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@iahu.ca, http://math.libtomcrypt.org
27
#define MIN(x,y) ((x)<(y)?(x):(y))
29
#define MAX(x,y) ((x)>(y)?(x):(y))
34
/* C++ compilers don't like assigning void * to mp_digit * */
35
#define OPT_CAST(x) (x *)
39
/* C on the other hand doesn't care */
44
/* some default configurations.
46
* A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
47
* A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
49
* At the very least a mp_digit must be able to hold 7 bits
50
* [any size beyond that is ok provided it doesn't overflow the data type]
53
typedef unsigned char mp_digit;
54
typedef unsigned short mp_word;
55
#elif defined(MP_16BIT)
56
typedef unsigned short mp_digit;
57
typedef unsigned long mp_word;
58
#elif defined(MP_64BIT)
59
/* for GCC only on supported platforms */
61
typedef unsigned long long ulong64;
62
typedef signed long long long64;
65
typedef ulong64 mp_digit;
66
typedef unsigned long mp_word __attribute__ ((mode(TI)));
70
/* this is the default case, 28-bit digits */
72
/* this is to make porting into LibTomCrypt easier :-) */
74
#if defined(_MSC_VER) || defined(__BORLANDC__)
75
typedef unsigned __int64 ulong64;
76
typedef signed __int64 long64;
78
typedef unsigned long long ulong64;
79
typedef signed long long long64;
83
typedef unsigned long mp_digit;
84
typedef ulong64 mp_word;
87
/* this is an extension that uses 31-bit digits */
90
/* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
96
/* define heap macros */
98
/* default to libc stuff */
100
#define XMALLOC malloc
102
#define XREALLOC realloc
103
#define XCALLOC calloc
105
/* prototypes for our heap functions */
106
extern void *XMALLOC(size_t n);
107
extern void *REALLOC(void *p, size_t n);
108
extern void *XCALLOC(size_t n, size_t s);
109
extern void XFREE(void *p);
114
/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
116
#define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */
119
#define MP_DIGIT_BIT DIGIT_BIT
120
#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
121
#define MP_DIGIT_MAX MP_MASK
124
#define MP_LT -1 /* less than */
125
#define MP_EQ 0 /* equal to */
126
#define MP_GT 1 /* greater than */
128
#define MP_ZPOS 0 /* positive integer */
129
#define MP_NEG 1 /* negative */
131
#define MP_OKAY 0 /* ok result */
132
#define MP_MEM -2 /* out of mem */
133
#define MP_VAL -3 /* invalid input */
134
#define MP_RANGE MP_VAL
136
#define MP_YES 1 /* yes response */
137
#define MP_NO 0 /* no response */
139
/* Primality generation flags */
140
#define LTM_PRIME_BBS 0x0001 /* BBS style prime */
141
#define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
142
#define LTM_PRIME_2MSB_OFF 0x0004 /* force 2nd MSB to 0 */
143
#define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
147
/* you'll have to tune these... */
148
extern int KARATSUBA_MUL_CUTOFF,
149
KARATSUBA_SQR_CUTOFF,
153
/* define this to use lower memory usage routines (exptmods mostly) */
154
/* #define MP_LOW_MEM */
156
/* default precision */
159
#define MP_PREC 64 /* default digits of precision */
161
#define MP_PREC 8 /* default digits of precision */
165
/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
166
#define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
168
/* the infamous mp_int structure */
170
int used, alloc, sign;
174
/* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
175
typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
178
#define USED(m) ((m)->used)
179
#define DIGIT(m,k) ((m)->dp[(k)])
180
#define SIGN(m) ((m)->sign)
182
/* error code to char* string */
183
char *mp_error_to_string(int code);
185
/* ---> init and deinit bignum functions <--- */
187
int mp_init(mp_int *a);
190
void mp_clear(mp_int *a);
192
/* init a null terminated series of arguments */
193
int mp_init_multi(mp_int *mp, ...);
195
/* clear a null terminated series of arguments */
196
void mp_clear_multi(mp_int *mp, ...);
198
/* exchange two ints */
199
void mp_exch(mp_int *a, mp_int *b);
201
/* shrink ram required for a bignum */
202
int mp_shrink(mp_int *a);
204
/* grow an int to a given size */
205
int mp_grow(mp_int *a, int size);
207
/* init to a given number of digits */
208
int mp_init_size(mp_int *a, int size);
210
/* ---> Basic Manipulations <--- */
211
#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
212
#define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
213
#define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
