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782 lines
29 KiB
C
782 lines
29 KiB
C
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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#ifndef BN_H_
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#define BN_H_
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#include <stdint.h>
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#include <stddef.h>
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#include <limits.h>
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#ifdef LTM_NO_FILE
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# warning LTM_NO_FILE has been deprecated, use MP_NO_FILE.
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# define MP_NO_FILE
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#endif
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#ifndef MP_NO_FILE
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# include <stdio.h>
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#endif
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#ifdef MP_8BIT
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# ifdef _MSC_VER
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# pragma message("8-bit (MP_8BIT) support is deprecated and will be dropped completely in the next version.")
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# else
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# warning "8-bit (MP_8BIT) support is deprecated and will be dropped completely in the next version."
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# endif
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#endif
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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__)) && !defined(MP_64BIT)
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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_64BIT) || defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT))
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# if defined(__GNUC__) && !defined(__hppa)
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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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#ifdef MP_DIGIT_BIT
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# error Defining MP_DIGIT_BIT is disallowed, use MP_8/16/31/32/64BIT
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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 MP_DIGIT_BIT + 1 bits
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* A "mp_word" must be able to hold 2*MP_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 private_mp_word;
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# define MP_DIGIT_BIT 7
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#elif defined(MP_16BIT)
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typedef uint16_t mp_digit;
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typedef uint32_t private_mp_word;
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# define MP_DIGIT_BIT 15
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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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#if defined(__GNUC__)
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typedef unsigned long private_mp_word __attribute__((mode(TI)));
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#endif
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# define MP_DIGIT_BIT 60
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#else
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typedef uint32_t mp_digit;
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typedef uint64_t private_mp_word;
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# ifdef MP_31BIT
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/*
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* This is an extension that uses 31-bit digits.
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* Please be aware that not all functions support this size, especially s_mp_mul_digs_fast
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* will be reduced to work on small numbers only:
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* Up to 8 limbs, 248 bits instead of up to 512 limbs, 15872 bits with MP_28BIT.
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*/
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# define MP_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 MP_DIGIT_BIT 28
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# define MP_28BIT
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# endif
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#endif
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/* mp_word is a private type */
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#define mp_word MP_DEPRECATED_PRAGMA("mp_word has been made private") private_mp_word
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#define MP_SIZEOF_MP_DIGIT (MP_DEPRECATED_PRAGMA("MP_SIZEOF_MP_DIGIT has been deprecated, use sizeof (mp_digit)") sizeof (mp_digit))
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#define MP_MASK ((((mp_digit)1)<<((mp_digit)MP_DIGIT_BIT))-((mp_digit)1))
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#define MP_DIGIT_MAX MP_MASK
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/* Primality generation flags */
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#define MP_PRIME_BBS 0x0001 /* BBS style prime */
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#define MP_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
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#define MP_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
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#define LTM_PRIME_BBS (MP_DEPRECATED_PRAGMA("LTM_PRIME_BBS has been deprecated, use MP_PRIME_BBS") MP_PRIME_BBS)
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#define LTM_PRIME_SAFE (MP_DEPRECATED_PRAGMA("LTM_PRIME_SAFE has been deprecated, use MP_PRIME_SAFE") MP_PRIME_SAFE)
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#define LTM_PRIME_2MSB_ON (MP_DEPRECATED_PRAGMA("LTM_PRIME_2MSB_ON has been deprecated, use MP_PRIME_2MSB_ON") MP_PRIME_2MSB_ON)
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#ifdef MP_USE_ENUMS
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typedef enum {
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MP_ZPOS = 0, /* positive */
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MP_NEG = 1 /* negative */
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} mp_sign;
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typedef enum {
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MP_LT = -1, /* less than */
