ |
6374 int | 6765 int |
6375 mp_sqr (mp_int * a, mp_int * b) | 6766 mp_sqr (mp_int * a, mp_int * b) |
6376 { | 6767 { |
6377 int res; | 6768 int res; |
6378 | 6769 |
6770 #ifdef BN_MP_TOOM_SQR_C | |
6379 /* use Toom-Cook? */ | 6771 /* use Toom-Cook? */ |
6380 if (a->used >= TOOM_SQR_CUTOFF) { | 6772 if (a->used >= TOOM_SQR_CUTOFF) { |
6381 res = mp_toom_sqr(a, b); | 6773 res = mp_toom_sqr(a, b); |
6382 /* Karatsuba? */ | 6774 /* Karatsuba? */ |
6383 } else if (a->used >= KARATSUBA_SQR_CUTOFF) { | 6775 } else |
6776 #endif | |
6777 #ifdef BN_MP_KARATSUBA_SQR_C | |
6778 if (a->used >= KARATSUBA_SQR_CUTOFF) { | |
6384 res = mp_karatsuba_sqr (a, b); | 6779 res = mp_karatsuba_sqr (a, b); |
6385 } else { | 6780 } else |
6781 #endif | |
6782 { | |
6783 #ifdef BN_FAST_S_MP_SQR_C | |
6386 /* can we use the fast comba multiplier? */ | 6784 /* can we use the fast comba multiplier? */ |
6387 if ((a->used * 2 + 1) < MP_WARRAY && | 6785 if ((a->used * 2 + 1) < MP_WARRAY && |
6388 a->used < | 6786 a->used < |
6389 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) { | 6787 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) { |
6390 res = fast_s_mp_sqr (a, b); | 6788 res = fast_s_mp_sqr (a, b); |
6391 } else { | 6789 } else |
6790 #endif | |
6791 #ifdef BN_S_MP_SQR_C | |
6392 res = s_mp_sqr (a, b); | 6792 res = s_mp_sqr (a, b); |
6393 } | 6793 #else |
6794 res = MP_VAL; | |
6795 #endif | |
6394 } | 6796 } |
6395 b->sign = MP_ZPOS; | 6797 b->sign = MP_ZPOS; |
6396 return res; | 6798 return res; |
6397 } | 6799 } |
6800 #endif | |
6398 | 6801 |
6399 /* End: bn_mp_sqr.c */ | 6802 /* End: bn_mp_sqr.c */ |
6400 | 6803 |
6401 /* Start: bn_mp_sqrmod.c */ | 6804 /* Start: bn_mp_sqrmod.c */ |
6402 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6805 #include <tommath.h> |
6403 * | 6806 #ifdef BN_MP_SQRMOD_C |
6404 * LibTomMath is a library that provides multiple-precision | 6807 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6405 * integer arithmetic as well as number theoretic functionality. | 6808 * |
6406 * | 6809 * LibTomMath is a library that provides multiple-precision |
6407 * The library was designed directly after the MPI library by | 6810 * integer arithmetic as well as number theoretic functionality. |
6408 * Michael Fromberger but has been written from scratch with | 6811 * |
6409 * additional optimizations in place. | 6812 * The library was designed directly after the MPI library by |
6410 * | 6813 * Michael Fromberger but has been written from scratch with |
6411 * The library is free for all purposes without any express | 6814 * additional optimizations in place. |
6412 * guarantee it works. | 6815 * |
6413 * | 6816 * The library is free for all purposes without any express |
6414 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6817 * guarantee it works. |
6415 */ | 6818 * |
6416 #include <tommath.h> | 6819 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6820 */ | |
6417 | 6821 |
6418 /* c = a * a (mod b) */ | 6822 /* c = a * a (mod b) */ |
6419 int | 6823 int |
6420 mp_sqrmod (mp_int * a, mp_int * b, mp_int * c) | 6824 mp_sqrmod (mp_int * a, mp_int * b, mp_int * c) |
6421 { | 6825 { |
6432 } | 6836 } |
6433 res = mp_mod (&t, b, c); | 6837 res = mp_mod (&t, b, c); |
6434 mp_clear (&t); | 6838 mp_clear (&t); |
6435 return res; | 6839 return res; |
6436 } | 6840 } |
6841 #endif | |
6437 | 6842 |
6438 /* End: bn_mp_sqrmod.c */ | 6843 /* End: bn_mp_sqrmod.c */ |
6439 | 6844 |
6440 /* Start: bn_mp_sqrt.c */ | 6845 /* Start: bn_mp_sqrt.c */ |
6441 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6846 #include <tommath.h> |
6442 * | 6847 #ifdef BN_MP_SQRT_C |
6443 * LibTomMath is a library that provides multiple-precision | 6848 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6444 * integer arithmetic as well as number theoretic functionality. | 6849 * |
6445 * | 6850 * LibTomMath is a library that provides multiple-precision |
6446 * The library was designed directly after the MPI library by | 6851 * integer arithmetic as well as number theoretic functionality. |
6447 * Michael Fromberger but has been written from scratch with | 6852 * |
6448 * additional optimizations in place. | 6853 * The library was designed directly after the MPI library by |
6449 * | 6854 * Michael Fromberger but has been written from scratch with |
6450 * The library is free for all purposes without any express | 6855 * additional optimizations in place. |
6451 * guarantee it works. | 6856 * |
6452 * | 6857 * The library is free for all purposes without any express |
6453 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6858 * guarantee it works. |
6454 */ | 6859 * |
6455 #include <tommath.h> | 6860 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6861 */ | |
6456 | 6862 |
6457 /* this function is less generic than mp_n_root, simpler and faster */ | 6863 /* this function is less generic than mp_n_root, simpler and faster */ |
6458 int mp_sqrt(mp_int *arg, mp_int *ret) | 6864 int mp_sqrt(mp_int *arg, mp_int *ret) |
6459 { | 6865 { |
6460 int res; | 6866 int res; |
6511 E1: mp_clear(&t2); | 6917 E1: mp_clear(&t2); |
6512 E2: mp_clear(&t1); | 6918 E2: mp_clear(&t1); |
6513 return res; | 6919 return res; |
6514 } | 6920 } |
6515 | 6921 |
6922 #endif | |
6516 | 6923 |
6517 /* End: bn_mp_sqrt.c */ | 6924 /* End: bn_mp_sqrt.c */ |
6518 | 6925 |
6519 /* Start: bn_mp_sub.c */ | 6926 /* Start: bn_mp_sub.c */ |
6520 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6927 #include <tommath.h> |
6521 * | 6928 #ifdef BN_MP_SUB_C |
6522 * LibTomMath is a library that provides multiple-precision | 6929 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6523 * integer arithmetic as well as number theoretic functionality. | 6930 * |
6524 * | 6931 * LibTomMath is a library that provides multiple-precision |
6525 * The library was designed directly after the MPI library by | 6932 * integer arithmetic as well as number theoretic functionality. |
6526 * Michael Fromberger but has been written from scratch with | 6933 * |
6527 * additional optimizations in place. | 6934 * The library was designed directly after the MPI library by |
