bignum.c File Reference

#include "mbedtls/config.h"
#include "mbedtls/bignum.h"
#include "mbedtls/bn_mul.h"
#include <string.h>
#include "mbedtls/platform.h"

Include dependency graph for bignum.c:

Macros
#define	ciL   (sizeof(mbedtls_mpi_uint)) /* chars in limb */
#define	biL   (ciL << 3) /* bits in limb */
#define	biH   (ciL << 2) /* half limb size */
#define	MPI_SIZE_T_MAX   ( (size_t) -1 ) /* SIZE_T_MAX is not standard */
#define	BITS_TO_LIMBS(i)   ( (i) / biL + ( (i) % biL != 0 ) )
#define	CHARS_TO_LIMBS(i)   ( (i) / ciL + ( (i) % ciL != 0 ) )
#define	GCD_PAIR_COUNT   3

Functions
static void	mbedtls_mpi_zeroize (mbedtls_mpi_uint *v, size_t n)
void	mbedtls_mpi_init (mbedtls_mpi *X)
	Initialize one MPI (make internal references valid) This just makes it ready to be set or freed, but does not define a value for the MPI. More...
void	mbedtls_mpi_free (mbedtls_mpi *X)
	Unallocate one MPI. More...
int	mbedtls_mpi_grow (mbedtls_mpi *X, size_t nblimbs)
	Enlarge to the specified number of limbs. More...
int	mbedtls_mpi_shrink (mbedtls_mpi *X, size_t nblimbs)
	Resize down, keeping at least the specified number of limbs. More...
int	mbedtls_mpi_copy (mbedtls_mpi *X, const mbedtls_mpi *Y)
	Copy the contents of Y into X. More...
void	mbedtls_mpi_swap (mbedtls_mpi *X, mbedtls_mpi *Y)
	Swap the contents of X and Y. More...
int	mbedtls_mpi_safe_cond_assign (mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign)
	Safe conditional assignement X = Y if assign is 1. More...
int	mbedtls_mpi_safe_cond_swap (mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap)
	Safe conditional swap X <-> Y if swap is 1. More...
int	mbedtls_mpi_lset (mbedtls_mpi *X, mbedtls_mpi_sint z)
	Set value from integer. More...
int	mbedtls_mpi_get_bit (const mbedtls_mpi *X, size_t pos)
	Get a specific bit from X. More...
int	mbedtls_mpi_set_bit (mbedtls_mpi *X, size_t pos, unsigned char val)
	Set a bit of X to a specific value of 0 or 1. More...
size_t	mbedtls_mpi_lsb (const mbedtls_mpi *X)
	Return the number of zero-bits before the least significant '1' bit. More...
static size_t	mbedtls_clz (const mbedtls_mpi_uint x)
size_t	mbedtls_mpi_bitlen (const mbedtls_mpi *X)
	Return the number of bits up to and including the most significant '1' bit'. More...
size_t	mbedtls_mpi_size (const mbedtls_mpi *X)
	Return the total size in bytes. More...
static int	mpi_get_digit (mbedtls_mpi_uint *d, int radix, char c)
int	mbedtls_mpi_read_string (mbedtls_mpi *X, int radix, const char *s)
	Import from an ASCII string. More...
static int	mpi_write_hlp (mbedtls_mpi *X, int radix, char **p)
int	mbedtls_mpi_write_string (const mbedtls_mpi *X, int radix, char *buf, size_t buflen, size_t *olen)
	Export into an ASCII string. More...
int	mbedtls_mpi_read_file (mbedtls_mpi *X, int radix, FILE *fin)
	Read MPI from a line in an opened file. More...
int	mbedtls_mpi_write_file (const char *p, const mbedtls_mpi *X, int radix, FILE *fout)
	Write X into an opened file, or stdout if fout is NULL. More...
int	mbedtls_mpi_read_binary (mbedtls_mpi *X, const unsigned char *buf, size_t buflen)
	Import X from unsigned binary data, big endian. More...
int	mbedtls_mpi_write_binary (const mbedtls_mpi *X, unsigned char *buf, size_t buflen)
	Export X into unsigned binary data, big endian. Always fills the whole buffer, which will start with zeros if the number is smaller. More...
int	mbedtls_mpi_shift_l (mbedtls_mpi *X, size_t count)
	Left-shift: X <<= count. More...
int	mbedtls_mpi_shift_r (mbedtls_mpi *X, size_t count)
	Right-shift: X >>= count. More...
int	mbedtls_mpi_cmp_abs (const mbedtls_mpi *X, const mbedtls_mpi *Y)
	Compare unsigned values. More...
int	mbedtls_mpi_cmp_mpi (const mbedtls_mpi *X, const mbedtls_mpi *Y)
	Compare signed values. More...
int	mbedtls_mpi_cmp_int (const mbedtls_mpi *X, mbedtls_mpi_sint z)
	Compare signed values. More...
int	mbedtls_mpi_add_abs (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
	Unsigned addition: X = |A| + |B|. More...
static void	mpi_sub_hlp (size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d)
int	mbedtls_mpi_sub_abs (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
	Unsigned subtraction: X = |A| - |B|. More...
int	mbedtls_mpi_add_mpi (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
	Signed addition: X = A + B. More...
int	mbedtls_mpi_sub_mpi (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
	Signed subtraction: X = A - B. More...
int	mbedtls_mpi_add_int (mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b)
	Signed addition: X = A + b. More...
int	mbedtls_mpi_sub_int (mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b)
	Signed subtraction: X = A - b. More...
static void	mpi_mul_hlp (size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b)
int	mbedtls_mpi_mul_mpi (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
	Baseline multiplication: X = A * B. More...
int	mbedtls_mpi_mul_int (mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b)
	Baseline multiplication: X = A * b. More...
static mbedtls_mpi_uint	mbedtls_int_div_int (mbedtls_mpi_uint u1, mbedtls_mpi_uint u0, mbedtls_mpi_uint d, mbedtls_mpi_uint *r)
int	mbedtls_mpi_div_mpi (mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B)
	Division by mbedtls_mpi: A = Q * B + R. More...
int	mbedtls_mpi_div_int (mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b)
	Division by int: A = Q * b + R. More...
int	mbedtls_mpi_mod_mpi (mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B)
	Modulo: R = A mod B. More...
int	mbedtls_mpi_mod_int (mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b)
	Modulo: r = A mod b. More...
static void	mpi_montg_init (mbedtls_mpi_uint *mm, const mbedtls_mpi *N)
static int	mpi_montmul (mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T)
static int	mpi_montred (mbedtls_mpi *A, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T)
int	mbedtls_mpi_exp_mod (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR)
	Sliding-window exponentiation: X = A^E mod N. More...
int	mbedtls_mpi_gcd (mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B)
	Greatest common divisor: G = gcd(A, B) More...
int	mbedtls_mpi_fill_random (mbedtls_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. More...
int	mbedtls_mpi_inv_mod (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N)
	Modular inverse: X = A^-1 mod N. More...
static int	mpi_check_small_factors (const mbedtls_mpi *X)
static int	mpi_miller_rabin (const mbedtls_mpi *X, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
int	mbedtls_mpi_is_prime (const mbedtls_mpi *X, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
	Miller-Rabin primality test. More...
int	mbedtls_mpi_gen_prime (mbedtls_mpi *X, size_t nbits, int dh_flag, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
	Prime number generation. More...
int	mbedtls_mpi_self_test (int verbose)
	Checkup routine. More...

