adbadc70f4
Header files which are located in the same directory that the file from where it is included must be included using `" "`, not `< >`. Otherwise the compiler (gcc 5) cannot understand `#include <tommath_class.h>` in `/usr/include/tommath/tommath.h`.
588 lines
18 KiB
C
588 lines
18 KiB
C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is a library that provides multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library was designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*/
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#ifndef BN_H_
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#define BN_H_
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#include <stdio.h>
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#include <stdlib.h>
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#include <stdint.h>
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#include <limits.h>
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#include "tommath_class.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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/* MS Visual C++ doesn't have a 128bit type for words, so fall back to 32bit MPI's (where words are 64bit) */
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#if defined(_MSC_VER) || defined(__LLP64__) || defined(__e2k__) || defined(__LCC__)
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# define MP_32BIT
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#endif
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/* detect 64-bit mode if possible */
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#if defined(__x86_64__) || defined(_M_X64) || defined(_M_AMD64) || \
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defined(__powerpc64__) || defined(__ppc64__) || defined(__PPC64__) || \
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defined(__s390x__) || defined(__arch64__) || defined(__aarch64__) || \
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defined(__sparcv9) || defined(__sparc_v9__) || defined(__sparc64__) || \
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defined(__ia64) || defined(__ia64__) || defined(__itanium__) || defined(_M_IA64) || \
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defined(__LP64__) || defined(_LP64) || defined(__64BIT__)
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# if !(defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT))
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# if defined(__GNUC__)
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/* we support 128bit integers only via: __attribute__((mode(TI))) */
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# define MP_64BIT
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# else
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/* otherwise we fall back to MP_32BIT even on 64bit platforms */
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# define MP_32BIT
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# endif
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# endif
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#endif
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/* some default configurations.
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*
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* A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
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* A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
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*
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* At the very least a mp_digit must be able to hold 7 bits
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* [any size beyond that is ok provided it doesn't overflow the data type]
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*/
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#ifdef MP_8BIT
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typedef uint8_t mp_digit;
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typedef uint16_t mp_word;
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# define MP_SIZEOF_MP_DIGIT 1
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# ifdef DIGIT_BIT
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# error You must not define DIGIT_BIT when using MP_8BIT
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# endif
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#elif defined(MP_16BIT)
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typedef uint16_t mp_digit;
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typedef uint32_t mp_word;
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# define MP_SIZEOF_MP_DIGIT 2
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# ifdef DIGIT_BIT
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# error You must not define DIGIT_BIT when using MP_16BIT
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# endif
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#elif defined(MP_64BIT)
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/* for GCC only on supported platforms */
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typedef uint64_t mp_digit;
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typedef unsigned long mp_word __attribute__((mode(TI)));
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# define DIGIT_BIT 60
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#else
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/* this is the default case, 28-bit digits */
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/* this is to make porting into LibTomCrypt easier :-) */
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typedef uint32_t mp_digit;
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typedef uint64_t mp_word;
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# ifdef MP_31BIT
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/* this is an extension that uses 31-bit digits */
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# define DIGIT_BIT 31
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# else
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/* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
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# define DIGIT_BIT 28
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# define MP_28BIT
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# endif
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#endif
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/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
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#ifndef DIGIT_BIT
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# define DIGIT_BIT (((CHAR_BIT * MP_SIZEOF_MP_DIGIT) - 1)) /* bits per digit */
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typedef uint_least32_t mp_min_u32;
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#else
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typedef mp_digit mp_min_u32;
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#endif
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#define MP_DIGIT_BIT DIGIT_BIT
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#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
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#define MP_DIGIT_MAX MP_MASK
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/* equalities */
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#define MP_LT -1 /* less than */
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#define MP_EQ 0 /* equal to */
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#define MP_GT 1 /* greater than */
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#define MP_ZPOS 0 /* positive integer */
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#define MP_NEG 1 /* negative */
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#define MP_OKAY 0 /* ok result */
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#define MP_MEM -2 /* out of mem */
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#define MP_VAL -3 /* invalid input */
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#define MP_RANGE MP_VAL
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#define MP_YES 1 /* yes response */
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#define MP_NO 0 /* no response */
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/* Primality generation flags */
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#define LTM_PRIME_BBS 0x0001 /* BBS style prime */
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#define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
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#define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
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typedef int mp_err;
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/* you'll have to tune these... */
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extern int KARATSUBA_MUL_CUTOFF,
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KARATSUBA_SQR_CUTOFF,
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TOOM_MUL_CUTOFF,
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TOOM_SQR_CUTOFF;
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/* define this to use lower memory usage routines (exptmods mostly) */
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/* #define MP_LOW_MEM */