6528 * | 6935 * Michael Fromberger but has been written from scratch with |
6529 * The library is free for all purposes without any express | 6936 * additional optimizations in place. |
6530 * guarantee it works. | 6937 * |
6531 * | 6938 * The library is free for all purposes without any express |
6532 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6939 * guarantee it works. |
6533 */ | 6940 * |
6534 #include <tommath.h> | 6941 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6942 */ | |
6535 | 6943 |
6536 /* high level subtraction (handles signs) */ | 6944 /* high level subtraction (handles signs) */ |
6537 int | 6945 int |
6538 mp_sub (mp_int * a, mp_int * b, mp_int * c) | 6946 mp_sub (mp_int * a, mp_int * b, mp_int * c) |
6539 { | 6947 { |
6568 } | 6976 } |
6569 } | 6977 } |
6570 return res; | 6978 return res; |
6571 } | 6979 } |
6572 | 6980 |
6981 #endif | |
6573 | 6982 |
6574 /* End: bn_mp_sub.c */ | 6983 /* End: bn_mp_sub.c */ |
6575 | 6984 |
6576 /* Start: bn_mp_sub_d.c */ | 6985 /* Start: bn_mp_sub_d.c */ |
6577 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 6986 #include <tommath.h> |
6578 * | 6987 #ifdef BN_MP_SUB_D_C |
6579 * LibTomMath is a library that provides multiple-precision | 6988 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6580 * integer arithmetic as well as number theoretic functionality. | 6989 * |
6581 * | 6990 * LibTomMath is a library that provides multiple-precision |
6582 * The library was designed directly after the MPI library by | 6991 * integer arithmetic as well as number theoretic functionality. |
6583 * Michael Fromberger but has been written from scratch with | 6992 * |
6584 * additional optimizations in place. | 6993 * The library was designed directly after the MPI library by |
6585 * | 6994 * Michael Fromberger but has been written from scratch with |
6586 * The library is free for all purposes without any express | 6995 * additional optimizations in place. |
6587 * guarantee it works. | 6996 * |
6588 * | 6997 * The library is free for all purposes without any express |
6589 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 6998 * guarantee it works. |
6590 */ | 6999 * |
6591 #include <tommath.h> | 7000 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7001 */ | |
6592 | 7002 |
6593 /* single digit subtraction */ | 7003 /* single digit subtraction */ |
6594 int | 7004 int |
6595 mp_sub_d (mp_int * a, mp_digit b, mp_int * c) | 7005 mp_sub_d (mp_int * a, mp_digit b, mp_int * c) |
6596 { | 7006 { |
6655 } | 7065 } |
6656 mp_clamp(c); | 7066 mp_clamp(c); |
6657 return MP_OKAY; | 7067 return MP_OKAY; |
6658 } | 7068 } |
6659 | 7069 |
7070 #endif | |
6660 | 7071 |
6661 /* End: bn_mp_sub_d.c */ | 7072 /* End: bn_mp_sub_d.c */ |
6662 | 7073 |
6663 /* Start: bn_mp_submod.c */ | 7074 /* Start: bn_mp_submod.c */ |
6664 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7075 #include <tommath.h> |
6665 * | 7076 #ifdef BN_MP_SUBMOD_C |
6666 * LibTomMath is a library that provides multiple-precision | 7077 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6667 * integer arithmetic as well as number theoretic functionality. | 7078 * |
6668 * | 7079 * LibTomMath is a library that provides multiple-precision |
6669 * The library was designed directly after the MPI library by | 7080 * integer arithmetic as well as number theoretic functionality. |
6670 * Michael Fromberger but has been written from scratch with | 7081 * |
6671 * additional optimizations in place. | 7082 * The library was designed directly after the MPI library by |
6672 * | 7083 * Michael Fromberger but has been written from scratch with |
6673 * The library is free for all purposes without any express | 7084 * additional optimizations in place. |
6674 * guarantee it works. | 7085 * |
6675 * | 7086 * The library is free for all purposes without any express |
6676 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7087 * guarantee it works. |
6677 */ | 7088 * |
6678 #include <tommath.h> | 7089 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7090 */ | |
6679 | 7091 |
6680 /* d = a - b (mod c) */ | 7092 /* d = a - b (mod c) */ |
6681 int | 7093 int |
6682 mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) | 7094 mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) |
6683 { | 7095 { |
6695 } | 7107 } |
6696 res = mp_mod (&t, c, d); | 7108 res = mp_mod (&t, c, d); |
6697 mp_clear (&t); | 7109 mp_clear (&t); |
6698 return res; | 7110 return res; |
6699 } | 7111 } |
7112 #endif | |
6700 | 7113 |
6701 /* End: bn_mp_submod.c */ | 7114 /* End: bn_mp_submod.c */ |
6702 | 7115 |
6703 /* Start: bn_mp_to_signed_bin.c */ | 7116 /* Start: bn_mp_to_signed_bin.c */ |
6704 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7117 #include <tommath.h> |
6705 * | 7118 #ifdef BN_MP_TO_SIGNED_BIN_C |
6706 * LibTomMath is a library that provides multiple-precision | 7119 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6707 * integer arithmetic as well as number theoretic functionality. | 7120 * |
6708 * | 7121 * LibTomMath is a library that provides multiple-precision |
6709 * The library was designed directly after the MPI library by | 7122 * integer arithmetic as well as number theoretic functionality. |
6710 * Michael Fromberger but has been written from scratch with | 7123 * |
6711 * additional optimizations in place. | 7124 * The library was designed directly after the MPI library by |
6712 * | 7125 * Michael Fromberger but has been written from scratch with |
6713 * The library is free for all purposes without any express | 7126 * additional optimizations in place. |
6714 * guarantee it works. | 7127 * |
6715 * | 7128 * The library is free for all purposes without any express |
6716 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7129 * guarantee it works. |
6717 */ | 7130 * |
6718 #include <tommath.h> | 7131 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7132 */ | |
6719 | 7133 |
6720 /* store in signed [big endian] format */ | 7134 /* store in signed [big endian] format */ |
6721 int | 7135 int |
6722 mp_to_signed_bin (mp_int * a, unsigned char *b) | 7136 mp_to_signed_bin (mp_int * a, unsigned char *b) |
6723 { | 7137 { |
