bignum.h File Reference

Multi-precision integer library. More...

#include <stdio.h>
#include <string.h>
#include "config.h"

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Data Structures
struct	mpi
	MPI structure. More...

Macros
#define	POLARSSL_ERR_MPI_FILE_IO_ERROR   -0x0002
	An error occurred while reading from or writing to a file.
#define	POLARSSL_ERR_MPI_BAD_INPUT_DATA   -0x0004
	Bad input parameters to function.
#define	POLARSSL_ERR_MPI_INVALID_CHARACTER   -0x0006
	There is an invalid character in the digit string.
#define	POLARSSL_ERR_MPI_BUFFER_TOO_SMALL   -0x0008
	The buffer is too small to write to.
#define	POLARSSL_ERR_MPI_NEGATIVE_VALUE   -0x000A
	The input arguments are negative or result in illegal output.
#define	POLARSSL_ERR_MPI_DIVISION_BY_ZERO   -0x000C
	The input argument for division is zero, which is not allowed.
#define	POLARSSL_ERR_MPI_NOT_ACCEPTABLE   -0x000E
	The input arguments are not acceptable.
#define	POLARSSL_ERR_MPI_MALLOC_FAILED   -0x0010
	Memory allocation failed.
#define	MPI_CHK(f)   if( ( ret = f ) != 0 ) goto cleanup
#define	POLARSSL_MPI_MAX_LIMBS   10000
#define	POLARSSL_MPI_WINDOW_SIZE   6
	Maximum windows size used.
#define	POLARSSL_MPI_MAX_SIZE   512
	Maximum number of bytes for usable MPIs.
#define	POLARSSL_MPI_MAX_BITS   ( 8 * POLARSSL_MPI_MAX_SIZE )
	Maximum number of bits for usable MPIs.
#define	POLARSSL_MPI_READ_BUFFER_SIZE   1250

Typedefs
typedef signed long	t_sint
typedef unsigned long	t_uint

Functions
void	mpi_init (mpi *X)
	Initialize one MPI.
void	mpi_free (mpi *X)
	Unallocate one MPI.
int	mpi_grow (mpi *X, size_t nblimbs)
	Enlarge to the specified number of limbs.
int	mpi_copy (mpi *X, const mpi *Y)
	Copy the contents of Y into X.
void	mpi_swap (mpi *X, mpi *Y)
	Swap the contents of X and Y.
int	mpi_lset (mpi *X, t_sint z)
	Set value from integer.
int	mpi_get_bit (mpi *X, size_t pos)
int	mpi_set_bit (mpi *X, size_t pos, unsigned char val)
size_t	mpi_lsb (const mpi *X)
	Return the number of least significant bits.
size_t	mpi_msb (const mpi *X)
	Return the number of most significant bits.
size_t	mpi_size (const mpi *X)
	Return the total size in bytes.
int	mpi_read_string (mpi *X, int radix, const char *s)
	Import from an ASCII string.
int	mpi_write_string (const mpi *X, int radix, char *s, size_t *slen)
	Export into an ASCII string.
int	mpi_read_file (mpi *X, int radix, FILE *fin)
	Read X from an opened file.
int	mpi_write_file (const char *p, const mpi *X, int radix, FILE *fout)
	Write X into an opened file, or stdout if fout is NULL.
int	mpi_read_binary (mpi *X, const unsigned char *buf, size_t buflen)
	Import X from unsigned binary data, big endian.
int	mpi_write_binary (const mpi *X, unsigned char *buf, size_t buflen)
	Export X into unsigned binary data, big endian.
int	mpi_shift_l (mpi *X, size_t count)
	Left-shift: X <<= count.
int	mpi_shift_r (mpi *X, size_t count)
	Right-shift: X >>= count.
int	mpi_cmp_abs (const mpi *X, const mpi *Y)
	Compare unsigned values.
int	mpi_cmp_mpi (const mpi *X, const mpi *Y)
	Compare signed values.
int	mpi_cmp_int (const mpi *X, t_sint z)
	Compare signed values.
int	mpi_add_abs (mpi *X, const mpi *A, const mpi *B)
	Unsigned addition: X = |A| + |B|.
int	mpi_sub_abs (mpi *X, const mpi *A, const mpi *B)
	Unsigned substraction: X = |A| - |B|.
int	mpi_add_mpi (mpi *X, const mpi *A, const mpi *B)
	Signed addition: X = A + B.
int	mpi_sub_mpi (mpi *X, const mpi *A, const mpi *B)
	Signed substraction: X = A - B.
int	mpi_add_int (mpi *X, const mpi *A, t_sint b)
	Signed addition: X = A + b.
int	mpi_sub_int (mpi *X, const mpi *A, t_sint b)
	Signed substraction: X = A - b.
int	mpi_mul_mpi (mpi *X, const mpi *A, const mpi *B)
	Baseline multiplication: X = A * B.
int	mpi_mul_int (mpi *X, const mpi *A, t_sint b)
	Baseline multiplication: X = A * b Note: b is an unsigned integer type, thus Negative values of b are ignored.
int	mpi_div_mpi (mpi *Q, mpi *R, const mpi *A, const mpi *B)
	Division by mpi: A = Q * B + R.
int	mpi_div_int (mpi *Q, mpi *R, const mpi *A, t_sint b)
	Division by int: A = Q * b + R.
int	mpi_mod_mpi (mpi *R, const mpi *A, const mpi *B)
	Modulo: R = A mod B.
int	mpi_mod_int (t_uint *r, const mpi *A, t_sint b)
	Modulo: r = A mod b.
int	mpi_exp_mod (mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR)
	Sliding-window exponentiation: X = A^E mod N.
int	mpi_fill_random (mpi *X, size_t size, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
	Fill an MPI X with size bytes of random.
int	mpi_gcd (mpi *G, const mpi *A, const mpi *B)
	Greatest common divisor: G = gcd(A, B)
int	mpi_inv_mod (mpi *X, const mpi *A, const mpi *N)
	Modular inverse: X = A^-1 mod N.
int	mpi_is_prime (mpi *X, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
	Miller-Rabin primality test.
int	mpi_gen_prime (mpi *X, size_t nbits, int dh_flag, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
	Prime number generation.
int	mpi_self_test (int verbose)
	Checkup routine.

