Skip to content

HTTPS clone URL

Subversion checkout URL

You can clone with HTTPS or Subversion.

Download ZIP
Fetching contributors…

Cannot retrieve contributors at this time

349 lines (256 sloc) 9.357 kb
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://libtommath.iahu.ca
*/
#ifndef BN_H_
#define BN_H_
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <ctype.h>
#include <limits.h>
#undef MIN
#define MIN(x,y) ((x)<(y)?(x):(y))
#undef MAX
#define MAX(x,y) ((x)>(y)?(x):(y))
#ifdef __cplusplus
extern "C" {
#endif
/* some default configurations.
*
* A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
* A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
*
* At the very least a mp_digit must be able to hold 7 bits
* [any size beyond that is ok provided it overflow the data type]
*/
#ifdef MP_8BIT
typedef unsigned char mp_digit;
typedef unsigned short mp_word;
#elif defined(MP_16BIT)
typedef unsigned short mp_digit;
typedef unsigned long mp_word;
#else
#ifndef CRYPT
#ifdef _MSC_VER
typedef unsigned __int64 ulong64;
typedef signed __int64 long64;
#else
typedef unsigned long long ulong64;
typedef signed long long long64;
#endif
#endif
/* default case */
typedef unsigned long mp_digit;
typedef ulong64 mp_word;
#define DIGIT_BIT 28
#endif
#ifndef DIGIT_BIT
#define DIGIT_BIT ((CHAR_BIT * sizeof(mp_digit) - 1)) /* bits per digit */
#endif
#define MP_DIGIT_BIT DIGIT_BIT
#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
#define MP_DIGIT_MAX MP_MASK
/* equalities */
#define MP_LT -1 /* less than */
#define MP_EQ 0 /* equal to */
#define MP_GT 1 /* greater than */
#define MP_ZPOS 0 /* positive integer */
#define MP_NEG 1 /* negative */
#define MP_OKAY 0 /* ok result */
#define MP_MEM -2 /* out of mem */
#define MP_VAL -3 /* invalid input */
#define MP_RANGE MP_VAL
typedef int mp_err;
/* you'll have to tune these... */
extern int KARATSUBA_MUL_CUTOFF,
KARATSUBA_SQR_CUTOFF,
MONTGOMERY_EXPT_CUTOFF;
#define MP_PREC 64 /* default digits of precision */
typedef struct {
int used, alloc, sign;
mp_digit *dp;
} mp_int;
#define USED(m) ((m)->used)
#define DIGIT(m,k) ((m)->dp[k])
#define SIGN(m) ((m)->sign)
/* ---> init and deinit bignum functions <--- */
/* init a bignum */
int mp_init(mp_int *a);
/* free a bignum */
void mp_clear(mp_int *a);
/* exchange two ints */
void mp_exch(mp_int *a, mp_int *b);
/* shrink ram required for a bignum */
int mp_shrink(mp_int *a);
/* ---> Basic Manipulations <--- */
#define mp_iszero(a) (((a)->used == 0) ? 1 : 0)
#define mp_iseven(a) (((a)->used == 0 || (((a)->dp[0] & 1) == 0)) ? 1 : 0)
#define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? 1 : 0)
/* set to zero */
void mp_zero(mp_int *a);
/* set to a digit */
void mp_set(mp_int *a, mp_digit b);
/* set a 32-bit const */
int mp_set_int(mp_int *a, unsigned long b);
/* grow an int to a given size */
int mp_grow(mp_int *a, int size);
/* init to a given number of digits */
int mp_init_size(mp_int *a, int size);
/* copy, b = a */
int mp_copy(mp_int *a, mp_int *b);
/* inits and copies, a = b */
int mp_init_copy(mp_int *a, mp_int *b);
/* trim unused digits */
void mp_clamp(mp_int *a);
/* ---> digit manipulation <--- */
/* right shift by "b" digits */
void mp_rshd(mp_int *a, int b);
/* left shift by "b" digits */
int mp_lshd(mp_int *a, int b);
/* c = a / 2^b */
int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d);
/* b = a/2 */
int mp_div_2(mp_int *a, mp_int *b);
/* c = a * 2^b */
int mp_mul_2d(mp_int *a, int b, mp_int *c);
/* b = a*2 */
int mp_mul_2(mp_int *a, mp_int *b);
/* c = a mod 2^d */
int mp_mod_2d(mp_int *a, int b, mp_int *c);
/* computes a = 2^b */
int mp_2expt(mp_int *a, int b);
/* makes a pseudo-random int of a given size */
int mp_rand(mp_int *a, int digits);
/* ---> binary operations <--- */
/* c = a XOR b */
int mp_xor(mp_int *a, mp_int *b, mp_int *c);
/* c = a OR b */
int mp_or(mp_int *a, mp_int *b, mp_int *c);
/* c = a AND b */
int mp_and(mp_int *a, mp_int *b, mp_int *c);
/* ---> Basic arithmetic <--- */
/* b = -a */
int mp_neg(mp_int *a, mp_int *b);
/* b = |a| */