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MP_EQ = 0, /* equal */
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MP_GT = 1 /* greater than */
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} mp_ord;
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typedef enum {
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MP_NO = 0,
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MP_YES = 1
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} mp_bool;
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typedef enum {
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MP_OKAY = 0, /* no error */
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MP_ERR = -1, /* unknown error */
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MP_MEM = -2, /* out of mem */
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MP_VAL = -3, /* invalid input */
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MP_ITER = -4, /* maximum iterations reached */
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MP_BUF = -5 /* buffer overflow, supplied buffer too small */
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} mp_err;
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typedef enum {
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MP_LSB_FIRST = -1,
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MP_MSB_FIRST = 1
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} mp_order;
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typedef enum {
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MP_LITTLE_ENDIAN = -1,
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MP_NATIVE_ENDIAN = 0,
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MP_BIG_ENDIAN = 1
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} mp_endian;
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#else
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typedef int mp_sign;
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#define MP_ZPOS 0 /* positive integer */
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#define MP_NEG 1 /* negative */
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typedef int mp_ord;
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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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typedef int mp_bool;
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#define MP_YES 1
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#define MP_NO 0
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typedef int mp_err;
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#define MP_OKAY 0 /* no error */
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#define MP_ERR -1 /* unknown error */
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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_DEPRECATED_PRAGMA("MP_RANGE has been deprecated in favor of MP_VAL") MP_VAL)
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#define MP_ITER -4 /* maximum iterations reached */
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#define MP_BUF -5 /* buffer overflow, supplied buffer too small */
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typedef int mp_order;
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#define MP_LSB_FIRST -1
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#define MP_MSB_FIRST 1
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typedef int mp_endian;
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#define MP_LITTLE_ENDIAN -1
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#define MP_NATIVE_ENDIAN 0
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#define MP_BIG_ENDIAN 1
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#endif
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/* tunable cutoffs */
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#ifndef MP_FIXED_CUTOFFS
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extern int
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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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#endif
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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 PRIVATE_MP_PREC 32 /* default digits of precision */
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# elif defined(MP_8BIT)
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# define PRIVATE_MP_PREC 16 /* default digits of precision */
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# else
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# define PRIVATE_MP_PREC 8 /* default digits of precision */
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# endif
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# define MP_PREC (MP_DEPRECATED_PRAGMA("MP_PREC is an internal macro") PRIVATE_MP_PREC)
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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 PRIVATE_MP_WARRAY (int)(1uLL << (((CHAR_BIT * sizeof(private_mp_word)) - (2 * MP_DIGIT_BIT)) + 1))
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#define MP_WARRAY (MP_DEPRECATED_PRAGMA("MP_WARRAY is an internal macro") PRIVATE_MP_WARRAY)
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#if defined(__GNUC__) && __GNUC__ >= 4
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# define MP_NULL_TERMINATED __attribute__((sentinel))
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#else
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# define MP_NULL_TERMINATED
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#endif
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/*
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* MP_WUR - warn unused result
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* ---------------------------
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*
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* The result of functions annotated with MP_WUR must be
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* checked and cannot be ignored.
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*
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* Most functions in libtommath return an error code.
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* This error code must be checked in order to prevent crashes or invalid
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* results.
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*
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* If you still want to avoid the error checks for quick and dirty programs
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* without robustness guarantees, you can `#define MP_WUR` before including
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* tommath.h, disabling the warnings.
