465 lines
13 KiB
C
465 lines
13 KiB
C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is library that provides for multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library is designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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*/
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#ifndef BN_H_
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#define BN_H_
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#include <stdio.h>
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#include <string.h>
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#include <stdlib.h>
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#include <ctype.h>
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#include <limits.h>
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#undef MIN
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#define MIN(x,y) ((x)<(y)?(x):(y))
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#undef MAX
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#define MAX(x,y) ((x)>(y)?(x):(y))
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#ifdef __cplusplus
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extern "C" {
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/* C++ compilers don't like assigning void * to mp_digit * */
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#define OPT_CAST (mp_digit *)
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#else
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/* C on the other hand doesn't care */
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#define OPT_CAST
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#endif
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/* some default configurations.
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*
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* A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
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* A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
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*
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* At the very least a mp_digit must be able to hold 7 bits
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* [any size beyond that is ok provided it doesn't overflow the data type]
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*/
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#ifdef MP_8BIT
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typedef unsigned char mp_digit;
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typedef unsigned short mp_word;
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#elif defined(MP_16BIT)
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typedef unsigned short mp_digit;
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typedef unsigned long mp_word;
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#elif defined(MP_64BIT)
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/* for GCC only on supported platforms */
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#ifndef CRYPT
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typedef unsigned long long ulong64;
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typedef signed long long long64;
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#endif
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typedef ulong64 mp_digit;
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typedef unsigned long mp_word __attribute__ ((mode(TI)));
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#define DIGIT_BIT 60
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#else
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/* this is the default case, 28-bit digits */
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/* this is to make porting into LibTomCrypt easier :-) */
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#ifndef CRYPT
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#if defined(_MSC_VER) || defined(__BORLANDC__)
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typedef unsigned __int64 ulong64;
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typedef signed __int64 long64;
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#else
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typedef unsigned long long ulong64;
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typedef signed long long long64;
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#endif
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#endif
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typedef unsigned long mp_digit;
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typedef ulong64 mp_word;
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#ifdef MP_31BIT
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#define DIGIT_BIT 31
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#else
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#define DIGIT_BIT 28
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#endif
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#endif
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/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
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#ifndef DIGIT_BIT
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#define DIGIT_BIT ((CHAR_BIT * sizeof(mp_digit) - 1)) /* bits per digit */
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#endif
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#define MP_DIGIT_BIT DIGIT_BIT
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#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
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#define MP_DIGIT_MAX MP_MASK
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/* equalities */
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#define MP_LT -1 /* less than */
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#define MP_EQ 0 /* equal to */
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#define MP_GT 1 /* greater than */
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#define MP_ZPOS 0 /* positive integer */
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#define MP_NEG 1 /* negative */
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#define MP_OKAY 0 /* ok result */
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#define MP_MEM -2 /* out of mem */
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#define MP_VAL -3 /* invalid input */
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#define MP_RANGE MP_VAL
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typedef int mp_err;
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/* you'll have to tune these... */
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extern int KARATSUBA_MUL_CUTOFF,
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KARATSUBA_SQR_CUTOFF,
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TOOM_MUL_CUTOFF,
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TOOM_SQR_CUTOFF;
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/* various build options */
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#define MP_PREC 64 /* default digits of precision (must be power of two) */
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/* define this to use lower memory usage routines (exptmods mostly) */
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/* #define MP_LOW_MEM */
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/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
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#define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
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typedef struct {
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int used, alloc, sign;
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mp_digit *dp;
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} mp_int;
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#define USED(m) ((m)->used)
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#define DIGIT(m,k) ((m)->dp[k])
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#define SIGN(m) ((m)->sign)
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/* ---> init and deinit bignum functions <--- */
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/* init a bignum */
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int mp_init(mp_int *a);
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/* free a bignum */
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void mp_clear(mp_int *a);
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/* init a null terminated series of arguments */
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int mp_init_multi(mp_int *mp, ...);
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/* clear a null terminated series of arguments */
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void mp_clear_multi(mp_int *mp, ...);
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/* exchange two ints */
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void mp_exch(mp_int *a, mp_int *b);
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/* shrink ram required for a bignum */
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int mp_shrink(mp_int *a);
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/* grow an int to a given size */
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int mp_grow(mp_int *a, int size);
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/* init to a given number of digits */
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int mp_init_size(mp_int *a, int size);
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/* ---> Basic Manipulations <--- */
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#define mp_iszero(a) (((a)->used == 0) ? 1 : 0)
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#define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? 1 : 0)
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#define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? 1 : 0)