6727 return res; | 7141 return res; |
6728 } | 7142 } |
6729 b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1); | 7143 b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1); |
6730 return MP_OKAY; | 7144 return MP_OKAY; |
6731 } | 7145 } |
7146 #endif | |
6732 | 7147 |
6733 /* End: bn_mp_to_signed_bin.c */ | 7148 /* End: bn_mp_to_signed_bin.c */ |
6734 | 7149 |
6735 /* Start: bn_mp_to_unsigned_bin.c */ | 7150 /* Start: bn_mp_to_unsigned_bin.c */ |
6736 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7151 #include <tommath.h> |
6737 * | 7152 #ifdef BN_MP_TO_UNSIGNED_BIN_C |
6738 * LibTomMath is a library that provides multiple-precision | 7153 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6739 * integer arithmetic as well as number theoretic functionality. | 7154 * |
6740 * | 7155 * LibTomMath is a library that provides multiple-precision |
6741 * The library was designed directly after the MPI library by | 7156 * integer arithmetic as well as number theoretic functionality. |
6742 * Michael Fromberger but has been written from scratch with | 7157 * |
6743 * additional optimizations in place. | 7158 * The library was designed directly after the MPI library by |
6744 * | 7159 * Michael Fromberger but has been written from scratch with |
6745 * The library is free for all purposes without any express | 7160 * additional optimizations in place. |
6746 * guarantee it works. | 7161 * |
6747 * | 7162 * The library is free for all purposes without any express |
6748 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7163 * guarantee it works. |
6749 */ | 7164 * |
6750 #include <tommath.h> | 7165 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7166 */ | |
6751 | 7167 |
6752 /* store in unsigned [big endian] format */ | 7168 /* store in unsigned [big endian] format */ |
6753 int | 7169 int |
6754 mp_to_unsigned_bin (mp_int * a, unsigned char *b) | 7170 mp_to_unsigned_bin (mp_int * a, unsigned char *b) |
6755 { | 7171 { |
6774 } | 7190 } |
6775 bn_reverse (b, x); | 7191 bn_reverse (b, x); |
6776 mp_clear (&t); | 7192 mp_clear (&t); |
6777 return MP_OKAY; | 7193 return MP_OKAY; |
6778 } | 7194 } |
7195 #endif | |
6779 | 7196 |
6780 /* End: bn_mp_to_unsigned_bin.c */ | 7197 /* End: bn_mp_to_unsigned_bin.c */ |
6781 | 7198 |
6782 /* Start: bn_mp_toom_mul.c */ | 7199 /* Start: bn_mp_toom_mul.c */ |
6783 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7200 #include <tommath.h> |
6784 * | 7201 #ifdef BN_MP_TOOM_MUL_C |
6785 * LibTomMath is a library that provides multiple-precision | 7202 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
6786 * integer arithmetic as well as number theoretic functionality. | 7203 * |
6787 * | 7204 * LibTomMath is a library that provides multiple-precision |
6788 * The library was designed directly after the MPI library by | 7205 * integer arithmetic as well as number theoretic functionality. |
6789 * Michael Fromberger but has been written from scratch with | 7206 * |
6790 * additional optimizations in place. | 7207 * The library was designed directly after the MPI library by |
6791 * | 7208 * Michael Fromberger but has been written from scratch with |
6792 * The library is free for all purposes without any express | 7209 * additional optimizations in place. |
6793 * guarantee it works. | 7210 * |
6794 * | 7211 * The library is free for all purposes without any express |
6795 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7212 * guarantee it works. |
6796 */ | 7213 * |
6797 #include <tommath.h> | 7214 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
6798 | 7215 */ |
6799 /* multiplication using the Toom-Cook 3-way algorithm */ | 7216 |
7217 /* multiplication using the Toom-Cook 3-way algorithm | |
7218 * | |
7219 * Much more complicated than Karatsuba but has a lower asymptotic running time of | |
7220 * O(N**1.464). This algorithm is only particularly useful on VERY large | |
7221 * inputs (we're talking 1000s of digits here...). | |
7222 */ | |
6800 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) | 7223 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) |
6801 { | 7224 { |
6802 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; | 7225 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; |
6803 int res, B; | 7226 int res, B; |
6804 | 7227 |
7050 &a0, &a1, &a2, &b0, &b1, | 7473 &a0, &a1, &a2, &b0, &b1, |
7051 &b2, &tmp1, &tmp2, NULL); | 7474 &b2, &tmp1, &tmp2, NULL); |
7052 return res; | 7475 return res; |
7053 } | 7476 } |
7054 | 7477 |
7478 #endif | |
7055 | 7479 |
7056 /* End: bn_mp_toom_mul.c */ | 7480 /* End: bn_mp_toom_mul.c */ |
7057 | 7481 |
7058 /* Start: bn_mp_toom_sqr.c */ | 7482 /* Start: bn_mp_toom_sqr.c */ |
7059 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7483 #include <tommath.h> |
7060 * | 7484 #ifdef BN_MP_TOOM_SQR_C |
7061 * LibTomMath is a library that provides multiple-precision | 7485 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
7062 * integer arithmetic as well as number theoretic functionality. | 7486 * |
7063 * | 7487 * LibTomMath is a library that provides multiple-precision |
7064 * The library was designed directly after the MPI library by | 7488 * integer arithmetic as well as number theoretic functionality. |
7065 * Michael Fromberger but has been written from scratch with | 7489 * |
7066 * additional optimizations in place. | 7490 * The library was designed directly after the MPI library by |
7067 * | 7491 * Michael Fromberger but has been written from scratch with |
7068 * The library is free for all purposes without any express | 7492 * additional optimizations in place. |
7069 * guarantee it works. | 7493 * |
7070 * | 7494 * The library is free for all purposes without any express |
7071 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7495 * guarantee it works. |
7072 */ | 7496 * |
7073 #include <tommath.h> | 7497 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7498 */ | |
7074 | 7499 |
7075 /* squaring using Toom-Cook 3-way algorithm */ | 7500 /* squaring using Toom-Cook 3-way algorithm */ |
7076 int | 7501 int |
7077 mp_toom_sqr(mp_int *a, mp_int *b) | 7502 mp_toom_sqr(mp_int *a, mp_int *b) |
