1
/* LibTomMath, multiple-precision integer library -- Tom St Denis
3
* LibTomMath is a library that provides multiple-precision
4
* integer arithmetic as well as number theoretic functionality.
6
* The library was designed directly after the MPI library by
7
* Michael Fromberger but has been written from scratch with
8
* additional optimizations in place.
10
* The library is free for all purposes without any express
13
* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
18
#ifdef HAVE_SYSTEM_TOMMATH
30
#define BN_MP_READ_RADIX_C
31
#define BN_MP_RADIX_SMAP_C
32
#define BN_MP_SET_INT_C
33
#define BN_MP_MUL_2D_C
40
#define BN_MP_CMP_MAG_C
44
#define LTM_ALL /* FIXME: tk: limit to the above class */
45
#include "bignum_class.h"
50
/* C++ compilers don't like assigning void * to mp_digit * */
51
#define OPT_CAST(x) (x *)
55
/* C on the other hand doesn't care */
61
Don't enable this, some old gcc's have broken udivti3.
62
Also divisions get translated into libcalls, not worth using this mode.
63
/* detect 64-bit mode if possible */
64
#if defined(__x86_64__)
65
#if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
71
/* some default configurations.
73
* A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
74
* A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
76
* At the very least a mp_digit must be able to hold 7 bits
77
* [any size beyond that is ok provided it doesn't overflow the data type]
80
typedef unsigned char mp_digit;
81
typedef unsigned short mp_word;
82
#elif defined(MP_16BIT)
83
typedef unsigned short mp_digit;
84
typedef unsigned long mp_word;
85
#elif defined(MP_64BIT)
86
/* for GCC only on supported platforms */
88
typedef unsigned long long ulong64;
89
typedef signed long long long64;
92
typedef unsigned long mp_digit;
93
typedef unsigned long mp_word __attribute__ ((mode(TI)));
97
/* this is the default case, 28-bit digits */
99
/* this is to make porting into LibTomCrypt easier :-) */
101
#if defined(_MSC_VER) || defined(__BORLANDC__)
102
typedef unsigned __int64 ulong64;
103
typedef signed __int64 long64;
105
typedef unsigned long long ulong64;
106
typedef signed long long long64;
110
typedef unsigned long mp_digit;
111
typedef ulong64 mp_word;
114
/* this is an extension that uses 31-bit digits */
117
/* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
124
/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
126
#define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */
129
#define MP_DIGIT_BIT DIGIT_BIT
130
#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
131
#define MP_DIGIT_MAX MP_MASK
134
#define MP_LT -1 /* less than */
135
#define MP_EQ 0 /* equal to */
136
#define MP_GT 1 /* greater than */
138
#define MP_ZPOS 0 /* positive integer */
139
#define MP_NEG 1 /* negative */
141
#define MP_OKAY 0 /* ok result */
142
#define MP_MEM -2 /* out of mem */
143
#define MP_VAL -3 /* invalid input */
144
#define MP_RANGE MP_VAL
146
#define MP_YES 1 /* yes response */
147
#define MP_NO 0 /* no response */
149
/* Primality generation flags */
150
#define LTM_PRIME_BBS 0x0001 /* BBS style prime */
151
#define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
152
#define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
156
/* you'll have to tune these... */
157
extern int KARATSUBA_MUL_CUTOFF,
158
KARATSUBA_SQR_CUTOFF,
162
/* define this to use lower memory usage routines (exptmods mostly) */
163
/* #define MP_LOW_MEM */
165
/* default precision */
168
#define MP_PREC 32 /* default digits of precision */
170
#define MP_PREC 8 /* default digits of precision */
174
/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
175
#define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
177
/* the infamous mp_int structure */
179
int used, alloc, sign;
183
/* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
184
typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
187
#define USED(m) ((m)->used)
188
#define DIGIT(m,k) ((m)->dp[(k)])
189
#define SIGN(m) ((m)->sign)
191
/* error code to char* string */
192
const char *mp_error_to_string(int code);
194
/* ---> init and deinit bignum functions <--- */
196
int mp_init(mp_int *a);
199
void mp_clear(mp_int *a);
201
/* init a null terminated series of arguments */
202
int mp_init_multi(mp_int *mp, ...);
204
/* clear a null terminated series of arguments */
205
void mp_clear_multi(mp_int *mp, ...);
207
/* exchange two ints */
208
void mp_exch(mp_int *a, mp_int *b);
210
/* shrink ram required for a bignum */
211
int mp_shrink(mp_int *a);
213
/* grow an int to a given size */
214
int mp_grow(mp_int *a, int size);
216
/* init to a given number of digits */
217
int mp_init_size(mp_int *a, int size);
219
/* ---> Basic Manipulations <--- */
220
#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
221
#define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
222
#define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
225
void mp_zero(mp_int *a);
228
void mp_set(mp_int *a, mp_digit b);
230
/* set a 32-bit const */
231
int mp_set_int(mp_int *a, unsigned long b);
233
/* get a 32-bit value */
234
unsigned long mp_get_int(mp_int * a);
236
/* initialize and set a digit */
237
int mp_init_set (mp_int * a, mp_digit b);
239
/* initialize and set 32-bit value */
240
int mp_init_set_int (mp_int * a, unsigned long b);
243
int mp_copy(mp_int *a, mp_int *b);
245
/* inits and copies, a = b */
246
int mp_init_copy(mp_int *a, mp_int *b);
248
/* trim unused digits */
249