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/* set to zero */
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void mp_zero(mp_int *a);
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/* set to a digit */
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void mp_set(mp_int *a, mp_digit b);
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/* set a 32-bit const */
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int mp_set_int(mp_int *a, unsigned int b);
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/* copy, b = a */
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int mp_copy(mp_int *a, mp_int *b);
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/* inits and copies, a = b */
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int mp_init_copy(mp_int *a, mp_int *b);
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/* trim unused digits */
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void mp_clamp(mp_int *a);
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/* ---> digit manipulation <--- */
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/* right shift by "b" digits */
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void mp_rshd(mp_int *a, int b);
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/* left shift by "b" digits */
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int mp_lshd(mp_int *a, int b);
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/* c = a / 2**b */
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int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d);
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/* b = a/2 */
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int mp_div_2(mp_int *a, mp_int *b);
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/* c = a * 2**b */
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int mp_mul_2d(mp_int *a, int b, mp_int *c);
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/* b = a*2 */
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int mp_mul_2(mp_int *a, mp_int *b);
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/* c = a mod 2**d */
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int mp_mod_2d(mp_int *a, int b, mp_int *c);
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/* computes a = 2**b */
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int mp_2expt(mp_int *a, int b);
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/* Counts the number of lsbs which are zero before the first zero bit */
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int mp_cnt_lsb(mp_int *a);
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/* makes a pseudo-random int of a given size */
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int mp_rand(mp_int *a, int digits);
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/* ---> binary operations <--- */
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/* c = a XOR b */
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int mp_xor(mp_int *a, mp_int *b, mp_int *c);
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/* c = a OR b */
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int mp_or(mp_int *a, mp_int *b, mp_int *c);
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/* c = a AND b */
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int mp_and(mp_int *a, mp_int *b, mp_int *c);
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/* ---> Basic arithmetic <--- */
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/* b = -a */
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int mp_neg(mp_int *a, mp_int *b);
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/* b = |a| */
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int mp_abs(mp_int *a, mp_int *b);
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/* compare a to b */
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int mp_cmp(mp_int *a, mp_int *b);
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/* compare |a| to |b| */
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int mp_cmp_mag(mp_int *a, mp_int *b);
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/* c = a + b */
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int mp_add(mp_int *a, mp_int *b, mp_int *c);
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/* c = a - b */
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int mp_sub(mp_int *a, mp_int *b, mp_int *c);
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/* c = a * b */
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int mp_mul(mp_int *a, mp_int *b, mp_int *c);
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/* b = a*a */
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int mp_sqr(mp_int *a, mp_int *b);
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/* a/b => cb + d == a */
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int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
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/* c = a mod b, 0 <= c < b */
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int mp_mod(mp_int *a, mp_int *b, mp_int *c);
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/* ---> single digit functions <--- */
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/* compare against a single digit */
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int mp_cmp_d(mp_int *a, mp_digit b);
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/* c = a + b */
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int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
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/* c = a - b */
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int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
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/* c = a * b */
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int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
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/* a/b => cb + d == a */
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int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
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/* a/3 => 3c + d == a */
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int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
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/* c = a**b */
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int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
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/* c = a mod b, 0 <= c < b */
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int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
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/* ---> number theory <--- */
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/* d = a + b (mod c) */
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int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
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/* d = a - b (mod c) */
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int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
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/* d = a * b (mod c) */
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int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
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/* c = a * a (mod b) */
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int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);
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/* c = 1/a (mod b) */
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int mp_invmod(mp_int *a, mp_int *b, mp_int *c);
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/* c = (a, b) */
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int mp_gcd(mp_int *a, mp_int *b, mp_int *c);
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/* c = [a, b] or (a*b)/(a, b) */
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int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
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/* finds one of the b'th root of a, such that |c|**b <= |a|
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*
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* returns error if a < 0 and b is even
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*/
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int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
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/* shortcut for square root */
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#define mp_sqrt(a, b) mp_n_root(a, 2, b)
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/* computes the jacobi c = (a | n) (or Legendre if b is prime) */
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int mp_jacobi(mp_int *a, mp_int *n, int *c);
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/* used to setup the Barrett reduction for a given modulus b */
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int mp_reduce_setup(mp_int *a, mp_int *b);
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/* Barrett Reduction, computes a (mod b) with a precomputed value c
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*
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* Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
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* compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
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*/
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int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
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/* setups the montgomery reduction */
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int mp_montgomery_setup(mp_int *a, mp_digit *mp);
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/* computes a = B**n mod b without division or multiplication useful for
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* normalizing numbers in a Montgomery system.