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*/
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#ifndef MP_WUR
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# if defined(__GNUC__) && __GNUC__ >= 4
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# define MP_WUR __attribute__((warn_unused_result))
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# else
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# define MP_WUR
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# endif
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#endif
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#if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 405)
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# define MP_DEPRECATED(x) __attribute__((deprecated("replaced by " #x)))
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# define PRIVATE_MP_DEPRECATED_PRAGMA(s) _Pragma(#s)
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# define MP_DEPRECATED_PRAGMA(s) PRIVATE_MP_DEPRECATED_PRAGMA(GCC warning s)
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#elif defined(_MSC_VER) && _MSC_VER >= 1500
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# define MP_DEPRECATED(x) __declspec(deprecated("replaced by " #x))
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# define MP_DEPRECATED_PRAGMA(s) __pragma(message(s))
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#else
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# define MP_DEPRECATED(s)
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# define MP_DEPRECATED_PRAGMA(s)
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#endif
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#define DIGIT_BIT (MP_DEPRECATED_PRAGMA("DIGIT_BIT macro is deprecated, MP_DIGIT_BIT instead") MP_DIGIT_BIT)
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#define USED(m) (MP_DEPRECATED_PRAGMA("USED macro is deprecated, use z->used instead") (m)->used)
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#define DIGIT(m, k) (MP_DEPRECATED_PRAGMA("DIGIT macro is deprecated, use z->dp instead") (m)->dp[(k)])
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#define SIGN(m) (MP_DEPRECATED_PRAGMA("SIGN macro is deprecated, use z->sign instead") (m)->sign)
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/* the infamous mp_int structure */
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typedef struct {
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int used, alloc;
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mp_sign 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 private_mp_prime_callback(unsigned char *dst, int len, void *dat);
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typedef private_mp_prime_callback MP_DEPRECATED(mp_rand_source) ltm_prime_callback;
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/* error code to char* string */
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const char *mp_error_to_string(mp_err code) MP_WUR;
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/* ---> init and deinit bignum functions <--- */
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/* init a bignum */
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mp_err mp_init(mp_int *a) MP_WUR;
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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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mp_err mp_init_multi(mp_int *mp, ...) MP_NULL_TERMINATED MP_WUR;
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/* clear a null terminated series of arguments */
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void mp_clear_multi(mp_int *mp, ...) MP_NULL_TERMINATED;
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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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mp_err mp_shrink(mp_int *a) MP_WUR;
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/* grow an int to a given size */
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mp_err mp_grow(mp_int *a, int size) MP_WUR;
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/* init to a given number of digits */
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mp_err mp_init_size(mp_int *a, int size) MP_WUR;
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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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mp_bool mp_iseven(const mp_int *a) MP_WUR;
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mp_bool mp_isodd(const mp_int *a) MP_WUR;
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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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/* get and set doubles */
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double mp_get_double(const mp_int *a) MP_WUR;
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mp_err mp_set_double(mp_int *a, double b) MP_WUR;
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/* get integer, set integer and init with integer (int32_t) */
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int32_t mp_get_i32(const mp_int *a) MP_WUR;
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void mp_set_i32(mp_int *a, int32_t b);
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mp_err mp_init_i32(mp_int *a, int32_t b) MP_WUR;
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/* get integer, set integer and init with integer, behaves like two complement for negative numbers (uint32_t) */
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#define mp_get_u32(a) ((uint32_t)mp_get_i32(a))
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void mp_set_u32(mp_int *a, uint32_t b);
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mp_err mp_init_u32(mp_int *a, uint32_t b) MP_WUR;
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/* get integer, set integer and init with integer (int64_t) */
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int64_t mp_get_i64(const mp_int *a) MP_WUR;
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void mp_set_i64(mp_int *a, int64_t b);
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mp_err mp_init_i64(mp_int *a, int64_t b) MP_WUR;
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/* get integer, set integer and init with integer, behaves like two complement for negative numbers (uint64_t) */
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#define mp_get_u64(a) ((uint64_t)mp_get_i64(a))
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void mp_set_u64(mp_int *a, uint64_t b);
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mp_err mp_init_u64(mp_int *a, uint64_t b) MP_WUR;
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/* get magnitude */
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uint32_t mp_get_mag_u32(const mp_int *a) MP_WUR;
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uint64_t mp_get_mag_u64(const mp_int *a) MP_WUR;
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unsigned long mp_get_mag_ul(const mp_int *a) MP_WUR;