7078 { | 7503 { |
7274 ERR: | 7699 ERR: |
7275 mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL); | 7700 mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL); |
7276 return res; | 7701 return res; |
7277 } | 7702 } |
7278 | 7703 |
7704 #endif | |
7279 | 7705 |
7280 /* End: bn_mp_toom_sqr.c */ | 7706 /* End: bn_mp_toom_sqr.c */ |
7281 | 7707 |
7282 /* Start: bn_mp_toradix.c */ | 7708 /* Start: bn_mp_toradix.c */ |
7283 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7709 #include <tommath.h> |
7284 * | 7710 #ifdef BN_MP_TORADIX_C |
7285 * LibTomMath is a library that provides multiple-precision | 7711 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
7286 * integer arithmetic as well as number theoretic functionality. | 7712 * |
7287 * | 7713 * LibTomMath is a library that provides multiple-precision |
7288 * The library was designed directly after the MPI library by | 7714 * integer arithmetic as well as number theoretic functionality. |
7289 * Michael Fromberger but has been written from scratch with | 7715 * |
7290 * additional optimizations in place. | 7716 * The library was designed directly after the MPI library by |
7291 * | 7717 * Michael Fromberger but has been written from scratch with |
7292 * The library is free for all purposes without any express | 7718 * additional optimizations in place. |
7293 * guarantee it works. | 7719 * |
7294 * | 7720 * The library is free for all purposes without any express |
7295 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7721 * guarantee it works. |
7296 */ | 7722 * |
7297 #include <tommath.h> | 7723 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7724 */ | |
7298 | 7725 |
7299 /* stores a bignum as a ASCII string in a given radix (2..64) */ | 7726 /* stores a bignum as a ASCII string in a given radix (2..64) */ |
7300 int mp_toradix (mp_int * a, char *str, int radix) | 7727 int mp_toradix (mp_int * a, char *str, int radix) |
7301 { | 7728 { |
7302 int res, digs; | 7729 int res, digs; |
7347 | 7774 |
7348 mp_clear (&t); | 7775 mp_clear (&t); |
7349 return MP_OKAY; | 7776 return MP_OKAY; |
7350 } | 7777 } |
7351 | 7778 |
7779 #endif | |
7352 | 7780 |
7353 /* End: bn_mp_toradix.c */ | 7781 /* End: bn_mp_toradix.c */ |
7354 | 7782 |
7355 /* Start: bn_mp_toradix_n.c */ | 7783 /* Start: bn_mp_toradix_n.c */ |
7356 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7784 #include <tommath.h> |
7357 * | 7785 #ifdef BN_MP_TORADIX_N_C |
7358 * LibTomMath is a library that provides multiple-precision | 7786 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
7359 * integer arithmetic as well as number theoretic functionality. | 7787 * |
7360 * | 7788 * LibTomMath is a library that provides multiple-precision |
7361 * The library was designed directly after the MPI library by | 7789 * integer arithmetic as well as number theoretic functionality. |
7362 * Michael Fromberger but has been written from scratch with | 7790 * |
7363 * additional optimizations in place. | 7791 * The library was designed directly after the MPI library by |
7364 * | 7792 * Michael Fromberger but has been written from scratch with |
7365 * The library is free for all purposes without any express | 7793 * additional optimizations in place. |
7366 * guarantee it works. | 7794 * |
7367 * | 7795 * The library is free for all purposes without any express |
7368 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7796 * guarantee it works. |
7369 */ | 7797 * |
7370 #include <tommath.h> | 7798 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7799 */ | |
7371 | 7800 |
7372 /* stores a bignum as a ASCII string in a given radix (2..64) | 7801 /* stores a bignum as a ASCII string in a given radix (2..64) |
7373 * | 7802 * |
7374 * Stores upto maxlen-1 chars and always a NULL byte | 7803 * Stores upto maxlen-1 chars and always a NULL byte |
7375 */ | 7804 */ |
7434 | 7863 |
7435 mp_clear (&t); | 7864 mp_clear (&t); |
7436 return MP_OKAY; | 7865 return MP_OKAY; |
7437 } | 7866 } |
7438 | 7867 |
7868 #endif | |
7439 | 7869 |
7440 /* End: bn_mp_toradix_n.c */ | 7870 /* End: bn_mp_toradix_n.c */ |
7441 | 7871 |
7442 /* Start: bn_mp_unsigned_bin_size.c */ | 7872 /* Start: bn_mp_unsigned_bin_size.c */ |
7443 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7873 #include <tommath.h> |
7444 * | 7874 #ifdef BN_MP_UNSIGNED_BIN_SIZE_C |
7445 * LibTomMath is a library that provides multiple-precision | 7875 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
7446 * integer arithmetic as well as number theoretic functionality. | 7876 * |
7447 * | 7877 * LibTomMath is a library that provides multiple-precision |
7448 * The library was designed directly after the MPI library by | 7878 * integer arithmetic as well as number theoretic functionality. |
7449 * Michael Fromberger but has been written from scratch with | 7879 * |
7450 * additional optimizations in place. | 7880 * The library was designed directly after the MPI library by |
7451 * | 7881 * Michael Fromberger but has been written from scratch with |
7452 * The library is free for all purposes without any express | 7882 * additional optimizations in place. |
7453 * guarantee it works. | 7883 * |
7454 * | 7884 * The library is free for all purposes without any express |
7455 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7885 * guarantee it works. |
7456 */ | 7886 * |
7457 #include <tommath.h> | 7887 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7888 */ | |
7458 | 7889 |
7459 /* get the size for an unsigned equivalent */ | 7890 /* get the size for an unsigned equivalent */ |
7460 int | 7891 int |
7461 mp_unsigned_bin_size (mp_int * a) | 7892 mp_unsigned_bin_size (mp_int * a) |
7462 { | 7893 { |
7463 int size = mp_count_bits (a); | 7894 int size = mp_count_bits (a); |
7464 return (size / 8 + ((size & 7) != 0 ? 1 : 0)); | 7895 return (size / 8 + ((size & 7) != 0 ? 1 : 0)); |
7465 } | 7896 } |
7897 #endif | |
7466 | 7898 |
7467 /* End: bn_mp_unsigned_bin_size.c */ | 7899 /* End: bn_mp_unsigned_bin_size.c */ |
7468 | 7900 |
7469 /* Start: bn_mp_xor.c */ | 7901 /* Start: bn_mp_xor.c */ |
7470 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7902 #include <tommath.h> |
