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Diffstat (limited to 'generic/tclTomMath.h')
| -rw-r--r-- | generic/tclTomMath.h | 813 |
1 files changed, 813 insertions, 0 deletions
diff --git a/generic/tclTomMath.h b/generic/tclTomMath.h new file mode 100644 index 0000000..df54ff5 --- /dev/null +++ b/generic/tclTomMath.h @@ -0,0 +1,813 @@ +/* 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, tstdenis82@gmail.com, http://math.libtomcrypt.com + */ +#ifndef BN_H_ +#define BN_H_ + +#include "tclTomMathDecls.h" +#ifndef MODULE_SCOPE +#define MODULE_SCOPE extern +#endif + + + +#ifdef __cplusplus +extern "C" { +#endif + +/* detect 64-bit mode if possible */ +#if defined(NEVER) /* 128-bit ints fail in too many places */ +# if !(defined(MP_32BIT) || 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 uint8_t mp_digit; +#define MP_DIGIT_DECLARED +#endif +#ifndef MP_WORD_DECLARED +typedef uint16_t mp_word; +#define MP_WORD_DECLARED +#endif +# define MP_SIZEOF_MP_DIGIT 1 +# ifdef DIGIT_BIT +# error You must not define DIGIT_BIT when using MP_8BIT +# endif +#elif defined(MP_16BIT) +#ifndef MP_DIGIT_DECLARED +typedef uint16_t mp_digit; +#define MP_DIGIT_DECLARED +#endif +#ifndef MP_WORD_DECLARED +typedef uint32_t mp_word; +#define MP_WORD_DECLARED +#endif +# define MP_SIZEOF_MP_DIGIT 2 +# ifdef DIGIT_BIT +# error You must not define DIGIT_BIT when using MP_16BIT +# endif +#elif defined(MP_64BIT) +/* for GCC only on supported platforms */ +#ifndef MP_DIGIT_DECLARED +typedef uint64_t mp_digit; +#define MP_DIGIT_DECLARED +#endif +# if defined(_WIN32) +#ifndef MP_WORD_DECLARED +typedef unsigned __int128 mp_word; +#define MP_WORD_DECLARED +#endif +# elif defined(__GNUC__) +typedef unsigned long mp_word __attribute__((mode(TI))); +# else +/* it seems you have a problem + * but we assume you can somewhere define your own uint128_t */ +#ifndef MP_WORD_DECLARED +typedef uint128_t mp_word; +#define MP_WORD_DECLARED +#endif +# endif + +# define DIGIT_BIT 60 +#else +/* this is the default case, 28-bit digits */ + +/* this is to make porting into LibTomCrypt easier :-) */ +#ifndef MP_DIGIT_DECLARED +typedef uint32_t mp_digit; +#define MP_DIGIT_DECLARED +#endif +#ifndef MP_WORD_DECLARED +typedef uint64_t mp_word; +#define MP_WORD_DECLARED +#endif + +# 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 + +/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ +#ifndef DIGIT_BIT +# define DIGIT_BIT (((CHAR_BIT * MP_SIZEOF_MP_DIGIT) - 1)) /* bits per digit */ +typedef uint_least32_t mp_min_u32; +#else +typedef mp_digit mp_min_u32; +#endif + +/* use arc4random on platforms that support it */ +#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__) +# define MP_GEN_RANDOM() arc4random() +# define MP_GEN_RANDOM_MAX 0xffffffff +#endif + +/* use rand() as fall-back if there's no better rand function */ +#ifndef MP_GEN_RANDOM +# define MP_GEN_RANDOM() rand() +# define MP_GEN_RANDOM_MAX RAND_MAX +#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 */ +const 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] & 1u) == 0u)) ? MP_YES : MP_NO) +#define mp_isodd(a) ((((a)->used > 0) && (((a)->dp[0] & 1u) == 1u)) ? MP_YES : MP_NO) +#define mp_isneg(a) (((a)->sign != MP_ZPOS) ? 