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unsigned long long mp_get_mag_ull(const mp_int *a) MP_WUR;
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/* get integer, set integer (long) */
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long mp_get_l(const mp_int *a) MP_WUR;
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void mp_set_l(mp_int *a, long b);
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mp_err mp_init_l(mp_int *a, long b) MP_WUR;
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/* get integer, set integer (unsigned long) */
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#define mp_get_ul(a) ((unsigned long)mp_get_l(a))
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void mp_set_ul(mp_int *a, unsigned long b);
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mp_err mp_init_ul(mp_int *a, unsigned long b) MP_WUR;
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/* get integer, set integer (long long) */
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long long mp_get_ll(const mp_int *a) MP_WUR;
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void mp_set_ll(mp_int *a, long long b);
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mp_err mp_init_ll(mp_int *a, long long b) MP_WUR;
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/* get integer, set integer (unsigned long long) */
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#define mp_get_ull(a) ((unsigned long long)mp_get_ll(a))
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void mp_set_ull(mp_int *a, unsigned long long b);
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mp_err mp_init_ull(mp_int *a, unsigned long long b) MP_WUR;
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/* set to single unsigned digit, up to MP_DIGIT_MAX */
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void mp_set(mp_int *a, mp_digit b);
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mp_err mp_init_set(mp_int *a, mp_digit b) MP_WUR;
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/* get integer, set integer and init with integer (deprecated) */
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MP_DEPRECATED(mp_get_mag_u32/mp_get_u32) unsigned long mp_get_int(const mp_int *a) MP_WUR;
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MP_DEPRECATED(mp_get_mag_ul/mp_get_ul) unsigned long mp_get_long(const mp_int *a) MP_WUR;
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MP_DEPRECATED(mp_get_mag_ull/mp_get_ull) unsigned long long mp_get_long_long(const mp_int *a) MP_WUR;
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MP_DEPRECATED(mp_set_ul) mp_err mp_set_int(mp_int *a, unsigned long b);
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MP_DEPRECATED(mp_set_ul) mp_err mp_set_long(mp_int *a, unsigned long b);
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MP_DEPRECATED(mp_set_ull) mp_err mp_set_long_long(mp_int *a, unsigned long long b);
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MP_DEPRECATED(mp_init_ul) mp_err mp_init_set_int(mp_int *a, unsigned long b) MP_WUR;
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/* copy, b = a */
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mp_err mp_copy(const mp_int *a, mp_int *b) MP_WUR;
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/* inits and copies, a = b */
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mp_err mp_init_copy(mp_int *a, const mp_int *b) MP_WUR;
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/* trim unused digits */
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void mp_clamp(mp_int *a);
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/* export binary data */
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MP_DEPRECATED(mp_pack) mp_err mp_export(void *rop, size_t *countp, int order, size_t size,
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int endian, size_t nails, const mp_int *op) MP_WUR;
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/* import binary data */
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MP_DEPRECATED(mp_unpack) mp_err mp_import(mp_int *rop, size_t count, int order,
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size_t size, int endian, size_t nails,
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const void *op) MP_WUR;
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/* unpack binary data */
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mp_err mp_unpack(mp_int *rop, size_t count, mp_order order, size_t size, mp_endian endian,
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size_t nails, const void *op) MP_WUR;
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/* pack binary data */
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size_t mp_pack_count(const mp_int *a, size_t nails, size_t size) MP_WUR;
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mp_err mp_pack(void *rop, size_t maxcount, size_t *written, mp_order order, size_t size,
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mp_endian endian, size_t nails, const mp_int *op) MP_WUR;
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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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mp_err mp_lshd(mp_int *a, int b) MP_WUR;
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/* c = a / 2**b, implemented as c = a >> b */
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mp_err mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d) MP_WUR;
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/* b = a/2 */
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mp_err mp_div_2(const mp_int *a, mp_int *b) MP_WUR;
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/* a/3 => 3c + d == a */
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mp_err mp_div_3(const mp_int *a, mp_int *c, mp_digit *d) MP_WUR;
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/* c = a * 2**b, implemented as c = a << b */
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mp_err mp_mul_2d(const mp_int *a, int b, mp_int *c) MP_WUR;
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/* b = a*2 */
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mp_err mp_mul_2(const mp_int *a, mp_int *b) MP_WUR;
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|
|
/* c = a mod 2**b */
|
|
mp_err mp_mod_2d(const mp_int *a, int b, mp_int *c) MP_WUR;
|
|
|
|
/* computes a = 2**b */
|
|
mp_err mp_2expt(mp_int *a, int b) MP_WUR;
|
|
|
|
/* Counts the number of lsbs which are zero before the first zero bit */
|
|
int mp_cnt_lsb(const mp_int *a) MP_WUR;
|
|
|
|
/* I Love Earth! */
|
|
|
|
/* makes a pseudo-random mp_int of a given size */
|
|
mp_err mp_rand(mp_int *a, int digits) MP_WUR;
|
|
/* makes a pseudo-random small int of a given size */
|
|
MP_DEPRECATED(mp_rand) mp_err mp_rand_digit(mp_digit *r) MP_WUR;
|
|
/* use custom random data source instead of source provided the platform */
|
|
void mp_rand_source(mp_err(*source)(void *out, size_t size));