Variables
static const int	small_prime []
static const int	gcd_pairs [GCD_PAIR_COUNT][3]

Macro Definition Documentation

biH

#define biH   (ciL << 2) /* half limb size */

biL

#define biL   (ciL << 3) /* bits in limb */

BITS_TO_LIMBS

#define BITS_TO_LIMBS

(

i

)

( (i) / biL + ( (i) % biL != 0 ) )

CHARS_TO_LIMBS

#define CHARS_TO_LIMBS

(

i

)

( (i) / ciL + ( (i) % ciL != 0 ) )

ciL

#define ciL   (sizeof(mbedtls_mpi_uint)) /* chars in limb */

GCD_PAIR_COUNT

#define GCD_PAIR_COUNT   3

MPI_SIZE_T_MAX

#define MPI_SIZE_T_MAX   ( (size_t) -1 ) /* SIZE_T_MAX is not standard */

Function Documentation

mbedtls_clz()

static size_t mbedtls_clz ( const mbedtls_mpi_uint  x )

static

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mbedtls_int_div_int()

static mbedtls_mpi_uint mbedtls_int_div_int ( mbedtls_mpi_uint  u1, mbedtls_mpi_uint  u0, mbedtls_mpi_uint  d, mbedtls_mpi_uint *  r  )

static

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mbedtls_mpi_add_abs()

int mbedtls_mpi_add_abs	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		const mbedtls_mpi *	B
	)

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

Parameters

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

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_add_int()

int mbedtls_mpi_add_int	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		mbedtls_mpi_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, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_add_mpi()

int mbedtls_mpi_add_mpi	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		const mbedtls_mpi *	B
	)

Signed addition: X = A + B.