Detailed Description

Multi-precision integer library.

Copyright (C) 2006-2010, Brainspark B.V.

This file is part of PolarSSL (http://www.polarssl.org) Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>

All rights reserved.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

Definition in file bignum.h.

Macro Definition Documentation

#define MPI_CHK

(

f

)

if( ( ret = f ) != 0 ) goto cleanup

Definition at line 44 of file bignum.h.

#define POLARSSL_ERR_MPI_BAD_INPUT_DATA   -0x0004

Bad input parameters to function.

Definition at line 36 of file bignum.h.

Referenced by FCT_BGN().

#define POLARSSL_ERR_MPI_BUFFER_TOO_SMALL   -0x0008

The buffer is too small to write to.

Definition at line 38 of file bignum.h.

Referenced by FCT_BGN().

#define POLARSSL_ERR_MPI_DIVISION_BY_ZERO   -0x000C

The input argument for division is zero, which is not allowed.

Definition at line 40 of file bignum.h.

Referenced by FCT_BGN().

#define POLARSSL_ERR_MPI_FILE_IO_ERROR   -0x0002

An error occurred while reading from or writing to a file.

Definition at line 35 of file bignum.h.

Referenced by FCT_BGN().

#define POLARSSL_ERR_MPI_INVALID_CHARACTER   -0x0006

There is an invalid character in the digit string.

Definition at line 37 of file bignum.h.

Referenced by FCT_BGN().

#define POLARSSL_ERR_MPI_MALLOC_FAILED   -0x0010

Memory allocation failed.

Definition at line 42 of file bignum.h.

#define POLARSSL_ERR_MPI_NEGATIVE_VALUE   -0x000A

The input arguments are negative or result in illegal output.

Definition at line 39 of file bignum.h.

Referenced by FCT_BGN().

#define POLARSSL_ERR_MPI_NOT_ACCEPTABLE   -0x000E

The input arguments are not acceptable.

Definition at line 41 of file bignum.h.

Referenced by FCT_BGN().

#define POLARSSL_MPI_MAX_BITS   ( 8 * POLARSSL_MPI_MAX_SIZE )

Maximum number of bits for usable MPIs.