|
|
|
|
#ifdef MP_PRNG_ENABLE_LTM_RNG
|
|
# warning MP_PRNG_ENABLE_LTM_RNG has been deprecated, use mp_rand_source instead.
|
|
/* 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 <--- */
|
|
|
|
/* 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
|
|
*/
|
|
MP_DEPRECATED(s_mp_get_bit) int mp_get_bit(const mp_int *a, int b) MP_WUR;
|
|
|
|
/* c = a XOR b (two complement) */
|
|
MP_DEPRECATED(mp_xor) mp_err mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* c = a OR b (two complement) */
|
|
MP_DEPRECATED(mp_or) mp_err mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* c = a AND b (two complement) */
|
|
MP_DEPRECATED(mp_and) mp_err mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
mp_err mp_and(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* b = ~a (bitwise not, two complement) */
|
|
mp_err mp_complement(const mp_int *a, mp_int *b) MP_WUR;
|
|
|
|
/* right shift with sign extension */
|
|
MP_DEPRECATED(mp_signed_rsh) mp_err mp_tc_div_2d(const mp_int *a, int b, mp_int *c) MP_WUR;
|
|
mp_err mp_signed_rsh(const mp_int *a, int b, mp_int *c) MP_WUR;
|
|
|
|
/* ---> Basic arithmetic <--- */
|
|
|
|
/* b = -a */
|
|
mp_err mp_neg(const mp_int *a, mp_int *b) MP_WUR;
|
|
|
|
/* b = |a| */
|
|
mp_err mp_abs(const mp_int *a, mp_int *b) MP_WUR;
|
|
|
|
/* compare a to b */
|
|
mp_ord mp_cmp(const mp_int *a, const mp_int *b) MP_WUR;
|
|
|
|
/* compare |a| to |b| */
|
|
mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b) MP_WUR;
|
|
|
|
/* c = a + b */
|
|
mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* c = a - b */
|
|
mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* c = a * b */
|
|
mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* b = a*a */
|
|
mp_err mp_sqr(const mp_int *a, mp_int *b) MP_WUR;
|
|
|
|
/* a/b => cb + d == a */
|
|
mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) MP_WUR;
|
|
|
|
/* c = a mod b, 0 <= c < b */
|
|
mp_err mp_mod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* Increment "a" by one like "a++". Changes input! */
|
|
mp_err mp_incr(mp_int *a) MP_WUR;
|
|
|
|
/* Decrement "a" by one like "a--". Changes input! */
|
|
mp_err mp_decr(mp_int *a) MP_WUR;
|
|
|
|
/* ---> single digit functions <--- */
|
|
|
|
/* compare against a single digit */
|
|
mp_ord mp_cmp_d(const mp_int *a, mp_digit b) MP_WUR;
|
|
|
|
/* c = a + b */
|
|
mp_err mp_add_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
|
|
|
|
/* c = a - b */
|
|
mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
|
|
|
|
/* c = a * b */
|
|
mp_err mp_mul_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
|
|
|
|
/* a/b => cb + d == a */
|
|
mp_err mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d) MP_WUR;
|
|
|
|
/* c = a mod b, 0 <= c < b */
|
|
mp_err mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c) MP_WUR;
|
|
|
|
/* ---> number theory <--- */
|
|
|
|
/* d = a + b (mod c) */
|
|
mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR;
|
|
|
|
/* d = a - b (mod c) */
|
|
mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR;
|
|
|
|
/* d = a * b (mod c) */
|
|
mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR;
|
|
|
|
/* c = a * a (mod b) */
|
|
mp_err mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* c = 1/a (mod b) */
|
|
mp_err mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* c = (a, b) */
|
|
mp_err mp_gcd(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* produces value such that U1*a + U2*b = U3 */
|
|
mp_err mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) MP_WUR;
|
|
|
|
/* c = [a, b] or (a*b)/(a, b) */
|
|
