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Diffstat (limited to 'generic/tclTomMath.h')
| -rw-r--r-- | generic/tclTomMath.h | 836 |
1 files changed, 836 insertions, 0 deletions
diff --git a/generic/tclTomMath.h b/generic/tclTomMath.h new file mode 100644 index 0000000..550dafa --- /dev/null +++ b/generic/tclTomMath.h @@ -0,0 +1,836 @@ +/* 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@gmail.com, 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 |