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kc3-lang/libtommath/tommath.h
Tom St Denis
- tommath.h
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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, 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