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*/
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int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
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/* computes x/R == x (mod N) via Montgomery Reduction */
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int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
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/* returns 1 if a is a valid DR modulus */
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int mp_dr_is_modulus(mp_int *a);
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/* sets the value of "d" required for mp_dr_reduce */
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void mp_dr_setup(mp_int *a, mp_digit *d);
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/* reduces a modulo b using the Diminished Radix method */
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int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
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/* returns true if a can be reduced with mp_reduce_2k */
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int mp_reduce_is_2k(mp_int *a);
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/* determines k value for 2k reduction */
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int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
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/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
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int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit k);
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/* d = a**b (mod c) */
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int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
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/* ---> Primes <--- */
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/* number of primes */
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#ifdef MP_8BIT
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#define PRIME_SIZE 31
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#else
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#define PRIME_SIZE 256
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#endif
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/* table of first PRIME_SIZE primes */
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extern const mp_digit __prime_tab[];
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/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
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int mp_prime_is_divisible(mp_int *a, int *result);
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/* performs one Fermat test of "a" using base "b".
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* Sets result to 0 if composite or 1 if probable prime
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*/
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int mp_prime_fermat(mp_int *a, mp_int *b, int *result);
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/* performs one Miller-Rabin test of "a" using base "b".
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* Sets result to 0 if composite or 1 if probable prime
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*/
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int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
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/* performs t rounds of Miller-Rabin on "a" using the first
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* t prime bases. Also performs an initial sieve of trial
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* division. Determines if "a" is prime with probability
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* of error no more than (1/4)**t.
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*
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* Sets result to 1 if probably prime, 0 otherwise
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*/
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int mp_prime_is_prime(mp_int *a, int t, int *result);
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/* finds the next prime after the number "a" using "t" trials
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* of Miller-Rabin.
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*/
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int mp_prime_next_prime(mp_int *a, int t);
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/* ---> radix conversion <--- */
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int mp_count_bits(mp_int *a);
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int mp_unsigned_bin_size(mp_int *a);
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int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
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int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
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int mp_signed_bin_size(mp_int *a);
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int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
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int mp_to_signed_bin(mp_int *a, unsigned char *b);
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int mp_read_radix(mp_int *a, char *str, int radix);
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int mp_toradix(mp_int *a, char *str, int radix);
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int mp_radix_size(mp_int *a, int radix);
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int mp_fread(mp_int *a, int radix, FILE *stream);
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int mp_fwrite(mp_int *a, int radix, FILE *stream);
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#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
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#define mp_raw_size(mp) mp_signed_bin_size(mp)
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#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
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#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
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#define mp_mag_size(mp) mp_unsigned_bin_size(mp)
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#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
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#define mp_tobinary(M, S) mp_toradix((M), (S), 2)
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#define mp_tooctal(M, S) mp_toradix((M), (S), 8)
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#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
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#define mp_tohex(M, S) mp_toradix((M), (S), 16)
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/* lowlevel functions, do not call! */
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int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
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int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
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#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
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int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
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int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
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int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
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int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
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int fast_s_mp_sqr(mp_int *a, mp_int *b);
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int s_mp_sqr(mp_int *a, mp_int *b);
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int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
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int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
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int mp_karatsuba_sqr(mp_int *a, mp_int *b);
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int mp_toom_sqr(mp_int *a, mp_int *b);
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int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
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int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
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int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
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int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
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void bn_reverse(unsigned char *s, int len);
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extern const char *mp_s_rmap;
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#ifdef __cplusplus
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}
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#endif
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#endif
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