216
void mp_zero(mp_int *a);
219
void mp_set(mp_int *a, mp_digit b);
221
/* set a 32-bit const */
222
int mp_set_int(mp_int *a, unsigned long b);
224
/* get a 32-bit value */
225
unsigned long mp_get_int(mp_int * a);
227
/* initialize and set a digit */
228
int mp_init_set (mp_int * a, mp_digit b);
230
/* initialize and set 32-bit value */
231
int mp_init_set_int (mp_int * a, unsigned long b);
234
int mp_copy(mp_int *a, mp_int *b);
236
/* inits and copies, a = b */
237
int mp_init_copy(mp_int *a, mp_int *b);
239
/* trim unused digits */
240
void mp_clamp(mp_int *a);
242
/* ---> digit manipulation <--- */
244
/* right shift by "b" digits */
245
void mp_rshd(mp_int *a, int b);
247
/* left shift by "b" digits */
248
int mp_lshd(mp_int *a, int b);
251
int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d);
254
int mp_div_2(mp_int *a, mp_int *b);
257
int mp_mul_2d(mp_int *a, int b, mp_int *c);
260
int mp_mul_2(mp_int *a, mp_int *b);
263
int mp_mod_2d(mp_int *a, int b, mp_int *c);
265
/* computes a = 2**b */
266
int mp_2expt(mp_int *a, int b);
268
/* Counts the number of lsbs which are zero before the first zero bit */
269
int mp_cnt_lsb(mp_int *a);
273
/* makes a pseudo-random int of a given size */
274
int mp_rand(mp_int *a, int digits);
276
/* ---> binary operations <--- */
278
int mp_xor(mp_int *a, mp_int *b, mp_int *c);
281
int mp_or(mp_int *a, mp_int *b, mp_int *c);
284
int mp_and(mp_int *a, mp_int *b, mp_int *c);
286
/* ---> Basic arithmetic <--- */
289
int mp_neg(mp_int *a, mp_int *b);
292
int mp_abs(mp_int *a, mp_int *b);
295
int mp_cmp(mp_int *a, mp_int *b);
297
/* compare |a| to |b| */
298
int mp_cmp_mag(mp_int *a, mp_int *b);
301
int mp_add(mp_int *a, mp_int *b, mp_int *c);
304
int mp_sub(mp_int *a, mp_int *b, mp_int *c);
307
int mp_mul(mp_int *a, mp_int *b, mp_int *c);
310
int mp_sqr(mp_int *a, mp_int *b);
312
/* a/b => cb + d == a */
313
int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
315
/* c = a mod b, 0 <= c < b */
316
int mp_mod(mp_int *a, mp_int *b, mp_int *c);
318
/* ---> single digit functions <--- */
320
/* compare against a single digit */
321
int mp_cmp_d(mp_int *a, mp_digit b);
324
int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
327
int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
330
int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
332
/* a/b => cb + d == a */
333
int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
335
/* a/3 => 3c + d == a */
336
int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
339
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
341
/* c = a mod b, 0 <= c < b */
342
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
344
/* ---> number theory <--- */
346
/* d = a + b (mod c) */
347
int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
349
/* d = a - b (mod c) */
350
int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
352
/* d = a * b (mod c) */
353
int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
355
/* c = a * a (mod b) */
356
int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);
358
/* c = 1/a (mod b) */
359
int mp_invmod(mp_int *a, mp_int *b, mp_int *c);
362
int mp_gcd(mp_int *a, mp_int *b, mp_int *c);
364
/* produces value such that U1*a + U2*b = U3 */
365
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
367
/* c = [a, b] or (a*b)/(a, b) */
368
int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
370
/* finds one of the b'th root of a, such that |c|**b <= |a|
372
* returns error if a < 0 and b is even
374
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
376
/* special sqrt algo */
377
int mp_sqrt(mp_int *arg, mp_int *ret);
379
/* is number a square? */
380
int mp_is_square(mp_int *arg, int *ret);
382
/* computes the jacobi c = (a | n) (or Legendre if b is prime) */
383
int mp_jacobi(mp_int *a, mp_int *n, int *c);
385
/* used to setup the Barrett reduction for a given modulus b */
386
int mp_reduce_setup(mp_int *a, mp_int *b);
388
/* Barrett Reduction, computes a (mod b) with a precomputed value c
390
* Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
391
* compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
393
int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
395
/* setups the montgomery reduction */
396
int mp_montgomery_setup(mp_int *a, mp_digit *mp);
398
/* computes a = B**n mod b without division or multiplication useful for
399
* normalizing numbers in a Montgomery system.