mp_err mp_lcm(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
|
|
|
|
/* finds one of the b'th root of a, such that |c|**b <= |a|
|
|
*
|
|
* returns error if a < 0 and b is even
|
|
*/
|
|
mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c) MP_WUR;
|
|
MP_DEPRECATED(mp_root_u32) mp_err mp_n_root(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
|
|
MP_DEPRECATED(mp_root_u32) mp_err mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) MP_WUR;
|
|
|
|
/* special sqrt algo */
|
|
mp_err mp_sqrt(const mp_int *arg, mp_int *ret) MP_WUR;
|
|
|
|
/* special sqrt (mod prime) */
|
|
mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret) MP_WUR;
|
|
|
|
/* is number a square? */
|
|
mp_err mp_is_square(const mp_int *arg, mp_bool *ret) MP_WUR;
|
|
|
|
/* computes the jacobi c = (a | n) (or Legendre if b is prime) */
|
|
MP_DEPRECATED(mp_kronecker) mp_err mp_jacobi(const mp_int *a, const mp_int *n, int *c) MP_WUR;
|
|
|
|
/* computes the Kronecker symbol c = (a | p) (like jacobi() but with {a,p} in Z */
|
|
mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c) MP_WUR;
|
|
|
|
/* used to setup the Barrett reduction for a given modulus b */
|
|
mp_err mp_reduce_setup(mp_int *a, const mp_int *b) MP_WUR;
|
|
|
|
/* 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].
|
|
*/
|
|
mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu) MP_WUR;
|
|
|
|
/* setups the montgomery reduction */
|
|
mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho) MP_WUR;
|
|
|
|
/* computes a = B**n mod b without division or multiplication useful for
|
|
* normalizing numbers in a Montgomery system.
|
|
*/
|
|
mp_err mp_montgomery_calc_normalization(mp_int *a, const mp_int *b) MP_WUR;
|
|
|
|
/* computes x/R == x (mod N) via Montgomery Reduction */
|
|
mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho) MP_WUR;
|
|
|
|
/* returns 1 if a is a valid DR modulus */
|
|
mp_bool mp_dr_is_modulus(const mp_int *a) MP_WUR;
|
|
|
|
/* 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 */
|
|
mp_err mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k) MP_WUR;
|
|
|
|
/* returns true if a can be reduced with mp_reduce_2k */
|
|
mp_bool mp_reduce_is_2k(const mp_int *a) MP_WUR;
|
|
|
|
/* determines k value for 2k reduction */
|
|
mp_err mp_reduce_2k_setup(const mp_int *a, mp_digit *d) MP_WUR;
|
|
|
|
/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
|
|
mp_err mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d) MP_WUR;
|
|
|
|
/* returns true if a can be reduced with mp_reduce_2k_l */
|
|
mp_bool mp_reduce_is_2k_l(const mp_int *a) MP_WUR;
|
|
|
|
/* determines k value for 2k reduction */
|
|
mp_err mp_reduce_2k_setup_l(const mp_int *a, mp_int *d) MP_WUR;
|
|
|
|
/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
|
|
mp_err mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d) MP_WUR;
|
|
|
|
/* Y = G**X (mod P) */
|
|
mp_err mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y) MP_WUR;
|
|
|
|
/* ---> Primes <--- */
|
|
|
|
/* number of primes */
|
|
#ifdef MP_8BIT
|
|
# define PRIVATE_MP_PRIME_TAB_SIZE 31
|
|
#else
|
|
# define PRIVATE_MP_PRIME_TAB_SIZE 256
|
|
#endif
|
|
#define PRIME_SIZE (MP_DEPRECATED_PRAGMA("PRIME_SIZE has been made internal") PRIVATE_MP_PRIME_TAB_SIZE)
|
|
|
|
/* table of first PRIME_SIZE primes */
|
|
MP_DEPRECATED(internal) extern const mp_digit ltm_prime_tab[PRIVATE_MP_PRIME_TAB_SIZE];
|
|
|
|
/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
|
|
MP_DEPRECATED(mp_prime_is_prime) mp_err mp_prime_is_divisible(const mp_int *a, mp_bool *result) MP_WUR;
|
|
|
|
/* performs one Fermat test of "a" using base "b".