void mp_clamp(mp_int *a);
251
/* ---> digit manipulation <--- */
253
/* right shift by "b" digits */
254
void mp_rshd(mp_int *a, int b);
256
/* left shift by "b" digits */
257
int mp_lshd(mp_int *a, int b);
260
int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d);
263
int mp_div_2(mp_int *a, mp_int *b);
266
int mp_mul_2d(mp_int *a, int b, mp_int *c);
269
int mp_mul_2(mp_int *a, mp_int *b);
272
int mp_mod_2d(mp_int *a, int b, mp_int *c);
274
/* computes a = 2**b */
275
int mp_2expt(mp_int *a, int b);
277
/* Counts the number of lsbs which are zero before the first zero bit */
278
int mp_cnt_lsb(mp_int *a);
282
/* makes a pseudo-random int of a given size */
283
int mp_rand(mp_int *a, int digits);
285
/* ---> binary operations <--- */
287
int mp_xor(mp_int *a, mp_int *b, mp_int *c);
290
int mp_or(mp_int *a, mp_int *b, mp_int *c);
293
int mp_and(mp_int *a, mp_int *b, mp_int *c);
295
/* ---> Basic arithmetic <--- */
298
int mp_neg(mp_int *a, mp_int *b);
301
int mp_abs(mp_int *a, mp_int *b);
304
int mp_cmp(mp_int *a, mp_int *b);
306
/* compare |a| to |b| */
307
int mp_cmp_mag(mp_int *a, mp_int *b);
310
int mp_add(mp_int *a, mp_int *b, mp_int *c);
313
int mp_sub(mp_int *a, mp_int *b, mp_int *c);
316
int mp_mul(mp_int *a, mp_int *b, mp_int *c);
319
int mp_sqr(mp_int *a, mp_int *b);
321
/* a/b => cb + d == a */
322
int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
324
/* c = a mod b, 0 <= c < b */
325
int mp_mod(mp_int *a, mp_int *b, mp_int *c);
327
/* ---> single digit functions <--- */
329
/* compare against a single digit */
330
int mp_cmp_d(mp_int *a, mp_digit b);
333
int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
336
int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
339
int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
341
/* a/b => cb + d == a */
342
int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
344
/* a/3 => 3c + d == a */
345
int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
348
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
350
/* c = a mod b, 0 <= c < b */
351
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
353
/* ---> number theory <--- */
355
/* d = a + b (mod c) */
356
int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
358
/* d = a - b (mod c) */
359
int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
361
/* d = a * b (mod c) */
362
int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
364
/* c = a * a (mod b) */
365
int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);
367
/* c = 1/a (mod b) */
368
int mp_invmod(mp_int *a, mp_int *b, mp_int *c);
371
int mp_gcd(mp_int *a, mp_int *b, mp_int *c);
373
/* produces value such that U1*a + U2*b = U3 */
374
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
376
/* c = [a, b] or (a*b)/(a, b) */
377
int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
379
/* finds one of the b'th root of a, such that |c|**b <= |a|
381
* returns error if a < 0 and b is even
383
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
385
/* special sqrt algo */
386
int mp_sqrt(mp_int *arg, mp_int *ret);
388
/* is number a square? */
389
int mp_is_square(mp_int *arg, int *ret);
391
/* computes the jacobi c = (a | n) (or Legendre if b is prime) */
392
int mp_jacobi(mp_int *a, mp_int *n, int *c);
394
/* used to setup the Barrett reduction for a given modulus b */
395
int mp_reduce_setup(mp_int *a, mp_int *b);
397
/* Barrett Reduction, computes a (mod b) with a precomputed value c
399
* Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
400
* compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
402
int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
404
/* setups the montgomery reduction */
405
int mp_montgomery_setup(mp_int *a, mp_digit *mp);
407
/* computes a = B**n mod b without division or multiplication useful for
408
* normalizing numbers in a Montgomery system.
410
int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
412
/* computes x/R == x (mod N) via Montgomery Reduction */
413
int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
415
/* returns 1 if a is a valid DR modulus */
416
int mp_dr_is_modulus(mp_int *a);
418
/* sets the value of "d" required for mp_dr_reduce */
419
void mp_dr_setup(mp_int *a, mp_digit *d);
421
/* reduces a modulo b using the Diminished Radix method */
422
int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
424
/* returns true if a can be reduced with mp_reduce_2k */
425
int mp_reduce_is_2k(mp_int *a);
427
/* determines k value for 2k reduction */
428
int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
430
/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
431
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
433
/* returns true if a can be reduced with mp_reduce_2k_l */
434
int mp_reduce_is_2k_l(mp_int *a);
436
/* determines k value for 2k reduction */
437
int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
439
/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
440
int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
442
/* d = a**b (mod c) */
443
int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
445
/* ---> Primes <--- */
447
/* number of primes */
449
#define PRIME_SIZE 31
451
#define PRIME_SIZE 256
454
/* table of first PRIME_SIZE primes */
455
extern const mp_digit ltm_prime_tab[];
457
/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
458
int mp_prime_is_divisible(mp_int *a, int *result);
460
/* performs one Fermat test of "a" using base "b".