Parameters

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

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_bitlen()

size_t mbedtls_mpi_bitlen

(

const mbedtls_mpi *

X

)

Return the number of bits up to and including the most significant '1' bit'.

Note: Thus also the one-based index of the most significant '1' bit

Parameters

X	MPI to use

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mbedtls_mpi_cmp_abs()

int mbedtls_mpi_cmp_abs	(	const mbedtls_mpi *	X,
		const mbedtls_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|

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mbedtls_mpi_cmp_int()

int mbedtls_mpi_cmp_int	(	const mbedtls_mpi *	X,
		mbedtls_mpi_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

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mbedtls_mpi_cmp_mpi()

int mbedtls_mpi_cmp_mpi	(	const mbedtls_mpi *	X,
		const mbedtls_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

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mbedtls_mpi_copy()

int mbedtls_mpi_copy	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	Y
	)

Copy the contents of Y into X.

Parameters

X	Destination MPI
Y	Source MPI

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_div_int()

int mbedtls_mpi_div_int	(	mbedtls_mpi *	Q,
		mbedtls_mpi *	R,
		const mbedtls_mpi *	A,
		mbedtls_mpi_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, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0

Note

Either Q or R can be NULL.

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mbedtls_mpi_div_mpi()

int mbedtls_mpi_div_mpi	(	mbedtls_mpi *	Q,
		mbedtls_mpi *	R,
		const mbedtls_mpi *	A,
		const mbedtls_mpi *	B
	)

Division by mbedtls_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, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0

Note

Either Q or R can be NULL.

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mbedtls_mpi_exp_mod()

int mbedtls_mpi_exp_mod	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		const mbedtls_mpi *	E,
		const mbedtls_mpi *	N,
		mbedtls_mpi *	_RR
	)

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

Parameters

X	Destination MPI
A	Left-hand MPI
E	Exponent MPI
N	Modular MPI

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mbedtls_mpi_fill_random()

int mbedtls_mpi_fill_random	(	mbedtls_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, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_free()

void mbedtls_mpi_free

(

mbedtls_mpi *

X

)

Unallocate one MPI.

Parameters

X	One MPI to unallocate.

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mbedtls_mpi_gcd()

int mbedtls_mpi_gcd	(	mbedtls_mpi *	G,
		const mbedtls_mpi *	A,
		const mbedtls_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, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_gen_prime()

int mbedtls_mpi_gen_prime	(	mbedtls_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 <= MBEDTLS_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), MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3

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mbedtls_mpi_get_bit()

int mbedtls_mpi_get_bit	(	const mbedtls_mpi *	X,
		size_t	pos
	)

Get a specific bit from X.

Parameters

X	MPI to use
pos	Zero-based index of the bit in X

Returns

Either a 0 or a 1

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mbedtls_mpi_grow()

int mbedtls_mpi_grow	(	mbedtls_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, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_init()

void mbedtls_mpi_init

(

mbedtls_mpi *

X

)

Initialize one MPI (make internal references valid) This just makes it ready to be set or freed, but does not define a value for the MPI.

Parameters

X	One MPI to initialize.

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mbedtls_mpi_inv_mod()

int mbedtls_mpi_inv_mod	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		const mbedtls_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, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1, MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N.

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mbedtls_mpi_is_prime()

int mbedtls_mpi_is_prime	(	const mbedtls_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), MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime

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mbedtls_mpi_lsb()

size_t mbedtls_mpi_lsb

(

const mbedtls_mpi *

X

)

Return the number of zero-bits before the least significant '1' bit.

Note: Thus also the zero-based index of the least significant '1' bit

Parameters

X	MPI to use

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mbedtls_mpi_lset()

int mbedtls_mpi_lset	(	mbedtls_mpi *	X,
		mbedtls_mpi_sint	z
	)

Set value from integer.

Parameters

X	MPI to set
z	Value to use

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_mod_int()

int mbedtls_mpi_mod_int	(	mbedtls_mpi_uint *	r,
		const mbedtls_mpi *	A,
		mbedtls_mpi_sint	b
	)

Modulo: r = A mod b.

Parameters

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

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0, MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0

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mbedtls_mpi_mod_mpi()

int mbedtls_mpi_mod_mpi	(	mbedtls_mpi *	R,
		const mbedtls_mpi *	A,
		const mbedtls_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, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0, MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0

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mbedtls_mpi_mul_int()

int mbedtls_mpi_mul_int	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		mbedtls_mpi_uint	b
	)

Baseline multiplication: X = A * b.

