Multi-precision integer library. More...

Data Structures
struct	mbedtls_mpi
	MPI structure. More...
Typedefs
typedef struct mbedtls_mpi	mbedtls_mpi
	MPI structure.
Enumerations
enum	mbedtls_mpi_gen_prime_flag_t { MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002 }
	Flags for mbedtls_mpi_gen_prime() More...
Functions
void	mbedtls_mpi_init (mbedtls_mpi *X)
	Initialize an MPI context.
void	mbedtls_mpi_free (mbedtls_mpi *X)
	This function frees the components of an MPI context.
int	mbedtls_mpi_grow (mbedtls_mpi *X, size_t nblimbs)
	Enlarge an MPI to the specified number of limbs.
int	mbedtls_mpi_shrink (mbedtls_mpi *X, size_t nblimbs)
	This function resizes an MPI downwards, keeping at least the specified number of limbs.
int	mbedtls_mpi_copy (mbedtls_mpi X, const mbedtls_mpi Y)
	Make a copy of an MPI.
void	mbedtls_mpi_swap (mbedtls_mpi X, mbedtls_mpi Y)
	Swap the contents of two MPIs.
int	mbedtls_mpi_safe_cond_assign (mbedtls_mpi X, const mbedtls_mpi Y, unsigned char assign)
	Perform a safe conditional copy of MPI which doesn't reveal whether the condition was true or not.
int	mbedtls_mpi_safe_cond_swap (mbedtls_mpi X, mbedtls_mpi Y, unsigned char assign)
	Perform a safe conditional swap which doesn't reveal whether the condition was true or not.
int	mbedtls_mpi_lset (mbedtls_mpi *X, mbedtls_mpi_sint z)
	Store integer value in MPI.
int	mbedtls_mpi_get_bit (const mbedtls_mpi *X, size_t pos)
	Get a specific bit from an MPI.
int	mbedtls_mpi_set_bit (mbedtls_mpi *X, size_t pos, unsigned char val)
	Modify a specific bit in an MPI.
size_t	mbedtls_mpi_lsb (const mbedtls_mpi *X)
	Return the number of bits of value `0` before the least significant bit of value `1`.
size_t	mbedtls_mpi_bitlen (const mbedtls_mpi *X)
	Return the number of bits up to and including the most significant bit of value `1`.
size_t	mbedtls_mpi_size (const mbedtls_mpi *X)
	Return the total size of an MPI value in bytes.
int	mbedtls_mpi_read_string (mbedtls_mpi X, int radix, const char s)
	Import an MPI from an ASCII string.
int	mbedtls_mpi_write_string (const mbedtls_mpi X, int radix, char buf, size_t buflen, size_t *olen)
	Export an MPI to an ASCII string.
int	mbedtls_mpi_read_file (mbedtls_mpi X, int radix, FILE fin)
	Read an MPI from a line in an opened file.
int	mbedtls_mpi_write_file (const char p, const mbedtls_mpi X, int radix, FILE *fout)
	Export an MPI into an opened file.
int	mbedtls_mpi_read_binary (mbedtls_mpi X, const unsigned char buf, size_t buflen)
	Import an MPI from unsigned big endian binary data.
int	mbedtls_mpi_read_binary_le (mbedtls_mpi X, const unsigned char buf, size_t buflen)
	Import X from unsigned binary data, little endian.
int	mbedtls_mpi_write_binary (const mbedtls_mpi X, unsigned char buf, size_t buflen)
	Export X into unsigned binary data, big endian.
int	mbedtls_mpi_write_binary_le (const mbedtls_mpi X, unsigned char buf, size_t buflen)
	Export X into unsigned binary data, little endian.
int	mbedtls_mpi_shift_l (mbedtls_mpi *X, size_t count)
	Perform a left-shift on an MPI: X <<= count.
int	mbedtls_mpi_shift_r (mbedtls_mpi *X, size_t count)
	Perform a right-shift on an MPI: X >>= count.
int	mbedtls_mpi_cmp_abs (const mbedtls_mpi X, const mbedtls_mpi Y)
	Compare the absolute values of two MPIs.