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); +*/ + +/* set a platform dependent unsigned long value */ +/* +int mp_set_long(mp_int *a, unsigned long b); +*/ + +/* set a platform dependent unsigned long long value */ +/* +int mp_set_long_long(mp_int *a, unsigned long long b); +*/ + +/* get a 32-bit value */ +/* +unsigned long mp_get_int(const mp_int *a); +*/ + +/* get a platform dependent unsigned long value */ +/* +unsigned long mp_get_long(const mp_int *a); +*/ + +/* get a platform dependent unsigned long long value */ +/* +unsigned long long mp_get_long_long(const 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(const mp_int *a, mp_int *b); +*/ + +/* inits and copies, a = b */ +/* +int mp_init_copy(mp_int *a, const mp_int *b); +*/ + +/* trim unused digits */ +/* +void mp_clamp(mp_int *a); +*/ + +/* import binary data */ +/* +int mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails, const void *op); +*/ + +/* export binary data */ +/* +int mp_export(void *rop, size_t *countp, int order, size_t size, int endian, size_t nails, const mp_int *op); +*/ + +/* ---> 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, implemented as c = a >> b */ +/* +int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d); +*/ + +/* b = a/2 */ +/* +int mp_div_2(const mp_int *a, mp_int *b); +*/ + +/* c = a * 2**b, implemented as c = a << b */ +/* +int mp_mul_2d(const mp_int *a, int b, mp_int *c); +*/ + +/* b = a*2 */ +/* +int mp_mul_2(const mp_int *a, mp_int *b); +*/ + +/* c = a mod 2**b */ +/* +int mp_mod_2d(const 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(const 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(const mp_int *a, const mp_int *b, mp_int *c); +*/ + +/* c = a OR b */ +/* +int mp_or(const mp_int *a, const mp_int *b, mp_int *c); +*/ + +/* c = a AND b */ +/* +int mp_and(const mp_int *a, const mp_int *b, mp_int *c); +*/ + +/* ---> Basic arithmetic <--- */ + +/* b = -a */ +/* +int mp_neg(const mp_int *a, mp_int *b); +*/ + +/* b = |a| */ +/* +int mp_abs(const mp_int *a, mp_int *b); +*/ + +/* compare a to b */ +/* +int mp_cmp(const mp_int *a, const mp_int *b); +*/ + +/* compare |a| to |b| */ +/* +int mp_cmp_mag(const mp_int *a, const mp_int *b); +*/ + +/* c = a + b */ +/* +int mp_add(const mp_int *a, const mp_int *b, mp_int *c); +*/ + +/* c = a - b */ +/* +int mp_sub(const mp_int *a, const mp_int *b, mp_int *c); +*/ + +/* c = a * b */ +/* +int mp_mul(const mp_int *a, const mp_int *b, mp_int *c); +*/ + +/* b = a*a */ +/* +int mp_sqr(const mp_int *a, mp_int *b); +*/ + +/* a/b => cb + d == a */ +/* +int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d); +*/ + +/* c = a mod b, 0 <= c < b */ +/* +int mp_mod(const mp_int *a, const mp_int *b, mp_int *c); +*/ + +/* ---> single digit functions <--- */ + +/* compare against a single digit */ +/* +int mp_cmp_d(const mp_int *a, mp_digit b); +*/ + +/* c = a + b */ +/* +int mp_add_d(const mp_int *a, mp_digit b, mp_int *c); +*/ + +/* c = a - b */ +/* +int mp_sub_d(const mp_int *a, mp_digit b, mp_int *c); +*/ + +/* c = a * b */ +/* +int mp_mul_d(const mp_int *a, mp_digit b, mp_int *c); +*/ + +/* a/b => cb + d == a */ +/* +int mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d); +*/ + +/* a/3 => 3c + d == a */ +/* +int mp_div_3(const mp_int *a, mp_int *c, mp_digit *d); +*/ + +/* c = a**b */ +/* +int mp_expt_d(const mp_int *a, mp_digit b, mp_int *c); +*/ +/* +int mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast); +*/ + +/* c = a mod b, 0 <= c < b */ +/* +int mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c); +*/ + +/* ---> number theory <--- */ + +/* d = a + b (mod c) */ +/* +int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); +*/ + +/* d = a - b (mod c) */ +/* +int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); +*/ + +/* d = a * b (mod c) */ +/* +int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); +*/ + +/* c = a * a (mod b) */ +/* +int mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c); +*/ + +/* c = 1/a (mod b) */ +/* +int mp_invmod(const mp_int *a, const mp_int *b, mp_int *c); +*/ + +/* c = (a, b) */ +/* +int mp_gcd(const mp_int *a, const mp_int *b, mp_int *c); +*/ + +/* produces value such that U1*a + U2*b = U3 */ +/* +int mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3); +*/ + +/* c = [a, b] or (a*b)/(a, b) */ +/* +int