Definition at line 70 of file bignum.h.

#define POLARSSL_MPI_MAX_LIMBS   10000

Definition at line 49 of file bignum.h.

#define POLARSSL_MPI_MAX_SIZE   512

Maximum number of bytes for usable MPIs.

Definition at line 69 of file bignum.h.

#define POLARSSL_MPI_READ_BUFFER_SIZE   1250

Definition at line 80 of file bignum.h.

#define POLARSSL_MPI_WINDOW_SIZE   6

Maximum windows size used.

Definition at line 60 of file bignum.h.

Typedef Documentation

typedef signed long t_sint

Definition at line 95 of file bignum.h.

typedef unsigned long t_uint

Definition at line 96 of file bignum.h.

Function Documentation

int mpi_add_abs	(	mpi *	X,
		const mpi *	A,
		const mpi *	B
	)

Unsigned addition: X = |A| + |B|.

Parameters

X	Destination MPI
A	Left-hand MPI
B	Right-hand MPI

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

int mpi_add_int	(	mpi *	X,
		const mpi *	A,
		t_sint	b
	)

Signed addition: X = A + b.

Parameters

X	Destination MPI
A	Left-hand MPI
b	The integer value to add

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

int mpi_add_mpi	(	mpi *	X,
		const mpi *	A,
		const mpi *	B
	)

Signed addition: X = A + B.

Parameters

X	Destination MPI
A	Left-hand MPI
B	Right-hand MPI

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

int mpi_cmp_abs	(	const mpi *	X,
		const mpi *	Y
	)

Compare unsigned values.

Parameters

X	Left-hand MPI
Y	Right-hand MPI

Returns

1 if |X| is greater than |Y|, -1 if |X| is lesser than |Y| or 0 if |X| is equal to |Y|

Referenced by FCT_BGN().

int mpi_cmp_int	(	const mpi *	X,
		t_sint	z
	)

Compare signed values.

Parameters

X	Left-hand MPI
z	The integer value to compare to

Returns

1 if X is greater than z, -1 if X is lesser than z or 0 if X is equal to z

Referenced by FCT_BGN().

int mpi_cmp_mpi	(	const mpi *	X,
		const mpi *	Y
	)

Compare signed values.

Parameters

X	Left-hand MPI
Y	Right-hand MPI

Returns

1 if X is greater than Y, -1 if X is lesser than Y or 0 if X is equal to Y

Referenced by FCT_BGN().

int mpi_copy	(	mpi *	X,
		const mpi *	Y
	)

Copy the contents of Y into X.

Parameters

X	Destination MPI
Y	Source MPI

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

int mpi_div_int	(	mpi *	Q,
		mpi *	R,
		const mpi *	A,
		t_sint	b
	)

Division by int: A = Q * b + R.

Parameters

Q	Destination MPI for the quotient
R	Destination MPI for the rest value
A	Left-hand MPI
b	Integer to divide by

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0

Note

Either Q or R can be NULL.

Referenced by FCT_BGN().

int mpi_div_mpi	(	mpi *	Q,
		mpi *	R,
		const mpi *	A,
		const mpi *	B
	)

Division by mpi: A = Q * B + R.

Parameters

Q	Destination MPI for the quotient
R	Destination MPI for the rest value
A	Left-hand MPI
B	Right-hand MPI

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0

Note

Either Q or R can be NULL.

Referenced by FCT_BGN().

int mpi_exp_mod	(	mpi *	X,
		const mpi *	A,
		const mpi *	E,
		const mpi *	N,
		mpi *	_RR
	)

Sliding-window exponentiation: X = A^E mod N.

Parameters

X	Destination MPI
A	Left-hand MPI
E	Exponent MPI
N	Modular MPI
_RR	Speed-up MPI used for recalculations

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or even

Note

_RR is used to avoid re-computing R*R mod N across multiple calls, which speeds up things a bit. It can be set to NULL if the extra performance is unneeded.

Referenced by FCT_BGN().

int mpi_fill_random	(	mpi *	X,
		size_t	size,
		int(*)(void *, unsigned char *, size_t)	f_rng,
		void *	p_rng
	)

Fill an MPI X with size bytes of random.