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/* default precision */
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#ifndef MP_PREC
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# ifndef MP_LOW_MEM
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# define MP_PREC 32 /* default digits of precision */
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# else
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# define MP_PREC 8 /* default digits of precision */
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# endif
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#endif
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/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
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#define MP_WARRAY (1u << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) + 1))
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/* the infamous mp_int structure */
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typedef struct {
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int used, alloc, sign;
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mp_digit *dp;
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} mp_int;
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/* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
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typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
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#define USED(m) ((m)->used)
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#define DIGIT(m, k) ((m)->dp[(k)])
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#define SIGN(m) ((m)->sign)
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/* error code to char* string */
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const char *mp_error_to_string(int code);
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/* ---> init and deinit bignum functions <--- */
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/* init a bignum */
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int mp_init(mp_int *a);
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/* free a bignum */
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void mp_clear(mp_int *a);
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/* init a null terminated series of arguments */
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int mp_init_multi(mp_int *mp, ...);
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/* clear a null terminated series of arguments */
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void mp_clear_multi(mp_int *mp, ...);
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/* exchange two ints */
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void mp_exch(mp_int *a, mp_int *b);
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/* shrink ram required for a bignum */
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int mp_shrink(mp_int *a);
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/* grow an int to a given size */
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int mp_grow(mp_int *a, int size);
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/* init to a given number of digits */
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int mp_init_size(mp_int *a, int size);
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/* ---> Basic Manipulations <--- */
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#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
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#define mp_iseven(a) ((((a)->used == 0) || (((a)->dp[0] & 1u) == 0u)) ? MP_YES : MP_NO)
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#define mp_isodd(a) ((((a)->used > 0) && (((a)->dp[0] & 1u) == 1u)) ? MP_YES : MP_NO)
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#define mp_isneg(a) (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO)
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/* set to zero */
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void mp_zero(mp_int *a);
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/* set to a digit */
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void mp_set(mp_int *a, mp_digit b);
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/* set a double */
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int mp_set_double(mp_int *a, double b);
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/* set a 32-bit const */
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int mp_set_int(mp_int *a, unsigned long b);
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/* set a platform dependent unsigned long value */
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int mp_set_long(mp_int *a, unsigned long b);
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/* set a platform dependent unsigned long long value */
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int mp_set_long_long(mp_int *a, unsigned long long b);
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/* get a double */
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double mp_get_double(const mp_int *a);
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/* get a 32-bit value */
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unsigned long mp_get_int(const mp_int *a);
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/* get a platform dependent unsigned long value */
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unsigned long mp_get_long(const mp_int *a);
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/* get a platform dependent unsigned long long value */
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unsigned long long mp_get_long_long(const mp_int *a);
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/* initialize and set a digit */
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int mp_init_set(mp_int *a, mp_digit b);
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/* initialize and set 32-bit value */
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int mp_init_set_int(mp_int *a, unsigned long b);
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/* copy, b = a */
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int mp_copy(const mp_int *a, mp_int *b);
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/* inits and copies, a = b */
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int mp_init_copy(mp_int *a, const mp_int *b);
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/* trim unused digits */
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void mp_clamp(mp_int *a);
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/* import binary data */
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int mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails, const void *op);
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/* export binary data */
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int mp_export(void *rop, size_t *countp, int order, size_t size, int endian, size_t nails, const mp_int *op);
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/* ---> digit manipulation <--- */
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/* right shift by "b" digits */
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void mp_rshd(mp_int *a, int b);
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/* left shift by "b" digits */
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int mp_lshd(mp_int *a, int b);
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/* c = a / 2**b, implemented as c = a >> b */
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int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);
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/* b = a/2 */
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int mp_div_2(const mp_int *a, mp_int *b);
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/* c = a * 2**b, implemented as c = a << b */
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int mp_mul_2d(const mp_int *a, int b, mp_int *c);
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/* b = a*2 */
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int mp_mul_2(const mp_int *a, mp_int *b);
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/* c = a mod 2**b */
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int mp_mod_2d(const mp_int *a, int b, mp_int *c);
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/* computes a = 2**b */
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int mp_2expt(mp_int *a, int b);
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/* Counts the number of lsbs which are zero before the first zero bit */
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int mp_cnt_lsb(const mp_int *a);
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/* I Love Earth! */
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/* makes a pseudo-random int of a given size */
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int mp_rand(mp_int *a, int digits);
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#ifdef MP_PRNG_ENABLE_LTM_RNG
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/* as last resort we will fall back to libtomcrypt's rng_get_bytes()
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* in case you don't use libtomcrypt or use it w/o rng_get_bytes()
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* you have to implement it somewhere else, as it's required */