7471 * | 7903 #ifdef BN_MP_XOR_C |
7472 * LibTomMath is a library that provides multiple-precision | 7904 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
7473 * integer arithmetic as well as number theoretic functionality. | 7905 * |
7474 * | 7906 * LibTomMath is a library that provides multiple-precision |
7475 * The library was designed directly after the MPI library by | 7907 * integer arithmetic as well as number theoretic functionality. |
7476 * Michael Fromberger but has been written from scratch with | 7908 * |
7477 * additional optimizations in place. | 7909 * The library was designed directly after the MPI library by |
7478 * | 7910 * Michael Fromberger but has been written from scratch with |
7479 * The library is free for all purposes without any express | 7911 * additional optimizations in place. |
7480 * guarantee it works. | 7912 * |
7481 * | 7913 * The library is free for all purposes without any express |
7482 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7914 * guarantee it works. |
7483 */ | 7915 * |
7484 #include <tommath.h> | 7916 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7917 */ | |
7485 | 7918 |
7486 /* XOR two ints together */ | 7919 /* XOR two ints together */ |
7487 int | 7920 int |
7488 mp_xor (mp_int * a, mp_int * b, mp_int * c) | 7921 mp_xor (mp_int * a, mp_int * b, mp_int * c) |
7489 { | 7922 { |
7503 px = a->used; | 7936 px = a->used; |
7504 x = a; | 7937 x = a; |
7505 } | 7938 } |
7506 | 7939 |
7507 for (ix = 0; ix < px; ix++) { | 7940 for (ix = 0; ix < px; ix++) { |
7508 t.dp[ix] ^= x->dp[ix]; | 7941 |
7509 } | 7942 } |
7510 mp_clamp (&t); | 7943 mp_clamp (&t); |
7511 mp_exch (c, &t); | 7944 mp_exch (c, &t); |
7512 mp_clear (&t); | 7945 mp_clear (&t); |
7513 return MP_OKAY; | 7946 return MP_OKAY; |
7514 } | 7947 } |
7948 #endif | |
7515 | 7949 |
7516 /* End: bn_mp_xor.c */ | 7950 /* End: bn_mp_xor.c */ |
7517 | 7951 |
7518 /* Start: bn_mp_zero.c */ | 7952 /* Start: bn_mp_zero.c */ |
7519 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7953 #include <tommath.h> |
7520 * | 7954 #ifdef BN_MP_ZERO_C |
7521 * LibTomMath is a library that provides multiple-precision | 7955 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
7522 * integer arithmetic as well as number theoretic functionality. | 7956 * |
7523 * | 7957 * LibTomMath is a library that provides multiple-precision |
7524 * The library was designed directly after the MPI library by | 7958 * integer arithmetic as well as number theoretic functionality. |
7525 * Michael Fromberger but has been written from scratch with | 7959 * |
7526 * additional optimizations in place. | 7960 * The library was designed directly after the MPI library by |
7527 * | 7961 * Michael Fromberger but has been written from scratch with |
7528 * The library is free for all purposes without any express | 7962 * additional optimizations in place. |
7529 * guarantee it works. | 7963 * |
7530 * | 7964 * The library is free for all purposes without any express |
7531 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7965 * guarantee it works. |
7532 */ | 7966 * |
7533 #include <tommath.h> | 7967 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7968 */ | |
7534 | 7969 |
7535 /* set to zero */ | 7970 /* set to zero */ |
7536 void | 7971 void |
7537 mp_zero (mp_int * a) | 7972 mp_zero (mp_int * a) |
7538 { | 7973 { |
7539 a->sign = MP_ZPOS; | 7974 a->sign = MP_ZPOS; |
7540 a->used = 0; | 7975 a->used = 0; |
7541 memset (a->dp, 0, sizeof (mp_digit) * a->alloc); | 7976 memset (a->dp, 0, sizeof (mp_digit) * a->alloc); |
7542 } | 7977 } |
7978 #endif | |
7543 | 7979 |
7544 /* End: bn_mp_zero.c */ | 7980 /* End: bn_mp_zero.c */ |
7545 | 7981 |
7546 /* Start: bn_prime_sizes_tab.c */ | |
7547 /* LibTomMath, multiple-precision integer library -- Tom St Denis | |
7548 * | |
7549 * LibTomMath is a library that provides multiple-precision | |
7550 * integer arithmetic as well as number theoretic functionality. | |
7551 * | |
7552 * The library was designed directly after the MPI library by | |
7553 * Michael Fromberger but has been written from scratch with | |
7554 * additional optimizations in place. | |
7555 * | |
7556 * The library is free for all purposes without any express | |
7557 * guarantee it works. | |
7558 * | |
7559 * Tom St Denis, [email protected], http://math.libtomcrypt.org | |
7560 */ | |
7561 #include <tommath.h> | |
7562 | |
7563 /* this table gives the # of rabin miller trials for a prob of failure lower than 2^-96 */ | |
7564 static const struct { | |
7565 int k, t; | |
7566 } sizes[] = { | |
7567 { 128, 28 }, | |
7568 { 256, 16 }, | |
7569 { 384, 10 }, | |
7570 { 512, 7 }, | |
7571 { 640, 6 }, | |
7572 { 768, 5 }, | |
7573 { 896, 4 }, | |
7574 { 1024, 4 }, | |
7575 { 1152, 3 }, | |
7576 { 1280, 3 }, | |
7577 { 1408, 3 }, | |
7578 { 1536, 3 }, | |
7579 { 1664, 3 }, | |
7580 { 1792, 2 } }; | |
7581 | |
7582 /* returns # of RM trials required for a given bit size */ | |
7583 int mp_prime_rabin_miller_trials(int size) | |
7584 { | |
7585 int x; | |
7586 | |
7587 for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) { | |
7588 if (sizes[x].k == size) { | |
7589 return sizes[x].t; | |
7590 } else if (sizes[x].k > size) { | |
7591 return (x == 0) ? sizes[0].t : sizes[x - 1].t; | |
7592 } | |
7593 } | |
7594 return 1; | |
7595 } | |
7596 | |
7597 | |
7598 | |
7599 /* End: bn_prime_sizes_tab.c */ | |
7600 | |
7601 /* Start: bn_prime_tab.c */ | 7982 /* Start: bn_prime_tab.c */ |
7602 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 7983 #include <tommath.h> |
7603 * | 7984 #ifdef BN_PRIME_TAB_C |
7604 * LibTomMath is a library that provides multiple-precision | 7985 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
7605 * integer arithmetic as well as number theoretic functionality. | 7986 * |
7606 * | 7987 * LibTomMath is a library that provides multiple-precision |
7607 * The library was designed directly after the MPI library by | 7988 * integer arithmetic as well as number theoretic functionality. |
7608 * Michael Fromberger but has been written from scratch with | 7989 * |
