/* 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */#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 __cplusplusextern "C" {/* C++ compilers don't like assigning void * to mp_digit * */#define  OPT_CAST  (mp_digit *)#else/* C on the other hand doesn't care */#define  OPT_CAST#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   typedef unsigned char      mp_digit;   typedef unsigned short     mp_word;#elif defined(MP_16BIT)   typedef unsigned short     mp_digit;   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   typedef ulong64            mp_digit;   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   typedef unsigned long      mp_digit;   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 */#ifndef CRYPT   /* default to libc stuff */   #ifndef XMALLOC        #define XMALLOC  malloc       #define XFREE    free       #define XREALLOC realloc       #define XCALLOC  calloc   #endif   /* prototypes for our heap functions */   extern void *XMALLOC(size_t n);   extern void *REALLOC(void *p, size_t n);   extern void *XCALLOC(size_t n, size_t s);   extern void XFREE(void *p);#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 */typedef int           mp_err;/* you'll have to tune these... */extern int KARATSUBA_MUL_CUTOFF,           KARATSUBA_SQR_CUTOFF,           TOOM_MUL_CUTOFF,           TOOM_SQR_CUTOFF;/* various build options */#define MP_PREC                 64     /* default digits of precision *//* define this to use lower memory usage routines (exptmods mostly) *//* #define MP_LOW_MEM *//* 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 */typedef struct  {    int used, alloc, sign;    mp_digit *dp;} mp_int;/* 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);/* 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);/* 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*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 k);/* 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 */extern const mp_digit __prime_tab[];/* 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). */int mp_prime_random(mp_int *a, int t, int size, int bbs, 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, 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, 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 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);void bn_reverse(unsigned char *s, int len);extern const char *mp_s_rmap;#ifdef __cplusplus   }#endif#endif