|
|
* Sets result to 0 if composite or 1 if probable prime
|
|
*/
|
|
mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, mp_bool *result) MP_WUR;
|
|
|
|
/* performs one Miller-Rabin test of "a" using base "b".
|
|
* Sets result to 0 if composite or 1 if probable prime
|
|
*/
|
|
mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, mp_bool *result) MP_WUR;
|
|
|
|
/* 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) MP_WUR;
|
|
|
|
/* performs one strong Lucas-Selfridge test of "a".
|
|
* Sets result to 0 if composite or 1 if probable prime
|
|
*/
|
|
mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, mp_bool *result) MP_WUR;
|
|
|
|
/* performs one Frobenius test of "a" as described by Paul Underwood.
|
|
* Sets result to 0 if composite or 1 if probable prime
|
|
*/
|
|
mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result) MP_WUR;
|
|
|
|
/* 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
|
|
*/
|
|
mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result) MP_WUR;
|
|
|
|
/* 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
|
|
*/
|
|
mp_err mp_prime_next_prime(mp_int *a, int t, int bbs_style) MP_WUR;
|
|
|
|
/* 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_DEPRECATED_PRAGMA("mp_prime_random has been deprecated, use mp_prime_rand instead") mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?MP_PRIME_BBS:0, cb, dat))
|
|
|
|
/* makes a truly random prime of a given size (bits),
|
|
*
|
|
* Flags are as follows:
|
|
*
|
|
* MP_PRIME_BBS - make prime congruent to 3 mod 4
|
|
* MP_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies MP_PRIME_BBS)
|
|
* MP_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
|
|
*
|
|
*/
|
|
MP_DEPRECATED(mp_prime_rand) mp_err mp_prime_random_ex(mp_int *a, int t, int size, int flags,
|
|
private_mp_prime_callback cb, void *dat) MP_WUR;
|
|
mp_err mp_prime_rand(mp_int *a, int t, int size, int flags) MP_WUR;
|
|
|
|
/* Integer logarithm to integer base */
|
|
mp_err mp_log_u32(const mp_int *a, uint32_t base, uint32_t *c) MP_WUR;
|
|
|
|
/* c = a**b */
|
|
mp_err mp_expt_u32(const mp_int *a, uint32_t b, mp_int *c) MP_WUR;
|
|
MP_DEPRECATED(mp_expt_u32) mp_err mp_expt_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR;
|
|
MP_DEPRECATED(mp_expt_u32) mp_err mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) MP_WUR;
|
|
|
|
/* ---> radix conversion <--- */
|
|
int mp_count_bits(const mp_int *a) MP_WUR;
|
|
|
|
|
|
MP_DEPRECATED(mp_ubin_size) int mp_unsigned_bin_size(const mp_int *a) MP_WUR;
|
|
MP_DEPRECATED(mp_from_ubin) mp_err mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c) MP_WUR;
|
|
MP_DEPRECATED(mp_to_ubin) mp_err mp_to_unsigned_bin(const mp_int *a, unsigned char *b) MP_WUR;
|
|
MP_DEPRECATED(mp_to_ubin) mp_err mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) MP_WUR;
|
|
|
|
MP_DEPRECATED(mp_sbin_size) int mp_signed_bin_size(const mp_int *a) MP_WUR;
|
|
MP_DEPRECATED(mp_from_sbin) mp_err mp_read_signed_bin(mp_int *a, const unsigned char *b, int c) MP_WUR;
|
|
MP_DEPRECATED(mp_to_sbin) mp_err mp_to_signed_bin(const mp_int *a, unsigned char *b) MP_WUR;
|
|