mp_lcm(const mp_int *a, const 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(const mp_int *a, mp_digit b, mp_int *c); +*/ +/* +int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast); +*/ + +/* special sqrt algo */ +/* +int mp_sqrt(const mp_int *arg, mp_int *ret); +*/ + +/* special sqrt (mod prime) */ +/* +int mp_sqrtmod_prime(const mp_int *arg, const mp_int *prime, mp_int *ret); +*/ + +/* is number a square? */ +/* +int mp_is_square(const mp_int *arg, int *ret); +*/ + +/* computes the jacobi c = (a | n) (or Legendre if b is prime) */ +/* +int mp_jacobi(const mp_int *a, const mp_int *n, int *c); +*/ + +/* used to setup the Barrett reduction for a given modulus b */ +/* +int mp_reduce_setup(mp_int *a, const 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, const mp_int *b, const mp_int *c); +*/ + +/* setups the montgomery reduction */ +/* +int mp_montgomery_setup(const 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, const mp_int *b); +*/ + +/* computes x/R == x (mod N) via Montgomery Reduction */ +/* +int mp_montgomery_reduce(mp_int *a, const mp_int *m, mp_digit mp); +*/ + +/* returns 1 if a is a valid DR modulus */ +/* +int mp_dr_is_modulus(const mp_int *a); +*/ + +/* sets the value of "d" required for mp_dr_reduce */ +/* +void mp_dr_setup(const mp_int *a, mp_digit *d); +*/ + +/* reduces a modulo b using the Diminished Radix method */ +/* +int mp_dr_reduce(mp_int *a, const mp_int *b, mp_digit mp); +*/ + +/* returns true if a can be reduced with mp_reduce_2k */ +/* +int mp_reduce_is_2k(const mp_int *a); +*/ + +/* determines k value for 2k reduction */ +/* +int mp_reduce_2k_setup(const 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, const mp_int *n, mp_digit d); +*/ + +/* returns true if a can be reduced with mp_reduce_2k_l */ +/* +int mp_reduce_is_2k_l(const mp_int *a); +*/ + +/* determines k value for 2k reduction */ +/* +int mp_reduce_2k_setup_l(const 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, const mp_int *n, const mp_int *d); +*/ + +/* d = a**b (mod c) */ +/* +int mp_exptmod(const mp_int *a, const mp_int *b, const 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[PRIME_SIZE]; +#endif + +/* result=1 if a is divisible by one of the first PRIME_SIZE primes */ +/* +int mp_prime_is_divisible(const 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(const mp_int *a, const 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(const mp_int *a, const 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(const 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_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(const mp_int *a); +*/ + +/* +int mp_unsigned_bin_size(const mp_int *a); +*/ +/* +int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); +*/ +/* +int mp_to_unsigned_bin(const mp_int *a, unsigned char *b); +*/ +/* +int mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen); +*/ + +/* +int mp_signed_bin_size(const mp_int *a); +*/ +/* +int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); +*/ +/* +int mp_to_signed_bin(const mp_int *a, unsigned char *b); +*/ +/* +int mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen); +*/ + +/* +int mp_read_radix(mp_int *a, const char *str, int radix); +*/ +/* +int mp_toradix(const mp_int *a, char *str, int radix); +*/ +/* +int mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen); +*/ +/* +int mp_radix_size(const mp_int *a, int radix, int *size); +*/ + +#ifndef LTM_NO_FILE +/* +int mp_fread(mp_int *a, int radix, FILE *stream); +*/ +/* +int mp_fwrite(const mp_int *a, int radix, FILE *stream); +*/ +#endif + +#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) + +#ifdef __cplusplus +} +#endif + +#endif + + +/* ref: $Format:%D$ */ +/* git commit: $Format:%H$ */ +/* commit time: $Format:%ai$ */ + |