Parameters

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

Note

b is unsigned

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_mul_mpi()

int mbedtls_mpi_mul_mpi	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		const mbedtls_mpi *	B
	)

Baseline multiplication: X = A * B.

Parameters

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

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_read_binary()

int mbedtls_mpi_read_binary	(	mbedtls_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, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_read_file()

int mbedtls_mpi_read_file	(	mbedtls_mpi *	X,
		int	radix,
		FILE *	fin
	)

Read MPI from a line in an opened file.

Parameters

X	Destination MPI
radix	Input numeric base
fin	Input file handle

Returns

0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer is too small or a MBEDTLS_ERR_MPI_XXX error code

Note

On success, this function advances the file stream to the end of the current line or to EOF.

The function returns 0 on an empty line.

Leading whitespaces are ignored, as is a '0x' prefix for radix 16.

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mbedtls_mpi_read_string()

int mbedtls_mpi_read_string	(	mbedtls_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 MBEDTLS_ERR_MPI_XXX error code

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mbedtls_mpi_safe_cond_assign()

int mbedtls_mpi_safe_cond_assign	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	Y,
		unsigned char	assign
	)

Safe conditional assignement X = Y if assign is 1.

Parameters

X	MPI to conditionally assign to
Y	Value to be assigned
assign	1: perform the assignment, 0: keep X's original value

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,

Note

This function is equivalent to if( assign ) mbedtls_mpi_copy( X, Y ); except that it avoids leaking any information about whether the assignment was done or not (the above code may leak information through branch prediction and/or memory access patterns analysis).

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mbedtls_mpi_safe_cond_swap()

int mbedtls_mpi_safe_cond_swap	(	mbedtls_mpi *	X,
		mbedtls_mpi *	Y,
		unsigned char	assign
	)

Safe conditional swap X <-> Y if swap is 1.

Parameters

X	First mbedtls_mpi value
Y	Second mbedtls_mpi value
assign	1: perform the swap, 0: keep X and Y's original values

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,

Note

This function is equivalent to if( assign ) mbedtls_mpi_swap( X, Y ); except that it avoids leaking any information about whether the assignment was done or not (the above code may leak information through branch prediction and/or memory access patterns analysis).

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mbedtls_mpi_self_test()

int mbedtls_mpi_self_test

(

int

verbose

)

Checkup routine.

Returns

0 if successful, or 1 if the test failed

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mbedtls_mpi_set_bit()

int mbedtls_mpi_set_bit	(	mbedtls_mpi *	X,
		size_t	pos,
		unsigned char	val
	)

Set a bit of X to a specific value of 0 or 1.

Note

Will grow X if necessary to set a bit to 1 in a not yet existing limb. Will not grow if bit should be set to 0

Parameters

X	MPI to use
pos	Zero-based index of the bit in X
val	The value to set the bit to (0 or 1)

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1

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mbedtls_mpi_shift_l()

int mbedtls_mpi_shift_l	(	mbedtls_mpi *	X,
		size_t	count
	)

Left-shift: X <<= count.

Parameters

X	MPI to shift
count	Amount to shift

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_shift_r()

int mbedtls_mpi_shift_r	(	mbedtls_mpi *	X,
		size_t	count
	)

Right-shift: X >>= count.

Parameters

X	MPI to shift
count	Amount to shift

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_shrink()

int mbedtls_mpi_shrink	(	mbedtls_mpi *	X,
		size_t	nblimbs
	)

Resize down, keeping at least the specified number of limbs.

Parameters

X	MPI to shrink
nblimbs	The minimum number of limbs to keep

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_size()

size_t mbedtls_mpi_size

(

const mbedtls_mpi *

X

)

Return the total size in bytes.

Parameters

X	MPI to use

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mbedtls_mpi_sub_abs()

int mbedtls_mpi_sub_abs	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		const mbedtls_mpi *	B
	)

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

Parameters

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

Returns

0 if successful, MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A

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mbedtls_mpi_sub_int()

int mbedtls_mpi_sub_int	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		mbedtls_mpi_sint	b
	)

Signed subtraction: X = A - b.

Parameters

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

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_sub_mpi()

int mbedtls_mpi_sub_mpi	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		const mbedtls_mpi *	B
	)

Signed subtraction: X = A - B.

Parameters

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

Returns

0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed

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mbedtls_mpi_swap()

void mbedtls_mpi_swap	(	mbedtls_mpi *	X,
		mbedtls_mpi *	Y
	)

Swap the contents of X and Y.

