/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was 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, [email protected], http://math.libtomcrypt.com
*/
#ifndef BN_H_
#define BN_H_
#include <tclTomMathDecls.h>
#ifndef MODULE_SCOPE
#define MODULE_SCOPE extern
#endif
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <ctype.h>
#include <limits.h>
#ifndef MIN
#define MIN(x,y) ((x)<(y)?(x):(y))
#endif
#ifndef MAX
#define MAX(x,y) ((x)>(y)?(x):(y))
#endif
#ifdef __cplusplus
extern "C" {
/* C++ compilers don't like assigning void * to mp_digit * */
#define OPT_CAST(x) (x *)
#else
/* C on the other hand doesn't care */
#define OPT_CAST(x)
#endif
/* detect 64-bit mode if possible */
#if defined(NEVER) /* 128-bit ints fail in too many places */
#if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
#define MP_64BIT
#endif
#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 doesn't overflow the data type]
*/
#ifdef MP_8BIT
#ifndef MP_DIGIT_DECLARED
typedef unsigned char mp_digit;
#define MP_DIGIT_DECLARED
#endif
typedef unsigned short mp_word;
#elif defined(MP_16BIT)
#ifndef MP_DIGIT_DECLARED
typedef unsigned short mp_digit;
#define MP_DIGIT_DECLARED
#endif
typedef unsigned long mp_word;
#elif defined(MP_64BIT)
/* for GCC only on supported platforms */
#ifndef CRYPT
typedef unsigned long long ulong64;
typedef signed long long long64;
#endif
#ifndef MP_DIGIT_DECLARED
typedef unsigned long mp_digit;
#define MP_DIGIT_DECLARED
#endif
typedef unsigned long mp_word __attribute__ ((mode(TI)));
#define DIGIT_BIT 60
#else
/* this is the default case, 28-bit digits */
/* this is to make porting into LibTomCrypt easier :-) */
#ifndef CRYPT
#if defined(_MSC_VER) || defined(__BORLANDC__)
typedef unsigned __int64 ulong64;
typedef signed __int64 long64;
#else
typedef unsigned long long ulong64;
typedef signed long long long64;
#endif
#endif
#ifndef MP_DIGIT_DECLARED
typedef unsigned int mp_digit;
#define MP_DIGIT_DECLARED
#endif
typedef ulong64 mp_word;
#ifdef MP_31BIT
/* this is an extension that uses 31-bit digits */
#define DIGIT_BIT 31
#else
/* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
#define DIGIT_BIT 28
#define MP_28BIT
#endif
#endif
/* define heap macros */
#if 0 /* these are macros in tclTomMathDecls.h */
#ifndef CRYPT
/* default to libc stuff */
#ifndef XMALLOC
#define XMALLOC malloc
#define XFREE free
#define XREALLOC realloc
#define XCALLOC calloc
#else
/* prototypes for our heap functions */
extern void *XMALLOC(size_t n);
extern void *XREALLOC(void *p, size_t n);
extern void *XCALLOC(size_t n, size_t s);
extern void XFREE(void *p);
#endif
#endif
#endif
/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
#ifndef DIGIT_BIT
#define DIGIT_BIT ((int)((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
#define MP_YES 1 /* yes response */
#define MP_NO 0 /* no response */
/* Primality generation flags */
#define LTM_PRIME_BBS 0x0001 /* BBS style prime */
#define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
#define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
typedef int mp_err;
/* you'll have to tune these... */
#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE int KARATSUBA_MUL_CUTOFF,
KARATSUBA_SQR_CUTOFF,
TOOM_MUL_CUTOFF,
TOOM_SQR_CUTOFF;
#endif
/* define this to use lower memory usage routines (exptmods mostly) */
/* #define MP_LOW_MEM */
/* default precision */
#ifndef MP_PREC
#ifndef MP_LOW_MEM
#define MP_PREC 32 /* default digits of precision */
#else
#define MP_PREC 8 /* default digits of precision */
#endif
#endif
/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
#define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
/* the infamous mp_int structure */
#ifndef MP_INT_DECLARED
#define MP_INT_DECLARED
typedef struct mp_int mp_int;
#endif
struct mp_int {
int used, alloc, sign;
mp_digit *dp;
};
/* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
#define USED(m) ((m)->used)
#define DIGIT(m,k) ((m)->dp[(k)])
#define SIGN(m) ((m)->sign)
/* error code to char* string */
/*
char *mp_error_to_string(int code);
*/
/* ---> init and deinit bignum functions <--- */
/* init a bignum */
/*
int mp_init(mp_int *a);
*/
/* free a bignum */
/*
void mp_clear(mp_int *a);
*/
/* init a null terminated series of arguments */
/*
int mp_init_multi(mp_int *mp, ...);
*/
/* clear a null terminated series of arguments */
/*
void mp_clear_multi(mp_int *mp, ...);
*/
/* exchange two ints */
/*
void mp_exch(mp_int *a, mp_int *b);
*/
/* shrink ram required for a bignum */
/*
int mp_shrink(mp_int *a);
*/
/* 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);
*/
/* ---> Basic Manipulations <--- */
#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
#define mp_iseven(a) (((a)->used == 0 || (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
#define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
/* 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);
*/
/* get a 32-bit value */
unsigned long mp_get_int(mp_int * a);
/* initialize and set a digit */
/*
int mp_init_set (mp_int * a, mp_digit b);
*/
/* initialize and set 32-bit value */
/*
int mp_init_set_int (mp_int * a, unsigned long b);
*/
/* 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);
*/
/* Counts the number of lsbs which are zero before the first zero bit */
/*
int mp_cnt_lsb(mp_int *a);
*/
/* I Love Earth! */
/* 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*a */
/*
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);
*/
/* a/3 => 3c + d == a */
/*
int mp_div_3(mp_int *a, 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);
*/
/* produces value such that U1*a + U2*b = U3 */
/*
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
*/
/* 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);
*/
/* special sqrt algo */
/*
int mp_sqrt(mp_int *arg, mp_int *ret);
*/
/* is number a square? */
/*
int mp_is_square(mp_int *arg, int *ret);
*/
/* 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*b, note if 0 > a > -(b*b) 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 a = B**n mod b without division or multiplication useful for
* normalizing numbers in a Montgomery system.
