forked from ibphoenix/tomsfastmath
359 lines
9.6 KiB
C
359 lines
9.6 KiB
C
/* TomsFastMath, a fast ISO C bignum library.
|
|
*
|
|
* This project is meant to fill in where LibTomMath
|
|
* falls short. That is speed ;-)
|
|
*
|
|
* This project is public domain and free for all purposes.
|
|
*
|
|
* Tom St Denis, tomstdenis@iahu.ca
|
|
*/
|
|
#ifndef TFM_H_
|
|
#define TFM_H_
|
|
|
|
#include <stdio.h>
|
|
#include <string.h>
|
|
#include <stdlib.h>
|
|
#include <ctype.h>
|
|
#include <limits.h>
|
|
|
|
#undef MIN
|
|
#define MIN(x,y) ((x)<(y)?(x):(y))
|
|
#undef MAX
|
|
#define MAX(x,y) ((x)>(y)?(x):(y))
|
|
|
|
/* do we want large code? */
|
|
#define TFM_LARGE
|
|
|
|
/* do we want huge code (implies large)? The answer is, yes. */
|
|
#define TFM_HUGE
|
|
|
|
/* imply TFM_LARGE as required */
|
|
#if defined(TFM_HUGE)
|
|
#if !defined(TFM_LARGE)
|
|
#define TFM_LARGE
|
|
#endif
|
|
#endif
|
|
|
|
/* Max size of any number in bits. Basically the largest size you will be multiplying
|
|
* should be half [or smaller] of FP_MAX_SIZE-four_digit
|
|
*
|
|
* You can externally define this or it defaults to 4096-bits.
|
|
*/
|
|
#ifndef FP_MAX_SIZE
|
|
#define FP_MAX_SIZE (4096+(4*DIGIT_BIT))
|
|
#endif
|
|
|
|
/* will this lib work? */
|
|
#if (CHAR_BIT & 7)
|
|
#error CHAR_BIT must be a multiple of eight.
|
|
#endif
|
|
#if FP_MAX_SIZE % CHAR_BIT
|
|
#error FP_MAX_SIZE must be a multiple of CHAR_BIT
|
|
#endif
|
|
|
|
/* autodetect x86-64 and make sure we are using 64-bit digits with x86-64 asm */
|
|
#if defined(__x86_64__)
|
|
#if defined(TFM_X86) || defined(TFM_SSE2) || defined(TFM_ARM)
|
|
#error x86-64 detected, x86-32/SSE2/ARM optimizations are not valid!
|
|
#endif
|
|
#if !defined(TFM_X86_64) && !defined(TFM_NO_ASM)
|
|
#define TFM_X86_64
|
|
#endif
|
|
#endif
|
|
#if defined(TFM_X86_64)
|
|
#if !defined(FP_64BIT)
|
|
#define FP_64BIT
|
|
#endif
|
|
#endif
|
|
|
|
/* try to detect x86-32 */
|
|
#if defined(__i386__) && !defined(TFM_SSE2)
|
|
#if defined(TFM_X86_64) || defined(TFM_ARM)
|
|
#error x86-32 detected, x86-64/ARM optimizations are not valid!
|
|
#endif
|
|
#if !defined(TFM_X86) && !defined(TFM_NO_ASM)
|
|
#define TFM_X86
|
|
#endif
|
|
#endif
|
|
|
|
/* make sure we're 32-bit for x86-32/sse/arm */
|
|
#if (defined(TFM_X86) || defined(TFM_SSE2) || defined(TFM_ARM)) && defined(FP_64BIT)
|
|
#warning x86-32, SSE2 and ARM optimizations require 32-bit digits (undefining)
|
|
#undef FP_64BIT
|
|
#endif
|
|
|
|
/* multi asms? */
|
|
#ifdef TFM_X86
|
|
#define TFM_ASM
|
|
#endif
|
|
#ifdef TFM_X86_64
|
|
#ifdef TFM_ASM
|
|
#error TFM_ASM already defined!
