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tommath/tommath.h

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/* 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.
*
* SPDX-License-Identifier: Unlicense
*/
#ifndef BN_H_
#define BN_H_
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include "tommath_class.h"
#ifdef __cplusplus
extern "C" {
#endif
/* MS Visual C++ doesn't have a 128bit type for words, so fall back to 32bit MPI's (where words are 64bit) */
#if defined(_MSC_VER) || defined(__LLP64__) || defined(__e2k__) || defined(__LCC__)
# define MP_32BIT
#endif
/* detect 64-bit mode if possible */
#if defined(__x86_64__) || defined(_M_X64) || defined(_M_AMD64) || \
defined(__powerpc64__) || defined(__ppc64__) || defined(__PPC64__) || \
defined(__s390x__) || defined(__arch64__) || defined(__aarch64__) || \
defined(__sparcv9) || defined(__sparc_v9__) || defined(__sparc64__) || \
defined(__ia64) || defined(__ia64__) || defined(__itanium__) || defined(_M_IA64) || \
defined(__LP64__) || defined(_LP64) || defined(__64BIT__)
# if !(defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT))
# if defined(__GNUC__)
/* we support 128bit integers only via: __attribute__((mode(TI))) */
# define MP_64BIT
# else
/* otherwise we fall back to MP_32BIT even on 64bit platforms */
# define MP_32BIT
# endif
# 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
typedef uint8_t mp_digit;
typedef uint16_t mp_word;
# 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)
typedef uint16_t mp_digit;
typedef uint32_t mp_word;
# 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 */
typedef uint64_t 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 :-) */
typedef uint32_t mp_digit;
typedef uint64_t 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
/* 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
#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_ITER -4 /* Max. iterations reached */
#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... */
extern int KARATSUBA_MUL_CUTOFF,
KARATSUBA_SQR_CUTOFF,
TOOM_MUL_CUTOFF,
TOOM_SQR_CUTOFF;
/* 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 (1u << (((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 */
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 double */
int mp_set_double(mp_int *a, double 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 double */
double mp_get_double(const mp_int *a);
/* 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 mp_int of a given size */
int mp_rand(mp_int *a, int digits);
/* makes a pseudo-random small int of a given size */
int mp_rand_digit(mp_digit *r);
#ifdef MP_PRNG_ENABLE_LTM_RNG
/* A last resort to provide random data on systems without any of the other
* implemented ways to gather entropy.
* It is compatible with `rng_get_bytes()` from libtomcrypt so you could
* provide that one and then set `ltm_rng = rng_get_bytes;` */
extern unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void));
extern void (*ltm_rng_callback)(void);
#endif
/* ---> 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);
/* Checks the bit at position b and returns MP_YES
if the bit is 1, MP_NO if it is 0 and MP_VAL
in case of error */
int mp_get_bit(const mp_int *a, int b);
/* c = a XOR b (two complement) */
int mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c);
/* c = a OR b (two complement) */
int mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c);
/* c = a AND b (two complement) */
int mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c);
/* right shift (two complement) */
int mp_tc_div_2d(const mp_int *a, int b, mp_int *c);
/* ---> Basic arithmetic <--- */
/* b = ~a */
int mp_complement(const mp_int *a, mp_int *b);
/* 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 *n, 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);
/* computes the Kronecker symbol c = (a | p) (like jacobi() but with {a,p} in Z */
int mp_kronecker(const mp_int *a, const mp_int *p, 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 < x <= m*m, note if 0 > x > -(m*m) then you can merely
* compute the reduction as -1 * mp_reduce(mp_abs(x)) [pseudo code].
*/
int mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu);
/* setups the montgomery reduction */
int mp_montgomery_setup(const mp_int *n, mp_digit *rho);
/* 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 *x, const mp_int *n, mp_digit rho);
/* 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 n using the Diminished Radix method */
int mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k);
/* 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);
/* Y = G**X (mod P) */
int mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y);
/* ---> 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 ltm_prime_tab[PRIME_SIZE];
/* 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 one strong Lucas-Selfridge test of "a".
* Sets result to 0 if composite or 1 if probable prime
*/
int mp_prime_strong_lucas_selfridge(const mp_int *a, int *result);
/* performs one Frobenius test of "a" as described by Paul Underwood.
* Sets result to 0 if composite or 1 if probable prime
*/
int mp_prime_frobenius_underwood(const mp_int *N, int *result);
/* performs t random rounds of Miller-Rabin on "a" additional to
* bases 2 and 3. Also performs an initial sieve of trial
* division. Determines if "a" is prime with probability
* of error no more than (1/4)**t.
* Both a strong Lucas-Selfridge to complete the BPSW test
* and a separate Frobenius test are available at compile time.
* With t<0 a deterministic test is run for primes up to
* 318665857834031151167461. With t<13 (abs(t)-13) additional
* tests with sequential small primes are run starting at 43.
* Is Fips 186.4 compliant if called with t as computed by
* mp_prime_rabin_miller_trials();
*
* 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: $Format:%ai$ */
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