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- /* 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, [email protected], 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 __cplusplus
- extern "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
- #define DIGIT_BIT 31
- #else
- #define DIGIT_BIT 28
- #define MP_28BIT
- #endif
- #endif
- /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
- #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,
- TOOM_MUL_CUTOFF,
- TOOM_SQR_CUTOFF;
- /* various build options */
- #define MP_PREC 64 /* default digits of precision (must be power of two) */
- /* define this to use lower memory usage routines (exptmods mostly) */
- /* #define MP_LOW_MEM */
- /* have no cpu based mult? */
- /* #define SLOW_MULT */
- #ifdef SLOW_MULT
- #define MULT(x, y) s_mp_mult((x), (y))
- mp_word s_mp_mult(mp_digit, mp_digit);
- #else
- #define MULT(x, y) (((mp_word)(x)) * ((mp_word)(y)))
- #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))
- 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);
- /* 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) ? 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 int 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);
- /* 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);
- /* 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);
- /* 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.
- */
- int mp_prime_next_prime(mp_int *a, int t);
- /* ---> 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 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
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