|
|
#endif
|
|
#define TFM_ASM
|
|
#endif
|
|
#ifdef TFM_SSE2
|
|
#ifdef TFM_ASM
|
|
#error TFM_ASM already defined!
|
|
#endif
|
|
#define TFM_ASM
|
|
#endif
|
|
#ifdef TFM_ARM
|
|
#ifdef TFM_ASM
|
|
#error TFM_ASM already defined!
|
|
#endif
|
|
#define TFM_ASM
|
|
#endif
|
|
|
|
/* we want no asm? */
|
|
#ifdef TFM_NO_ASM
|
|
#undef TFM_X86
|
|
#undef TFM_X86_64
|
|
#undef TFM_SSE2
|
|
#undef TFM_ARM
|
|
#undef TFM_ASM
|
|
#endif
|
|
|
|
/* some default configurations.
|
|
*/
|
|
#if defined(FP_64BIT)
|
|
/* for GCC only on supported platforms */
|
|
#ifndef CRYPT
|
|
typedef unsigned long ulong64;
|
|
#endif
|
|
typedef ulong64 fp_digit;
|
|
typedef unsigned long fp_word __attribute__ ((mode(TI)));
|
|
#else
|
|
/* 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
|
|
typedef unsigned long fp_digit;
|
|
typedef ulong64 fp_word;
|
|
#endif
|
|
|
|
/* # of digits this is */
|
|
#define DIGIT_BIT (int)((CHAR_BIT) * sizeof(fp_digit))
|
|
#define FP_MASK (fp_digit)(-1)
|
|
#define FP_SIZE (FP_MAX_SIZE/DIGIT_BIT)
|
|
|
|
/* signs */
|
|
#define FP_ZPOS 0
|
|
#define FP_NEG 1
|
|
|
|
/* return codes */
|
|
#define FP_OKAY 0
|
|
#define FP_VAL 1
|
|
#define FP_MEM 2
|
|
|
|
/* equalities */
|
|
#define FP_LT -1 /* less than */
|
|
#define FP_EQ 0 /* equal to */
|
|
#define FP_GT 1 /* greater than */
|
|
|
|
/* replies */
|
|
#define FP_YES 1 /* yes response */
|
|
#define FP_NO 0 /* no response */
|
|
|
|
/* a FP type */
|
|
typedef struct {
|
|
fp_digit dp[FP_SIZE];
|
|
int used,
|
|
sign;
|
|
} fp_int;
|
|
|
|
/* functions */
|
|
|
|
/* returns a TFM ident string useful for debugging... */
|
|
const char *fp_ident(void);
|
|
|
|
/* initialize [or zero] an fp int */
|
|
#define fp_init(a) (void)memset((a), 0, sizeof(fp_int))
|
|
#define fp_zero(a) fp_init(a)
|
|
|
|
/* zero/even/odd ? */
|
|
#define fp_iszero(a) (((a)->used == 0) ? FP_YES : FP_NO)
|
|
#define fp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? FP_YES : FP_NO)
|
|
#define fp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? FP_YES : FP_NO)
|
|
|
|
/* set to a small digit */
|
|
void fp_set(fp_int *a, fp_digit b);
|
|
|
|
/* copy from a to b */
|
|
#define fp_copy(a, b) (void)(((a) != (b)) && memcpy((b), (a), sizeof(fp_int)))
|
|
#define fp_init_copy(a, b) fp_copy(b, a)
|
|
|
|
/* negate and absolute */
|
|
#define fp_neg(a, b) { fp_copy(a, b); (b)->sign ^= 1; }
|
|
#define fp_abs(a, b) { fp_copy(a, b); (b)->sign = 0; }
|
|
|
|
/* clamp digits */
|
|
#define fp_clamp(a) { while ((a)->used && (a)->dp[(a)->used-1] == 0) --((a)->used); (a)->sign = (a)->used ? (a)->sign : FP_ZPOS; }