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extern unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void));
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extern void (*ltm_rng_callback)(void);
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#endif
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/* ---> binary operations <--- */
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/* c = a XOR b */
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int mp_xor(const mp_int *a, const mp_int *b, mp_int *c);
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/* c = a OR b */
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int mp_or(const mp_int *a, const mp_int *b, mp_int *c);
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/* c = a AND b */
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int mp_and(const mp_int *a, const mp_int *b, mp_int *c);
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/* c = a XOR b (two complement) */
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int mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c);
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/* c = a OR b (two complement) */
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int mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c);
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/* c = a AND b (two complement) */
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int mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c);
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/* right shift (two complement) */
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int mp_tc_div_2d(const mp_int *a, int b, mp_int *c);
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/* ---> Basic arithmetic <--- */
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/* b = ~a */
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int mp_complement(const mp_int *a, mp_int *b);
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/* b = -a */
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int mp_neg(const mp_int *a, mp_int *b);
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/* b = |a| */
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int mp_abs(const mp_int *a, mp_int *b);
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/* compare a to b */
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int mp_cmp(const mp_int *a, const mp_int *b);
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/* compare |a| to |b| */
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int mp_cmp_mag(const mp_int *a, const mp_int *b);
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/* c = a + b */
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int mp_add(const mp_int *a, const mp_int *b, mp_int *c);
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/* c = a - b */
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int mp_sub(const mp_int *a, const mp_int *b, mp_int *c);
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/* c = a * b */
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int mp_mul(const mp_int *a, const mp_int *b, mp_int *c);
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/* b = a*a */
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int mp_sqr(const mp_int *a, mp_int *b);
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/* a/b => cb + d == a */
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int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d);
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/* c = a mod b, 0 <= c < b */
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int mp_mod(const mp_int *a, const mp_int *b, mp_int *c);
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/* ---> single digit functions <--- */
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/* compare against a single digit */
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int mp_cmp_d(const mp_int *a, mp_digit b);
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/* c = a + b */
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int mp_add_d(const mp_int *a, mp_digit b, mp_int *c);
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/* c = a - b */
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int mp_sub_d(const mp_int *a, mp_digit b, mp_int *c);
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/* c = a * b */
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int mp_mul_d(const mp_int *a, mp_digit b, mp_int *c);
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/* a/b => cb + d == a */
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int mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
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/* a/3 => 3c + d == a */
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int mp_div_3(const mp_int *a, mp_int *c, mp_digit *d);
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/* c = a**b */
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int mp_expt_d(const mp_int *a, mp_digit b, mp_int *c);
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int mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast);
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/* c = a mod b, 0 <= c < b */
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int mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c);
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/* ---> number theory <--- */
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/* d = a + b (mod c) */
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int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
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/* d = a - b (mod c) */
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int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
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/* d = a * b (mod c) */
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int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
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/* c = a * a (mod b) */
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int mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c);
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/* c = 1/a (mod b) */
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int mp_invmod(const mp_int *a, const mp_int *b, mp_int *c);
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/* c = (a, b) */
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int mp_gcd(const mp_int *a, const mp_int *b, mp_int *c);
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/* produces value such that U1*a + U2*b = U3 */
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int mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
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/* c = [a, b] or (a*b)/(a, b) */
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int mp_lcm(const mp_int *a, const mp_int *b, mp_int *c);
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/* finds one of the b'th root of a, such that |c|**b <= |a|
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*
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* returns error if a < 0 and b is even
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*/
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int mp_n_root(const mp_int *a, mp_digit b, mp_int *c);
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int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast);
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/* special sqrt algo */
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int mp_sqrt(const mp_int *arg, mp_int *ret);
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/* special sqrt (mod prime) */
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int mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret);
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/* is number a square? */
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int mp_is_square(const mp_int *arg, int *ret);
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/* computes the jacobi c = (a | n) (or Legendre if b is prime) */
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int mp_jacobi(const mp_int *a, const mp_int *n, int *c);
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/* used to setup the Barrett reduction for a given modulus b */
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int mp_reduce_setup(mp_int *a, const mp_int *b);
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/* Barrett Reduction, computes a (mod b) with a precomputed value c
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*
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* Assumes that 0 < x <= m*m, note if 0 > x > -(m*m) then you can merely
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* compute the reduction as -1 * mp_reduce(mp_abs(x)) [pseudo code].
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*/
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int mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu);
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/* setups the montgomery reduction */
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int mp_montgomery_setup(const mp_int *n, mp_digit *rho);
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/* computes a = B**n mod b without division or multiplication useful for
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* normalizing numbers in a Montgomery system.