Parameters

X	First MPI value
Y	Second MPI value

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mbedtls_mpi_write_binary()

int mbedtls_mpi_write_binary	(	const mbedtls_mpi *	X,
		unsigned char *	buf,
		size_t	buflen
	)

Export X into unsigned binary data, big endian. Always fills the whole buffer, which will start with zeros if the number is smaller.

Parameters

X	Source MPI
buf	Output buffer
buflen	Output buffer size

Returns

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

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mbedtls_mpi_write_file()

int mbedtls_mpi_write_file	(	const char *	p,
		const mbedtls_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 MBEDTLS_ERR_MPI_XXX error code

Note

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

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mbedtls_mpi_write_string()

int mbedtls_mpi_write_string	(	const mbedtls_mpi *	X,
		int	radix,
		char *	buf,
		size_t	buflen,
		size_t *	olen
	)

Export into an ASCII string.

Parameters

X	Source MPI
radix	Output numeric base
buf	Buffer to write the string to
buflen	Length of buf
olen	Length of the string written, including final NUL byte

Returns

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

Note

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

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mbedtls_mpi_zeroize()

static void mbedtls_mpi_zeroize ( mbedtls_mpi_uint *  v, size_t  n  )

static

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mpi_check_small_factors()

static int mpi_check_small_factors ( const mbedtls_mpi *  X )

static

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mpi_get_digit()

static int mpi_get_digit ( mbedtls_mpi_uint *  d, int  radix, char  c  )

static

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mpi_miller_rabin()

static int mpi_miller_rabin ( const mbedtls_mpi *  X, int(*)(void *, unsigned char *, size_t)  f_rng, void *  p_rng  )

static

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mpi_montg_init()

static void mpi_montg_init ( mbedtls_mpi_uint *  mm, const mbedtls_mpi *  N  )

static

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mpi_montmul()

static int mpi_montmul ( mbedtls_mpi *  A, const mbedtls_mpi *  B, const mbedtls_mpi *  N, mbedtls_mpi_uint  mm, const mbedtls_mpi *  T  )

static

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mpi_montred()

static int mpi_montred ( mbedtls_mpi *  A, const mbedtls_mpi *  N, mbedtls_mpi_uint  mm, const mbedtls_mpi *  T  )

static

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mpi_mul_hlp()

static void mpi_mul_hlp ( size_t  i, mbedtls_mpi_uint *  s, mbedtls_mpi_uint *  d, mbedtls_mpi_uint  b  )

static

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mpi_sub_hlp()

static void mpi_sub_hlp ( size_t  n, mbedtls_mpi_uint *  s, mbedtls_mpi_uint *  d  )

static

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mpi_write_hlp()

static int mpi_write_hlp ( mbedtls_mpi *  X, int  radix, char **  p  )

static

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Variable Documentation

gcd_pairs

const int gcd_pairs[GCD_PAIR_COUNT][3]

static

Initial value:

=
{
    { 693, 609, 21 },
    { 1764, 868, 28 },
    { 768454923, 542167814, 1 }
}

small_prime

const int small_prime[]

static

Initial value:

=
{
        3,    5,    7,   11,   13,   17,   19,   23,
       29,   31,   37,   41,   43,   47,   53,   59,
       61,   67,   71,   73,   79,   83,   89,   97,
      101,  103,  107,  109,  113,  127,  131,  137,
      139,  149,  151,  157,  163,  167,  173,  179,
      181,  191,  193,  197,  199,  211,  223,  227,
      229,  233,  239,  241,  251,  257,  263,  269,
      271,  277,  281,  283,  293,  307,  311,  313,
      317,  331,  337,  347,  349,  353,  359,  367,
      373,  379,  383,  389,  397,  401,  409,  419,
      421,  431,  433,  439,  443,  449,  457,  461,
      463,  467,  479,  487,  491,  499,  503,  509,
      521,  523,  541,  547,  557,  563,  569,  571,
      577,  587,  593,  599,  601,  607,  613,  617,
      619,  631,  641,  643,  647,  653,  659,  661,
      673,  677,  683,  691,  701,  709,  719,  727,
      733,  739,  743,  751,  757,  761,  769,  773,
      787,  797,  809,  811,  821,  823,  827,  829,
      839,  853,  857,  859,  863,  877,  881,  883,
      887,  907,  911,  919,  929,  937,  941,  947,
      953,  967,  971,  977,  983,  991,  997, -103
}