Parameters

X	Destination MPI
size	Size in bytes
f_rng	RNG function
p_rng	RNG parameter

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

void mpi_free

(

mpi *

X

)

Unallocate one MPI.

Parameters

X	One MPI to unallocate.

Referenced by FCT_BGN().

int mpi_gcd	(	mpi *	G,
		const mpi *	A,
		const mpi *	B
	)

Greatest common divisor: G = gcd(A, B)

Parameters

G	Destination MPI
A	Left-hand MPI
B	Right-hand MPI

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

int mpi_gen_prime	(	mpi *	X,
		size_t	nbits,
		int	dh_flag,
		int(*)(void *, unsigned char *, size_t)	f_rng,
		void *	p_rng
	)

Prime number generation.

Parameters

X	Destination MPI
nbits	Required size of X in bits ( 3 <= nbits <= POLARSSL_MPI_MAX_BITS )
dh_flag	If 1, then (X-1)/2 will be prime too
f_rng	RNG function
p_rng	RNG parameter

Returns

0 if successful (probably prime), POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, POLARSSL_ERR_MPI_BAD_INPUT_DATA if nbits is < 3

int mpi_get_bit	(	mpi *	X,
		size_t	pos
	)

Referenced by FCT_BGN().

int mpi_grow	(	mpi *	X,
		size_t	nblimbs
	)

Enlarge to the specified number of limbs.

Parameters

X	MPI to grow
nblimbs	The target number of limbs

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

void mpi_init

(

mpi *

X

)

Initialize one MPI.

Parameters

X	One MPI to initialize.

Referenced by FCT_BGN().

int mpi_inv_mod	(	mpi *	X,
		const mpi *	A,
		const mpi *	N
	)

Modular inverse: X = A^-1 mod N.

Parameters

X	Destination MPI
A	Left-hand MPI
N	Right-hand MPI

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or nil POLARSSL_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N

Referenced by FCT_BGN().

int mpi_is_prime	(	mpi *	X,
		int(*)(void *, unsigned char *, size_t)	f_rng,
		void *	p_rng
	)

Miller-Rabin primality test.

Parameters

X	MPI to check
f_rng	RNG function
p_rng	RNG parameter

Returns

0 if successful (probably prime), POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, POLARSSL_ERR_MPI_NOT_ACCEPTABLE if X is not prime

Referenced by FCT_BGN().

size_t mpi_lsb

(

const mpi *

X

)

Return the number of least significant bits.

Parameters

X	MPI to use

Referenced by FCT_BGN().

int mpi_lset	(	mpi *	X,
		t_sint	z
	)

Set value from integer.

Parameters

X	MPI to set
z	Value to use

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

int mpi_mod_int	(	t_uint *	r,
		const mpi *	A,
		t_sint	b
	)

Modulo: r = A mod b.

Parameters

r	Destination t_uint
A	Left-hand MPI
b	Integer to divide by

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0, POLARSSL_ERR_MPI_NEGATIVE_VALUE if b < 0

Referenced by FCT_BGN().

int mpi_mod_mpi	(	mpi *	R,
		const mpi *	A,
		const mpi *	B
	)

Modulo: R = A mod B.

Parameters

R	Destination MPI for the rest value
A	Left-hand MPI
B	Right-hand MPI

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0, POLARSSL_ERR_MPI_NEGATIVE_VALUE if B < 0

Referenced by FCT_BGN().

size_t mpi_msb

(

const mpi *

X

)

Return the number of most significant bits.

Parameters

X	MPI to use

Referenced by d2i_RSA_PUBKEY(), and FCT_BGN().

int mpi_mul_int	(	mpi *	X,
		const mpi *	A,
		t_sint	b
	)

Baseline multiplication: X = A * b Note: b is an unsigned integer type, thus Negative values of b are ignored.

Parameters

X	Destination MPI
A	Left-hand MPI
b	The integer value to multiply with

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

int mpi_mul_mpi	(	mpi *	X,
		const mpi *	A,
		const mpi *	B
	)

Baseline multiplication: X = A * B.