7609 * additional optimizations in place. | 7990 * The library was designed directly after the MPI library by |
7610 * | 7991 * Michael Fromberger but has been written from scratch with |
7611 * The library is free for all purposes without any express | 7992 * additional optimizations in place. |
7612 * guarantee it works. | 7993 * |
7613 * | 7994 * The library is free for all purposes without any express |
7614 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 7995 * guarantee it works. |
7615 */ | 7996 * |
7616 #include <tommath.h> | 7997 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
7998 */ | |
7617 const mp_digit __prime_tab[] = { | 7999 const mp_digit __prime_tab[] = { |
7618 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, | 8000 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, |
7619 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, | 8001 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, |
7620 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, | 8002 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, |
7621 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, | 8003 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, |
7652 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, | 8034 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, |
7653 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, | 8035 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, |
7654 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 | 8036 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 |
7655 #endif | 8037 #endif |
7656 }; | 8038 }; |
8039 #endif | |
7657 | 8040 |
7658 /* End: bn_prime_tab.c */ | 8041 /* End: bn_prime_tab.c */ |
7659 | 8042 |
7660 /* Start: bn_reverse.c */ | 8043 /* Start: bn_reverse.c */ |
7661 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 8044 #include <tommath.h> |
7662 * | 8045 #ifdef BN_REVERSE_C |
7663 * LibTomMath is a library that provides multiple-precision | 8046 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
7664 * integer arithmetic as well as number theoretic functionality. | 8047 * |
7665 * | 8048 * LibTomMath is a library that provides multiple-precision |
7666 * The library was designed directly after the MPI library by | 8049 * integer arithmetic as well as number theoretic functionality. |
7667 * Michael Fromberger but has been written from scratch with | 8050 * |
7668 * additional optimizations in place. | 8051 * The library was designed directly after the MPI library by |
7669 * | 8052 * Michael Fromberger but has been written from scratch with |
7670 * The library is free for all purposes without any express | 8053 * additional optimizations in place. |
7671 * guarantee it works. | 8054 * |
7672 * | 8055 * The library is free for all purposes without any express |
7673 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 8056 * guarantee it works. |
7674 */ | 8057 * |
7675 #include <tommath.h> | 8058 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
8059 */ | |
7676 | 8060 |
7677 /* reverse an array, used for radix code */ | 8061 /* reverse an array, used for radix code */ |
7678 void | 8062 void |
7679 bn_reverse (unsigned char *s, int len) | 8063 bn_reverse (unsigned char *s, int len) |
7680 { | 8064 { |
7689 s[iy] = t; | 8073 s[iy] = t; |
7690 ++ix; | 8074 ++ix; |
7691 --iy; | 8075 --iy; |
7692 } | 8076 } |
7693 } | 8077 } |
8078 #endif | |
7694 | 8079 |
7695 /* End: bn_reverse.c */ | 8080 /* End: bn_reverse.c */ |
7696 | 8081 |
7697 /* Start: bn_s_mp_add.c */ | 8082 /* Start: bn_s_mp_add.c */ |
7698 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 8083 #include <tommath.h> |
7699 * | 8084 #ifdef BN_S_MP_ADD_C |
7700 * LibTomMath is a library that provides multiple-precision | 8085 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
7701 * integer arithmetic as well as number theoretic functionality. | 8086 * |
7702 * | 8087 * LibTomMath is a library that provides multiple-precision |
7703 * The library was designed directly after the MPI library by | 8088 * integer arithmetic as well as number theoretic functionality. |
7704 * Michael Fromberger but has been written from scratch with | 8089 * |
7705 * additional optimizations in place. | 8090 * The library was designed directly after the MPI library by |
7706 * | 8091 * Michael Fromberger but has been written from scratch with |
7707 * The library is free for all purposes without any express | 8092 * additional optimizations in place. |
7708 * guarantee it works. | 8093 * |
7709 * | 8094 * The library is free for all purposes without any express |
7710 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 8095 * guarantee it works. |
7711 */ | 8096 * |
7712 #include <tommath.h> | 8097 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
8098 */ | |
7713 | 8099 |
7714 /* low level addition, based on HAC pp.594, Algorithm 14.7 */ | 8100 /* low level addition, based on HAC pp.594, Algorithm 14.7 */ |
7715 int | 8101 int |
7716 s_mp_add (mp_int * a, mp_int * b, mp_int * c) | 8102 s_mp_add (mp_int * a, mp_int * b, mp_int * c) |
7717 { | 8103 { |
7796 } | 8182 } |
7797 | 8183 |
7798 mp_clamp (c); | 8184 mp_clamp (c); |
7799 return MP_OKAY; | 8185 return MP_OKAY; |
7800 } | 8186 } |
8187 #endif | |
7801 | 8188 |
7802 /* End: bn_s_mp_add.c */ | 8189 /* End: bn_s_mp_add.c */ |
7803 | 8190 |
7804 /* Start: bn_s_mp_exptmod.c */ | 8191 /* Start: bn_s_mp_exptmod.c */ |
7805 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 8192 #include <tommath.h> |
7806 * | 8193 #ifdef BN_S_MP_EXPTMOD_C |
7807 * LibTomMath is a library that provides multiple-precision | 8194 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
7808 * integer arithmetic as well as number theoretic functionality. | 8195 * |
7809 * | 8196 * LibTomMath is a library that provides multiple-precision |
7810 * The library was designed directly after the MPI library by | 8197 * integer arithmetic as well as number theoretic functionality. |
7811 * Michael Fromberger but has been written from scratch with | 8198 * |
7812 * additional optimizations in place. | 8199 * The library was designed directly after the MPI library by |