461
* Sets result to 0 if composite or 1 if probable prime
463
int mp_prime_fermat(mp_int *a, mp_int *b, int *result);
465
/* performs one Miller-Rabin test of "a" using base "b".
466
* Sets result to 0 if composite or 1 if probable prime
468
int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
470
/* This gives [for a given bit size] the number of trials required
471
* such that Miller-Rabin gives a prob of failure lower than 2^-96
473
int mp_prime_rabin_miller_trials(int size);
475
/* performs t rounds of Miller-Rabin on "a" using the first
476
* t prime bases. Also performs an initial sieve of trial
477
* division. Determines if "a" is prime with probability
478
* of error no more than (1/4)**t.
480
* Sets result to 1 if probably prime, 0 otherwise
482
int mp_prime_is_prime(mp_int *a, int t, int *result);
484
/* finds the next prime after the number "a" using "t" trials
487
* bbs_style = 1 means the prime must be congruent to 3 mod 4
489
int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
491
/* makes a truly random prime of a given size (bytes),
492
* call with bbs = 1 if you want it to be congruent to 3 mod 4
494
* You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
495
* have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
498
* The prime generated will be larger than 2^(8*size).
500
#define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)
502
/* makes a truly random prime of a given size (bits),
504
* Flags are as follows:
506
* LTM_PRIME_BBS - make prime congruent to 3 mod 4
507
* LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
508
* LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
509
* LTM_PRIME_2MSB_ON - make the 2nd highest bit one
511
* You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
512
* have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
516
int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat);
518
/* ---> radix conversion <--- */
519
int mp_count_bits(mp_int *a);
521
int mp_unsigned_bin_size(mp_int *a);
522
int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c);
523
int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
524
int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
526
int mp_signed_bin_size(mp_int *a);
527
int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
528
int mp_to_signed_bin(mp_int *a, unsigned char *b);
529
int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
531
int mp_read_radix(mp_int *a, const char *str, int radix);
532
int mp_toradix(mp_int *a, char *str, int radix);
533
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
534
int mp_radix_size(mp_int *a, int radix, int *size);
536
int mp_fread(mp_int *a, int radix, FILE *stream);
537
int mp_fwrite(mp_int *a, int radix, FILE *stream);
539
#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
540
#define mp_raw_size(mp) mp_signed_bin_size(mp)
541
#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
542
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
543
#define mp_mag_size(mp) mp_unsigned_bin_size(mp)
544
#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
546
#define mp_tobinary(M, S) mp_toradix((M), (S), 2)
547
#define mp_tooctal(M, S) mp_toradix((M), (S), 8)
548
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
549
#define mp_tohex(M, S) mp_toradix((M), (S), 16)
551
/* lowlevel functions, do not call! */
552
int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
553
int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
554
#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
555
int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
556
int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
557
int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
558
int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
559
int fast_s_mp_sqr(mp_int *a, mp_int *b);
560
int s_mp_sqr(mp_int *a, mp_int *b);
561
int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
562
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
563
int mp_karatsuba_sqr(mp_int *a, mp_int *b);
564
int mp_toom_sqr(mp_int *a, mp_int *b);
565
int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
566
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
567
int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
568
int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
569
int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
570
void bn_reverse(unsigned char *s, int len);
572
extern const char *mp_s_rmap;
578
#endif /* HAVE_SYSTEM_TOMMATH */
583
/* $Source: /cvs/libtom/libtommath/tommath.h,v $ */
584
/* $Revision: 1.8 $ */
585
/* $Date: 2006/03/31 14:18:44 $ */
6
#include "bignum_fast.h"
9
#define mp_toradix_n(a,b,c,d) fp_toradix_n(a,b,c,d)
10
#define mp_init(a) (fp_init(a), 0)
13
#define mp_init_multi(a,b,c,d) (mp_init(a), mp_init(b), mp_init(c), 0)
15
#define mp_read_unsigned_bin(a,b,c) (fp_read_unsigned_bin(a, b, c), 0)
18
#define mp_clear_multi(...)
19
#define mp_copy(a,b) (fp_copy(a,b), 0)
20
#define mp_unsigned_bin_size fp_unsigned_bin_size
21
#define mp_to_unsigned_bin(a,b) (fp_to_unsigned_bin(a,b), 0)
22
#define mp_read_radix fp_read_radix
23
#define mp_exptmod fp_exptmod
24
#define mp_get_int(a) ((a)->used > 0 ? (a)->dp[0] : 0)
25
#define mp_set_int(a, b) fp_set(a, b)
26
#define mp_mul_2d fp_mul_2d
added
removed
libclamav/bignum.h