Parameters

X	Destination MPI
A	Left-hand MPI
B	Right-hand MPI

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

int mpi_read_binary	(	mpi *	X,
		const unsigned char *	buf,
		size_t	buflen
	)

Import X from unsigned binary data, big endian.

Parameters

X	Destination MPI
buf	Input buffer
buflen	Input buffer size

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by d2i_RSA_PUBKEY(), and FCT_BGN().

int mpi_read_file	(	mpi *	X,
		int	radix,
		FILE *	fin
	)

Read X from an opened file.

Parameters

X	Destination MPI
radix	Input numeric base
fin	Input file handle

Returns

0 if successful, POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer is too small or a POLARSSL_ERR_MPI_XXX error code

Referenced by FCT_BGN().

int mpi_read_string	(	mpi *	X,
		int	radix,
		const char *	s
	)

Import from an ASCII string.

Parameters

X	Destination MPI
radix	Input numeric base
s	Null-terminated string buffer

Returns

0 if successful, or a POLARSSL_ERR_MPI_XXX error code

Referenced by FCT_BGN().

int mpi_self_test

(

int

verbose

)

Checkup routine.

Returns

0 if successful, or 1 if the test failed

Referenced by FCT_BGN().

int mpi_set_bit	(	mpi *	X,
		size_t	pos,
		unsigned char	val
	)

Referenced by FCT_BGN().

int mpi_shift_l	(	mpi *	X,
		size_t	count
	)

Left-shift: X <<= count.

Parameters

X	MPI to shift
count	Amount to shift

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

int mpi_shift_r	(	mpi *	X,
		size_t	count
	)

Right-shift: X >>= count.

Parameters

X	MPI to shift
count	Amount to shift

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

size_t mpi_size

(

const mpi *

X

)

Return the total size in bytes.

Parameters

X	MPI to use

Referenced by FCT_BGN().

int mpi_sub_abs	(	mpi *	X,
		const mpi *	A,
		const mpi *	B
	)

Unsigned substraction: X = |A| - |B|.

Parameters

X	Destination MPI
A	Left-hand MPI
B	Right-hand MPI

Returns

0 if successful, POLARSSL_ERR_MPI_NEGATIVE_VALUE if B is greater than A

Referenced by FCT_BGN().

int mpi_sub_int	(	mpi *	X,
		const mpi *	A,
		t_sint	b
	)

Signed substraction: X = A - b.

Parameters

X	Destination MPI
A	Left-hand MPI
b	The integer value to subtract

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

int mpi_sub_mpi	(	mpi *	X,
		const mpi *	A,
		const mpi *	B
	)

Signed substraction: X = A - B.

Parameters

X	Destination MPI
A	Left-hand MPI
B	Right-hand MPI

Returns

0 if successful, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Referenced by FCT_BGN().

void mpi_swap	(	mpi *	X,
		mpi *	Y
	)

Swap the contents of X and Y.

Parameters

X	First MPI value
Y	Second MPI value

Referenced by FCT_BGN().

int mpi_write_binary	(	const mpi *	X,
		unsigned char *	buf,
		size_t	buflen
	)

Export X into unsigned binary data, big endian.

Parameters

X	Source MPI
buf	Output buffer
buflen	Output buffer size

Returns

0 if successful, POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough

Referenced by FCT_BGN().

int mpi_write_file	(	const char *	p,
		const mpi *	X,
		int	radix,
		FILE *	fout
	)

Write X into an opened file, or stdout if fout is NULL.

Parameters

p	Prefix, can be NULL
X	Source MPI
radix	Output numeric base
fout	Output file handle (can be NULL)

Returns

0 if successful, or a POLARSSL_ERR_MPI_XXX error code

Note

Set fout == NULL to print X on the console.

Referenced by FCT_BGN().

int mpi_write_string	(	const mpi *	X,
		int	radix,
		char *	s,
		size_t *	slen
	)

Export into an ASCII string.

Parameters

X	Source MPI
radix	Output numeric base
s	String buffer
slen	String buffer size

Returns

0 if successful, or a POLARSSL_ERR_MPI_XXX error code. *slen is always updated to reflect the amount of data that has (or would have) been written.

Note

Call this function with *slen = 0 to obtain the minimum required buffer size in *slen.

Referenced by FCT_BGN().