401
int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
403
/* computes x/R == x (mod N) via Montgomery Reduction */
404
int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
406
/* returns 1 if a is a valid DR modulus */
407
int mp_dr_is_modulus(mp_int *a);
409
/* sets the value of "d" required for mp_dr_reduce */
410
void mp_dr_setup(mp_int *a, mp_digit *d);
412
/* reduces a modulo b using the Diminished Radix method */
413
int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
415
/* returns true if a can be reduced with mp_reduce_2k */
416
int mp_reduce_is_2k(mp_int *a);
418
/* determines k value for 2k reduction */
419
int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
421
/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
422
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
424
/* d = a**b (mod c) */
425
int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
427
/* ---> Primes <--- */
429
/* number of primes */
431
#define PRIME_SIZE 31
433
#define PRIME_SIZE 256
436
/* table of first PRIME_SIZE primes */
437
extern const mp_digit __prime_tab[];
439
/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
440
int mp_prime_is_divisible(mp_int *a, int *result);
442
/* performs one Fermat test of "a" using base "b".
443
* Sets result to 0 if composite or 1 if probable prime
445
int mp_prime_fermat(mp_int *a, mp_int *b, int *result);
447
/* performs one Miller-Rabin test of "a" using base "b".
448
* Sets result to 0 if composite or 1 if probable prime
450
int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
452
/* This gives [for a given bit size] the number of trials required
453
* such that Miller-Rabin gives a prob of failure lower than 2^-96
455
int mp_prime_rabin_miller_trials(int size);
457
/* performs t rounds of Miller-Rabin on "a" using the first
458
* t prime bases. Also performs an initial sieve of trial
459
* division. Determines if "a" is prime with probability
460
* of error no more than (1/4)**t.
462
* Sets result to 1 if probably prime, 0 otherwise
464
int mp_prime_is_prime(mp_int *a, int t, int *result);
466
/* finds the next prime after the number "a" using "t" trials
469
* bbs_style = 1 means the prime must be congruent to 3 mod 4
471
int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
473
/* makes a truly random prime of a given size (bytes),
474
* call with bbs = 1 if you want it to be congruent to 3 mod 4
476
* You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
477
* have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
480
* The prime generated will be larger than 2^(8*size).
482
#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)
484
/* makes a truly random prime of a given size (bits),
486
* Flags are as follows:
488
* LTM_PRIME_BBS - make prime congruent to 3 mod 4
489
* LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
490
* LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
491
* LTM_PRIME_2MSB_ON - make the 2nd highest bit one
493
* You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
494
* have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
498
int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat);
500
/* ---> radix conversion <--- */
501
int mp_count_bits(mp_int *a);
503
int mp_unsigned_bin_size(mp_int *a);
504
int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
505
int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
507
int mp_signed_bin_size(mp_int *a);
508
int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
509
int mp_to_signed_bin(mp_int *a, unsigned char *b);
511
int mp_read_radix(mp_int *a, char *str, int radix);
512
int mp_toradix(mp_int *a, char *str, int radix);
513
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
514
int mp_radix_size(mp_int *a, int radix, int *size);
516
int mp_fread(mp_int *a, int radix, FILE *stream);
517
int mp_fwrite(mp_int *a, int radix, FILE *stream);
519
#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
520
#define mp_raw_size(mp) mp_signed_bin_size(mp)
521
#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
522
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
523
#define mp_mag_size(mp) mp_unsigned_bin_size(mp)
524
#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
526
#define mp_tobinary(M, S) mp_toradix((M), (S), 2)
527
#define mp_tooctal(M, S) mp_toradix((M), (S), 8)
528
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
529
#define mp_tohex(M, S) mp_toradix((M), (S), 16)
531
/* lowlevel functions, do not call! */
532
int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
533
int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
534
#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
535
int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
536
int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
537
int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
538
int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
539
int fast_s_mp_sqr(mp_int *a, mp_int *b);
540
int s_mp_sqr(mp_int *a, mp_int *b);
541
int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
542
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
543
int mp_karatsuba_sqr(mp_int *a, mp_int *b);
544
int mp_toom_sqr(mp_int *a, mp_int *b);
545
int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
546
int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
547
int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
548
int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
549
void bn_reverse(unsigned char *s, int len);
551
extern const char *mp_s_rmap;
added
removed
libtomcrypt/tommath.h