MP_DEPRECATED(mp_to_sbin) mp_err mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) MP_WUR;
|
|
|
|
size_t mp_ubin_size(const mp_int *a) MP_WUR;
|
|
mp_err mp_from_ubin(mp_int *a, const unsigned char *buf, size_t size) MP_WUR;
|
|
mp_err mp_to_ubin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) MP_WUR;
|
|
|
|
size_t mp_sbin_size(const mp_int *a) MP_WUR;
|
|
mp_err mp_from_sbin(mp_int *a, const unsigned char *buf, size_t size) MP_WUR;
|
|
mp_err mp_to_sbin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) MP_WUR;
|
|
|
|
mp_err mp_read_radix(mp_int *a, const char *str, int radix) MP_WUR;
|
|
MP_DEPRECATED(mp_to_radix) mp_err mp_toradix(const mp_int *a, char *str, int radix) MP_WUR;
|
|
MP_DEPRECATED(mp_to_radix) mp_err mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen) MP_WUR;
|
|
mp_err mp_to_radix(const mp_int *a, char *str, size_t maxlen, size_t *written, int radix) MP_WUR;
|
|
mp_err mp_radix_size(const mp_int *a, int radix, int *size) MP_WUR;
|
|
|
|
#ifndef MP_NO_FILE
|
|
mp_err mp_fread(mp_int *a, int radix, FILE *stream) MP_WUR;
|
|
mp_err mp_fwrite(const mp_int *a, int radix, FILE *stream) MP_WUR;
|
|
#endif
|
|
|
|
#define mp_read_raw(mp, str, len) (MP_DEPRECATED_PRAGMA("replaced by mp_read_signed_bin") mp_read_signed_bin((mp), (str), (len)))
|
|
#define mp_raw_size(mp) (MP_DEPRECATED_PRAGMA("replaced by mp_signed_bin_size") mp_signed_bin_size(mp))
|
|
#define mp_toraw(mp, str) (MP_DEPRECATED_PRAGMA("replaced by mp_to_signed_bin") mp_to_signed_bin((mp), (str)))
|
|
#define mp_read_mag(mp, str, len) (MP_DEPRECATED_PRAGMA("replaced by mp_read_unsigned_bin") mp_read_unsigned_bin((mp), (str), (len))
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#define mp_mag_size(mp) (MP_DEPRECATED_PRAGMA("replaced by mp_unsigned_bin_size") mp_unsigned_bin_size(mp))
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#define mp_tomag(mp, str) (MP_DEPRECATED_PRAGMA("replaced by mp_to_unsigned_bin") mp_to_unsigned_bin((mp), (str)))
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#define mp_tobinary(M, S) (MP_DEPRECATED_PRAGMA("replaced by mp_to_binary") mp_toradix((M), (S), 2))
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#define mp_tooctal(M, S) (MP_DEPRECATED_PRAGMA("replaced by mp_to_octal") mp_toradix((M), (S), 8))
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#define mp_todecimal(M, S) (MP_DEPRECATED_PRAGMA("replaced by mp_to_decimal") mp_toradix((M), (S), 10))
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#define mp_tohex(M, S) (MP_DEPRECATED_PRAGMA("replaced by mp_to_hex") mp_toradix((M), (S), 16))
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#define mp_to_binary(M, S, N) mp_to_radix((M), (S), (N), NULL, 2)
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#define mp_to_octal(M, S, N) mp_to_radix((M), (S), (N), NULL, 8)
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#define mp_to_decimal(M, S, N) mp_to_radix((M), (S), (N), NULL, 10)
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#define mp_to_hex(M, S, N) mp_to_radix((M), (S), (N), NULL, 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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