int mp_abs(mp_int *a, mp_int *b);
/* compare a to b */
int mp_cmp(mp_int *a, mp_int *b);
/* compare |a| to |b| */
int mp_cmp_mag(mp_int *a, mp_int *b);
/* c = a + b */
int mp_add(mp_int *a, mp_int *b, mp_int *c);
/* c = a - b */
int mp_sub(mp_int *a, mp_int *b, mp_int *c);
/* c = a * b */
int mp_mul(mp_int *a, mp_int *b, mp_int *c);
/* b = a^2 */
int mp_sqr(mp_int *a, mp_int *b);
/* a/b => cb + d == a */
int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
/* c = a mod b, 0 <= c < b */
int mp_mod(mp_int *a, mp_int *b, mp_int *c);
/* ---> single digit functions <--- */
/* compare against a single digit */
int mp_cmp_d(mp_int *a, mp_digit b);
/* c = a + b */
int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
/* c = a - b */
int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
/* c = a * b */
int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
/* a/b => cb + d == a */
int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
/* c = a^b */
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
/* c = a mod b, 0 <= c < b */
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
/* ---> number theory <--- */
/* d = a + b (mod c) */
int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
/* d = a - b (mod c) */
int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
/* d = a * b (mod c) */
int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
/* c = a * a (mod b) */
int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);
/* c = 1/a (mod b) */
int mp_invmod(mp_int *a, mp_int *b, mp_int *c);
/* c = (a, b) */
int mp_gcd(mp_int *a, mp_int *b, mp_int *c);
/* c = [a, b] or (a*b)/(a, b) */
int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
/* finds one of the b'th root of a, such that |c|^b <= |a|
*
* returns error if a < 0 and b is even
*/
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
/* shortcut for square root */
#define mp_sqrt(a, b) mp_n_root(a, 2, b)
/* computes the jacobi c = (a | n) (or Legendre if b is prime) */
int mp_jacobi(mp_int *a, mp_int *n, int *c);
/* used to setup the Barrett reduction for a given modulus b */
int mp_reduce_setup(mp_int *a, mp_int *b);
/* Barrett Reduction, computes a (mod b) with a precomputed value c
*
* Assumes that 0 < a <= b^2, note if 0 > a > -(b^2) then you can merely
* compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
*/
int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
/* setups the montgomery reduction */
int mp_montgomery_setup(mp_int *a, mp_digit *mp);
/* computes xR^-1 == x (mod N) via Montgomery Reduction */
int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
/* d = a^b (mod c) */
int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
/* ---> radix conversion <--- */
int mp_count_bits(mp_int *a);
int mp_unsigned_bin_size(mp_int *a);
int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
int mp_signed_bin_size(mp_int *a);
int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
int mp_to_signed_bin(mp_int *a, unsigned char *b);
int mp_read_radix(mp_int *a, char *str, int radix);
int mp_toradix(mp_int *a, char *str, int radix);
int mp_radix_size(mp_int *a, int radix);
#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
#define mp_raw_size(mp) mp_signed_bin_size(mp)
#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
#define mp_mag_size(mp) mp_unsigned_bin_size(mp)
#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
#define mp_tobinary(M, S) mp_toradix((M), (S), 2)
#define mp_tooctal(M, S) mp_toradix((M), (S), 8)
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
#define mp_tohex(M, S) mp_toradix((M), (S), 16)
/* lowlevel functions, do not call! */
int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int fast_s_mp_sqr(mp_int *a, mp_int *b);
int s_mp_sqr(mp_int *a, mp_int *b);
int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
int mp_karatsuba_sqr(mp_int *a, mp_int *b);
int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y);
void bn_reverse(unsigned char *s, int len);
#ifdef __cplusplus
}
#endif
#endif
Jump to Line
Something went wrong with that request. Please try again.