7813 * | 8200 * Michael Fromberger but has been written from scratch with |
7814 * The library is free for all purposes without any express | 8201 * additional optimizations in place. |
7815 * guarantee it works. | 8202 * |
7816 * | 8203 * The library is free for all purposes without any express |
7817 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 8204 * guarantee it works. |
7818 */ | 8205 * |
7819 #include <tommath.h> | 8206 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
8207 */ | |
7820 | 8208 |
7821 #ifdef MP_LOW_MEM | 8209 #ifdef MP_LOW_MEM |
7822 #define TAB_SIZE 32 | 8210 #define TAB_SIZE 32 |
7823 #else | 8211 #else |
7824 #define TAB_SIZE 256 | 8212 #define TAB_SIZE 256 |
8034 for (x = 1<<(winsize-1); x < (1 << winsize); x++) { | 8422 for (x = 1<<(winsize-1); x < (1 << winsize); x++) { |
8035 mp_clear (&M[x]); | 8423 mp_clear (&M[x]); |
8036 } | 8424 } |
8037 return err; | 8425 return err; |
8038 } | 8426 } |
8427 #endif | |
8039 | 8428 |
8040 /* End: bn_s_mp_exptmod.c */ | 8429 /* End: bn_s_mp_exptmod.c */ |
8041 | 8430 |
8042 /* Start: bn_s_mp_mul_digs.c */ | 8431 /* Start: bn_s_mp_mul_digs.c */ |
8043 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 8432 #include <tommath.h> |
8044 * | 8433 #ifdef BN_S_MP_MUL_DIGS_C |
8045 * LibTomMath is a library that provides multiple-precision | 8434 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
8046 * integer arithmetic as well as number theoretic functionality. | 8435 * |
8047 * | 8436 * LibTomMath is a library that provides multiple-precision |
8048 * The library was designed directly after the MPI library by | 8437 * integer arithmetic as well as number theoretic functionality. |
8049 * Michael Fromberger but has been written from scratch with | 8438 * |
8050 * additional optimizations in place. | 8439 * The library was designed directly after the MPI library by |
8051 * | 8440 * Michael Fromberger but has been written from scratch with |
8052 * The library is free for all purposes without any express | 8441 * additional optimizations in place. |
8053 * guarantee it works. | 8442 * |
8054 * | 8443 * The library is free for all purposes without any express |
8055 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 8444 * guarantee it works. |
8056 */ | 8445 * |
8057 #include <tommath.h> | 8446 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
8447 */ | |
8058 | 8448 |
8059 /* multiplies |a| * |b| and only computes upto digs digits of result | 8449 /* multiplies |a| * |b| and only computes upto digs digits of result |
8060 * HAC pp. 595, Algorithm 14.12 Modified so you can control how | 8450 * HAC pp. 595, Algorithm 14.12 Modified so you can control how |
8061 * many digits of output are created. | 8451 * many digits of output are created. |
8062 */ | 8452 */ |
8123 mp_exch (&t, c); | 8513 mp_exch (&t, c); |
8124 | 8514 |
8125 mp_clear (&t); | 8515 mp_clear (&t); |
8126 return MP_OKAY; | 8516 return MP_OKAY; |
8127 } | 8517 } |
8518 #endif | |
8128 | 8519 |
8129 /* End: bn_s_mp_mul_digs.c */ | 8520 /* End: bn_s_mp_mul_digs.c */ |
8130 | 8521 |
8131 /* Start: bn_s_mp_mul_high_digs.c */ | 8522 /* Start: bn_s_mp_mul_high_digs.c */ |
8132 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 8523 #include <tommath.h> |
8133 * | 8524 #ifdef BN_S_MP_MUL_HIGH_DIGS_C |
8134 * LibTomMath is a library that provides multiple-precision | 8525 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
8135 * integer arithmetic as well as number theoretic functionality. | 8526 * |
8136 * | 8527 * LibTomMath is a library that provides multiple-precision |
8137 * The library was designed directly after the MPI library by | 8528 * integer arithmetic as well as number theoretic functionality. |
8138 * Michael Fromberger but has been written from scratch with | 8529 * |
8139 * additional optimizations in place. | 8530 * The library was designed directly after the MPI library by |
8140 * | 8531 * Michael Fromberger but has been written from scratch with |
8141 * The library is free for all purposes without any express | 8532 * additional optimizations in place. |
8142 * guarantee it works. | 8533 * |
8143 * | 8534 * The library is free for all purposes without any express |
8144 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 8535 * guarantee it works. |
8145 */ | 8536 * |
8146 #include <tommath.h> | 8537 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
8538 */ | |
8147 | 8539 |
8148 /* multiplies |a| * |b| and does not compute the lower digs digits | 8540 /* multiplies |a| * |b| and does not compute the lower digs digits |
8149 * [meant to get the higher part of the product] | 8541 * [meant to get the higher part of the product] |
8150 */ | 8542 */ |
8151 int | 8543 int |
8156 mp_digit u; | 8548 mp_digit u; |
8157 mp_word r; | 8549 mp_word r; |
8158 mp_digit tmpx, *tmpt, *tmpy; | 8550 mp_digit tmpx, *tmpt, *tmpy; |
8159 | 8551 |
8160 /* can we use the fast multiplier? */ | 8552 /* can we use the fast multiplier? */ |
8553 #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C | |
8161 if (((a->used + b->used + 1) < MP_WARRAY) | 8554 if (((a->used + b->used + 1) < MP_WARRAY) |
8162 && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { | 8555 && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { |
8163 return fast_s_mp_mul_high_digs (a, b, c, digs); | 8556 return fast_s_mp_mul_high_digs (a, b, c, digs); |
8164 } | 8557 } |
8558 #endif | |
8165 | 8559 |
8166 if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) { | 8560 if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) { |
8167 return res; | 8561 return res; |
8168 } | 8562 } |
8169 t.used = a->used + b->used + 1; | 8563 t.used = a->used + b->used + 1; |
8200 mp_clamp (&t); | 8594 mp_clamp (&t); |
8201 mp_exch (&t, c); | 8595 mp_exch (&t, c); |
8202 mp_clear (&t); | 8596 mp_clear (&t); |
8203 return MP_OKAY; | 8597 return MP_OKAY; |
8204 } | 8598 } |
8599 #endif | |
8205 | 8600 |
8206 /* End: bn_s_mp_mul_high_digs.c */ | 8601 /* End: bn_s_mp_mul_high_digs.c */ |
8207 | 8602 |
8208 /* Start: bn_s_mp_sqr.c */ | 8603 /* Start: bn_s_mp_sqr.c */ |
8209 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 8604 #include <tommath.h> |