|
|
|
|
/* right shift x digits */
|
|
void fp_rshd(fp_int *a, int x);
|
|
|
|
/* left shift x digits */
|
|
void fp_lshd(fp_int *a, int x);
|
|
|
|
/* signed comparison */
|
|
int fp_cmp(fp_int *a, fp_int *b);
|
|
|
|
/* unsigned comparison */
|
|
int fp_cmp_mag(fp_int *a, fp_int *b);
|
|
|
|
/* power of 2 operations */
|
|
void fp_div_2d(fp_int *a, int b, fp_int *c, fp_int *d);
|
|
void fp_mod_2d(fp_int *a, int b, fp_int *c);
|
|
void fp_mul_2d(fp_int *a, int b, fp_int *c);
|
|
void fp_2expt (fp_int *a, int b);
|
|
void fp_mul_2(fp_int *a, fp_int *c);
|
|
void fp_div_2(fp_int *a, fp_int *c);
|
|
|
|
/* Counts the number of lsbs which are zero before the first zero bit */
|
|
int fp_cnt_lsb(fp_int *a);
|
|
|
|
/* c = a + b */
|
|
void fp_add(fp_int *a, fp_int *b, fp_int *c);
|
|
|
|
/* c = a - b */
|
|
void fp_sub(fp_int *a, fp_int *b, fp_int *c);
|
|
|
|
/* c = a * b */
|
|
void fp_mul(fp_int *a, fp_int *b, fp_int *c);
|
|
|
|
/* b = a*a */
|
|
void fp_sqr(fp_int *a, fp_int *b);
|
|
|
|
/* a/b => cb + d == a */
|
|
int fp_div(fp_int *a, fp_int *b, fp_int *c, fp_int *d);
|
|
|
|
/* c = a mod b, 0 <= c < b */
|
|
int fp_mod(fp_int *a, fp_int *b, fp_int *c);
|
|
|
|
/* compare against a single digit */
|
|
int fp_cmp_d(fp_int *a, fp_digit b);
|
|
|
|
/* c = a + b */
|
|
void fp_add_d(fp_int *a, fp_digit b, fp_int *c);
|
|
|
|
/* c = a - b */
|
|
void fp_sub_d(fp_int *a, fp_digit b, fp_int *c);
|
|
|
|
/* c = a * b */
|
|
void fp_mul_d(fp_int *a, fp_digit b, fp_int *c);
|
|
|
|
/* a/b => cb + d == a */
|
|
int fp_div_d(fp_int *a, fp_digit b, fp_int *c, fp_digit *d);
|
|
|
|
/* c = a mod b, 0 <= c < b */
|
|
int fp_mod_d(fp_int *a, fp_digit b, fp_digit *c);
|
|
|
|
/* ---> number theory <--- */
|
|
/* d = a + b (mod c) */
|
|
int fp_addmod(fp_int *a, fp_int *b, fp_int *c, fp_int *d);
|
|
|
|
/* d = a - b (mod c) */
|
|
int fp_submod(fp_int *a, fp_int *b, fp_int *c, fp_int *d);
|
|
|
|
/* d = a * b (mod c) */
|
|
int fp_mulmod(fp_int *a, fp_int *b, fp_int *c, fp_int *d);
|
|
|
|
/* c = a * a (mod b) */
|
|
int fp_sqrmod(fp_int *a, fp_int *b, fp_int *c);
|
|
|
|
/* c = 1/a (mod b) */
|
|
int fp_invmod(fp_int *a, fp_int *b, fp_int *c);
|
|
|
|
/* c = (a, b) */
|
|
void fp_gcd(fp_int *a, fp_int *b, fp_int *c);
|
|
|
|
/* c = [a, b] */
|
|
void fp_lcm(fp_int *a, fp_int *b, fp_int *c);
|
|
|
|
/* setups the montgomery reduction */
|
|
int fp_montgomery_setup(fp_int *a, fp_digit *mp);
|
|
|
|
/* computes a = B**n mod b without division or multiplication useful for
|
|
* normalizing numbers in a Montgomery system.