*/
/*
int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
*/
/* computes x/R == x (mod N) via Montgomery Reduction */
/*
int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
*/
/* returns 1 if a is a valid DR modulus */
/*
int mp_dr_is_modulus(mp_int *a);
*/
/* sets the value of "d" required for mp_dr_reduce */
/*
void mp_dr_setup(mp_int *a, mp_digit *d);
*/
/* reduces a modulo b using the Diminished Radix method */
/*
int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
*/
/* returns true if a can be reduced with mp_reduce_2k */
/*
int mp_reduce_is_2k(mp_int *a);
*/
/* determines k value for 2k reduction */
/*
int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
*/
/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
/*
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
*/
/* returns true if a can be reduced with mp_reduce_2k_l */
/*
int mp_reduce_is_2k_l(mp_int *a);
*/
/* determines k value for 2k reduction */
/*
int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
*/
/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
/*
int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
*/
/* d = a**b (mod c) */
/*
int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
*/
/* ---> Primes <--- */
/* number of primes */
#ifdef MP_8BIT
#define PRIME_SIZE 31
#else
#define PRIME_SIZE 256
#endif
/* table of first PRIME_SIZE primes */
#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE const mp_digit ltm_prime_tab[];
#endif
/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
/*
int mp_prime_is_divisible(mp_int *a, int *result);
*/
/* performs one Fermat test of "a" using base "b".
* Sets result to 0 if composite or 1 if probable prime
*/
/*
int mp_prime_fermat(mp_int *a, mp_int *b, int *result);
*/
/* performs one Miller-Rabin test of "a" using base "b".
* Sets result to 0 if composite or 1 if probable prime
*/
/*
int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
*/
/* This gives [for a given bit size] the number of trials required
* such that Miller-Rabin gives a prob of failure lower than 2^-96
*/
/*
int mp_prime_rabin_miller_trials(int size);
*/
/* performs t rounds of Miller-Rabin on "a" using the first
* t prime bases. Also performs an initial sieve of trial
* division. Determines if "a" is prime with probability
* of error no more than (1/4)**t.
*
* Sets result to 1 if probably prime, 0 otherwise
*/
/*
int mp_prime_is_prime(mp_int *a, int t, int *result);
*/
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
*
* bbs_style = 1 means the prime must be congruent to 3 mod 4
*/
/*
int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
*/
/* makes a truly random prime of a given size (bytes),
* call with bbs = 1 if you want it to be congruent to 3 mod 4
*
* You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
* have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
* so it can be NULL
*
* The prime generated will be larger than 2^(8*size).
*/
#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)
/* makes a truly random prime of a given size (bits),
*
* Flags are as follows:
*
* LTM_PRIME_BBS - make prime congruent to 3 mod 4
* LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
* LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
* LTM_PRIME_2MSB_ON - make the 2nd highest bit one
*
* You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
* have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
* so it can be NULL
*
*/
/*
int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat);
*/
/* ---> 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, const unsigned char *b, int c);
*/
/*
int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
*/
/*
int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
*/
/*
int mp_signed_bin_size(mp_int *a);
*/
/*
int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
*/
/*
int mp_to_signed_bin(mp_int *a, unsigned char *b);
*/
/*
int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
*/
/*
int mp_read_radix(mp_int *a, const char *str, int radix);
*/
/*
int mp_toradix(mp_int *a, char *str, int radix);
*/
/*
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
*/
/*
int mp_radix_size(mp_int *a, int radix, int *size);
*/
/*
int mp_fread(mp_int *a, int radix, FILE *stream);
*/
/*
int mp_fwrite(mp_int *a, int radix, FILE *stream);
*/
#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_toom_mul(mp_int *a, mp_int *b, mp_int *c);
*/
/*
int mp_karatsuba_sqr(mp_int *a, mp_int *b);
*/
/*
int mp_toom_sqr(mp_int *a, mp_int *b);
*/
/*
int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
*/
/*
int mp_invmod_slow (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, int mode);
*/
/*
int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
*/
/*
void bn_reverse(unsigned char *s, int len);
*/
#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE const char *mp_s_rmap;
#endif
#ifdef __cplusplus
}
#endif
#endif
/* $Source: /cvsroot/tcl/tcl/generic/tclTomMath.h,v $ */
/* Based on Tom's version 1.8 */
/* $Revision: 1.10.4.1 $ */
/* $Date: 2009/10/06 16:30:39 $ */
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