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*/
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int mp_montgomery_calc_normalization(mp_int *a, const mp_int *b);
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/* computes x/R == x (mod N) via Montgomery Reduction */
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int mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho);
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/* returns 1 if a is a valid DR modulus */
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int mp_dr_is_modulus(const mp_int *a);
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/* sets the value of "d" required for mp_dr_reduce */
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void mp_dr_setup(const mp_int *a, mp_digit *d);
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/* reduces a modulo n using the Diminished Radix method */
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int mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k);
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/* returns true if a can be reduced with mp_reduce_2k */
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int mp_reduce_is_2k(const mp_int *a);
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/* determines k value for 2k reduction */
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int mp_reduce_2k_setup(const mp_int *a, mp_digit *d);
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/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
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int mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d);
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/* returns true if a can be reduced with mp_reduce_2k_l */
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int mp_reduce_is_2k_l(const mp_int *a);
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/* determines k value for 2k reduction */
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int mp_reduce_2k_setup_l(const mp_int *a, mp_int *d);
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/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
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int mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d);
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/* Y = G**X (mod P) */
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int mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y);
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/* ---> Primes <--- */
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/* number of primes */
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#ifdef MP_8BIT
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# define PRIME_SIZE 31
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#else
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# define PRIME_SIZE 256
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#endif
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/* table of first PRIME_SIZE primes */
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extern const mp_digit ltm_prime_tab[PRIME_SIZE];
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/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
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int mp_prime_is_divisible(const mp_int *a, int *result);
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/* performs one Fermat test of "a" using base "b".
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* Sets result to 0 if composite or 1 if probable prime
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*/
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int mp_prime_fermat(const mp_int *a, const mp_int *b, int *result);
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/* performs one Miller-Rabin test of "a" using base "b".
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* Sets result to 0 if composite or 1 if probable prime
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*/
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int mp_prime_miller_rabin(const mp_int *a, const mp_int *b, int *result);
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/* This gives [for a given bit size] the number of trials required
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* such that Miller-Rabin gives a prob of failure lower than 2^-96
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*/
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int mp_prime_rabin_miller_trials(int size);
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/* performs t rounds of Miller-Rabin on "a" using the first
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* t prime bases. Also performs an initial sieve of trial
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* division. Determines if "a" is prime with probability
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* of error no more than (1/4)**t.
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*
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* Sets result to 1 if probably prime, 0 otherwise
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*/
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int mp_prime_is_prime(const mp_int *a, int t, int *result);
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/* finds the next prime after the number "a" using "t" trials
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* of Miller-Rabin.
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*
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* bbs_style = 1 means the prime must be congruent to 3 mod 4
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*/
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int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
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/* makes a truly random prime of a given size (bytes),
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* call with bbs = 1 if you want it to be congruent to 3 mod 4
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*
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* You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
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* have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
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* so it can be NULL
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*
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* The prime generated will be larger than 2^(8*size).
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*/
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#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)
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/* makes a truly random prime of a given size (bits),
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*
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* Flags are as follows:
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*
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* LTM_PRIME_BBS - make prime congruent to 3 mod 4
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* LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
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* LTM_PRIME_2MSB_ON - make the 2nd highest bit one
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*
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* You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
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* have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
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* so it can be NULL
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*
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*/
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int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat);
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/* ---> radix conversion <--- */
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int mp_count_bits(const mp_int *a);
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int mp_unsigned_bin_size(const mp_int *a);
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int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c);
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int mp_to_unsigned_bin(const mp_int *a, unsigned char *b);
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int mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen);
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int mp_signed_bin_size(const mp_int *a);
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int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
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int mp_to_signed_bin(const mp_int *a, unsigned char *b);
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int mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen);
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int mp_read_radix(mp_int *a, const char *str, int radix);
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int mp_toradix(const mp_int *a, char *str, int radix);
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int mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen);
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int mp_radix_size(const mp_int *a, int radix, int *size);
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#ifndef LTM_NO_FILE
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int mp_fread(mp_int *a, int radix, FILE *stream);
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int mp_fwrite(const mp_int *a, int radix, FILE *stream);
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#endif
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#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
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#define mp_raw_size(mp) mp_signed_bin_size(mp)
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#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
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#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
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#define mp_mag_size(mp) mp_unsigned_bin_size(mp)
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#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
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#define mp_tobinary(M, S) mp_toradix((M), (S), 2)
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#define mp_tooctal(M, S) mp_toradix((M), (S), 8)
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#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
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#define mp_tohex(M, S) mp_toradix((M), (S), 16)
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#ifdef __cplusplus
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}
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#endif
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#endif
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/* ref: $Format:%D$ */
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/* git commit: $Format:%H$ */
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/* commit time: $Format:%ai$ */
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