|
|
*/
|
|
void fp_montgomery_calc_normalization(fp_int *a, fp_int *b);
|
|
|
|
/* computes x/R == x (mod N) via Montgomery Reduction */
|
|
void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp);
|
|
|
|
/* d = a**b (mod c) */
|
|
int fp_exptmod(fp_int *a, fp_int *b, fp_int *c, fp_int *d);
|
|
|
|
/* primality stuff */
|
|
|
|
/* perform a Miller-Rabin test of a to the base b and store result in "result" */
|
|
void fp_prime_miller_rabin (fp_int * a, fp_int * b, int *result);
|
|
|
|
/* 256 trial divisions + 8 Miller-Rabins, returns FP_YES if probable prime */
|
|
int fp_isprime(fp_int *a);
|
|
|
|
/* Primality generation flags */
|
|
#define TFM_PRIME_BBS 0x0001 /* BBS style prime */
|
|
#define TFM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
|
|
#define TFM_PRIME_2MSB_OFF 0x0004 /* force 2nd MSB to 0 */
|
|
#define TFM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
|
|
|
|
/* callback for fp_prime_random, should fill dst with random bytes and return how many read [upto len] */
|
|
typedef int tfm_prime_callback(unsigned char *dst, int len, void *dat);
|
|
|
|
#define fp_prime_random(a, t, size, bbs, cb, dat) fp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?TFM_PRIME_BBS:0, cb, dat)
|
|
|
|
int fp_prime_random_ex(fp_int *a, int t, int size, int flags, tfm_prime_callback cb, void *dat);
|
|
|
|
/* radix conersions */
|
|
int fp_count_bits(fp_int *a);
|
|
|
|
int fp_unsigned_bin_size(fp_int *a);
|
|
void fp_read_unsigned_bin(fp_int *a, unsigned char *b, int c);
|
|
void fp_to_unsigned_bin(fp_int *a, unsigned char *b);
|
|
|
|
int fp_signed_bin_size(fp_int *a);
|
|
void fp_read_signed_bin(fp_int *a, unsigned char *b, int c);
|
|
void fp_to_signed_bin(fp_int *a, unsigned char *b);
|
|
|
|
int fp_read_radix(fp_int *a, char *str, int radix);
|
|
int fp_toradix(fp_int *a, char *str, int radix);
|
|
int fp_toradix_n(fp_int * a, char *str, int radix, int maxlen);
|
|
|
|
|
|
/* VARIOUS LOW LEVEL STUFFS */
|
|
void s_fp_add(fp_int *a, fp_int *b, fp_int *c);
|
|
void s_fp_sub(fp_int *a, fp_int *b, fp_int *c);
|
|
void bn_reverse(unsigned char *s, int len);
|
|
void fp_mul_comba(fp_int *A, fp_int *B, fp_int *C);
|
|
#ifdef TFM_HUGE
|
|
void fp_mul_comba32(fp_int *A, fp_int *B, fp_int *C);
|
|
#endif
|
|
#ifdef TFM_LARGE
|
|
void fp_mul_comba16(fp_int *A, fp_int *B, fp_int *C);
|
|
#endif
|
|
void fp_mul_comba8(fp_int *A, fp_int *B, fp_int *C);
|
|
void fp_mul_comba4(fp_int *A, fp_int *B, fp_int *C);
|
|
|
|
void fp_sqr_comba(fp_int *A, fp_int *B);
|
|
void fp_sqr_comba4(fp_int *A, fp_int *B);
|
|
void fp_sqr_comba8(fp_int *A, fp_int *B);
|
|
#ifdef TFM_LARGE
|
|
void fp_sqr_comba16(fp_int *A, fp_int *B);
|
|
#endif
|
|
#ifdef TFM_HUGE
|
|
void fp_sqr_comba32(fp_int *A, fp_int *B);
|
|
void fp_sqr_comba64(fp_int *A, fp_int *B);
|
|
#endif
|
|
extern const char *fp_s_rmap;
|
|
|
|
#endif
|
|
|