8210 * | 8605 #ifdef BN_S_MP_SQR_C |
8211 * LibTomMath is a library that provides multiple-precision | 8606 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
8212 * integer arithmetic as well as number theoretic functionality. | 8607 * |
8213 * | 8608 * LibTomMath is a library that provides multiple-precision |
8214 * The library was designed directly after the MPI library by | 8609 * integer arithmetic as well as number theoretic functionality. |
8215 * Michael Fromberger but has been written from scratch with | 8610 * |
8216 * additional optimizations in place. | 8611 * The library was designed directly after the MPI library by |
8217 * | 8612 * Michael Fromberger but has been written from scratch with |
8218 * The library is free for all purposes without any express | 8613 * additional optimizations in place. |
8219 * guarantee it works. | 8614 * |
8220 * | 8615 * The library is free for all purposes without any express |
8221 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 8616 * guarantee it works. |
8222 */ | 8617 * |
8223 #include <tommath.h> | 8618 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
8619 */ | |
8224 | 8620 |
8225 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ | 8621 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ |
8226 int | 8622 int |
8227 s_mp_sqr (mp_int * a, mp_int * b) | 8623 s_mp_sqr (mp_int * a, mp_int * b) |
8228 { | 8624 { |
8283 mp_clamp (&t); | 8679 mp_clamp (&t); |
8284 mp_exch (&t, b); | 8680 mp_exch (&t, b); |
8285 mp_clear (&t); | 8681 mp_clear (&t); |
8286 return MP_OKAY; | 8682 return MP_OKAY; |
8287 } | 8683 } |
8684 #endif | |
8288 | 8685 |
8289 /* End: bn_s_mp_sqr.c */ | 8686 /* End: bn_s_mp_sqr.c */ |
8290 | 8687 |
8291 /* Start: bn_s_mp_sub.c */ | 8688 /* Start: bn_s_mp_sub.c */ |
8292 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 8689 #include <tommath.h> |
8293 * | 8690 #ifdef BN_S_MP_SUB_C |
8294 * LibTomMath is a library that provides multiple-precision | 8691 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
8295 * integer arithmetic as well as number theoretic functionality. | 8692 * |
8296 * | 8693 * LibTomMath is a library that provides multiple-precision |
8297 * The library was designed directly after the MPI library by | 8694 * integer arithmetic as well as number theoretic functionality. |
8298 * Michael Fromberger but has been written from scratch with | 8695 * |
8299 * additional optimizations in place. | 8696 * The library was designed directly after the MPI library by |
8300 * | 8697 * Michael Fromberger but has been written from scratch with |
8301 * The library is free for all purposes without any express | 8698 * additional optimizations in place. |
8302 * guarantee it works. | 8699 * |
8303 * | 8700 * The library is free for all purposes without any express |
8304 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 8701 * guarantee it works. |
8305 */ | 8702 * |
8306 #include <tommath.h> | 8703 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
8704 */ | |
8307 | 8705 |
8308 /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ | 8706 /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ |
8309 int | 8707 int |
8310 s_mp_sub (mp_int * a, mp_int * b, mp_int * c) | 8708 s_mp_sub (mp_int * a, mp_int * b, mp_int * c) |
8311 { | 8709 { |
8370 | 8768 |
8371 mp_clamp (c); | 8769 mp_clamp (c); |
8372 return MP_OKAY; | 8770 return MP_OKAY; |
8373 } | 8771 } |
8374 | 8772 |
8773 #endif | |
8375 | 8774 |
8376 /* End: bn_s_mp_sub.c */ | 8775 /* End: bn_s_mp_sub.c */ |
8377 | 8776 |
8378 /* Start: bncore.c */ | 8777 /* Start: bncore.c */ |
8379 /* LibTomMath, multiple-precision integer library -- Tom St Denis | 8778 #include <tommath.h> |
8380 * | 8779 #ifdef BNCORE_C |
8381 * LibTomMath is a library that provides multiple-precision | 8780 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
8382 * integer arithmetic as well as number theoretic functionality. | 8781 * |
8383 * | 8782 * LibTomMath is a library that provides multiple-precision |
8384 * The library was designed directly after the MPI library by | 8783 * integer arithmetic as well as number theoretic functionality. |
8385 * Michael Fromberger but has been written from scratch with | 8784 * |
8386 * additional optimizations in place. | 8785 * The library was designed directly after the MPI library by |
8387 * | 8786 * Michael Fromberger but has been written from scratch with |
8388 * The library is free for all purposes without any express | 8787 * additional optimizations in place. |
8389 * guarantee it works. | 8788 * |
8390 * | 8789 * The library is free for all purposes without any express |
8391 * Tom St Denis, [email protected], http://math.libtomcrypt.org | 8790 * guarantee it works. |
8392 */ | 8791 * |
8393 #include <tommath.h> | 8792 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
8793 */ | |
8394 | 8794 |
8395 /* Known optimal configurations | 8795 /* Known optimal configurations |
8396 | 8796 |
8397 CPU /Compiler /MUL CUTOFF/SQR CUTOFF | 8797 CPU /Compiler /MUL CUTOFF/SQR CUTOFF |
8398 ------------------------------------------------------------- | 8798 ------------------------------------------------------------- |
8399 Intel P4 /GCC v3.2 / 70/ 108 | 8799 Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) |
8400 AMD Athlon XP /GCC v3.2 / 109/ 127 | 8800 |
8401 | |
8402 */ | 8801 */ |
8403 | 8802 |
8404 /* configured for a AMD XP Thoroughbred core with etc/tune.c */ | 8803 int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */ |
8405 int KARATSUBA_MUL_CUTOFF = 109, /* Min. number of digits before Karatsuba multiplication is used. */ | 8804 KARATSUBA_SQR_CUTOFF = 128, /* Min. number of digits before Karatsuba squaring is used. */ |
8406 KARATSUBA_SQR_CUTOFF = 127, /* Min. number of digits before Karatsuba squaring is used. */ | |
8407 | 8805 |
8408 TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ | 8806 TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ |
8409 TOOM_SQR_CUTOFF = 400; | 8807 TOOM_SQR_CUTOFF = 400; |
8808 #endif | |
8410 | 8809 |
8411 /* End: bncore.c */ | 8810 /* End: bncore.c */ |
8412 | 8811 |
8413 | 8812 |
8414 /* EOF */ | 8813 /* EOF */ |