int	mbedtls_mpi_cmp_mpi (const mbedtls_mpi X, const mbedtls_mpi Y)
	Compare two MPIs.
int	mbedtls_mpi_cmp_int (const mbedtls_mpi *X, mbedtls_mpi_sint z)
	Compare an MPI with an integer.
int	mbedtls_mpi_add_abs (mbedtls_mpi X, const mbedtls_mpi A, const mbedtls_mpi *B)
	Perform an unsigned addition of MPIs: X = \|A\| + \|B\|.
int	mbedtls_mpi_sub_abs (mbedtls_mpi X, const mbedtls_mpi A, const mbedtls_mpi *B)
	Perform an unsigned subtraction of MPIs: X = \|A\| - \|B\|.
int	mbedtls_mpi_add_mpi (mbedtls_mpi X, const mbedtls_mpi A, const mbedtls_mpi *B)
	Perform a signed addition of MPIs: X = A + B.
int	mbedtls_mpi_sub_mpi (mbedtls_mpi X, const mbedtls_mpi A, const mbedtls_mpi *B)
	Perform a signed subtraction of MPIs: X = A - B.
int	mbedtls_mpi_add_int (mbedtls_mpi X, const mbedtls_mpi A, mbedtls_mpi_sint b)
	Perform a signed addition of an MPI and an integer: X = A + b.
int	mbedtls_mpi_sub_int (mbedtls_mpi X, const mbedtls_mpi A, mbedtls_mpi_sint b)
	Perform a signed subtraction of an MPI and an integer: X = A - b.
int	mbedtls_mpi_mul_mpi (mbedtls_mpi X, const mbedtls_mpi A, const mbedtls_mpi *B)
	Perform a multiplication of two MPIs: X = A * B.
int	mbedtls_mpi_mul_int (mbedtls_mpi X, const mbedtls_mpi A, mbedtls_mpi_uint b)
	Perform a multiplication of an MPI with an unsigned integer: X = A * b.
int	mbedtls_mpi_div_mpi (mbedtls_mpi Q, mbedtls_mpi R, const mbedtls_mpi A, const mbedtls_mpi B)
	Perform a division with remainder of two MPIs: A = Q * B + R.
int	mbedtls_mpi_div_int (mbedtls_mpi Q, mbedtls_mpi R, const mbedtls_mpi *A, mbedtls_mpi_sint b)
	Perform a division with remainder of an MPI by an integer: A = Q * b + R.
int	mbedtls_mpi_mod_mpi (mbedtls_mpi R, const mbedtls_mpi A, const mbedtls_mpi *B)
	Perform a modular reduction.
int	mbedtls_mpi_mod_int (mbedtls_mpi_uint r, const mbedtls_mpi A, mbedtls_mpi_sint b)
	Perform a modular reduction with respect to an integer.
int	mbedtls_mpi_exp_mod (mbedtls_mpi X, const mbedtls_mpi A, const mbedtls_mpi E, const mbedtls_mpi N, mbedtls_mpi *_RR)
	Perform a sliding-window exponentiation: X = A^E mod N.
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 with a number of random bytes.
int	mbedtls_mpi_gcd (mbedtls_mpi G, const mbedtls_mpi A, const mbedtls_mpi *B)
	Compute the greatest common divisor: G = gcd(A, B)
int	mbedtls_mpi_inv_mod (mbedtls_mpi X, const mbedtls_mpi A, const mbedtls_mpi *N)
	Compute the modular inverse: X = A^-1 mod N.
MBEDTLS_DEPRECATED int	mbedtls_mpi_is_prime (const mbedtls_mpi X, int(f_rng)(void , unsigned char , size_t), void *p_rng)
	Perform a Miller-Rabin primality test with error probability of 2^-80.
int	mbedtls_mpi_is_prime_ext (const mbedtls_mpi X, int rounds, int(f_rng)(void , unsigned char , size_t), void *p_rng)
	Miller-Rabin primality test.
int	mbedtls_mpi_gen_prime (mbedtls_mpi X, size_t nbits, int flags, int(f_rng)(void , unsigned char , size_t), void *p_rng)
	Generate a prime number.
int	mbedtls_mpi_self_test (int verbose)
	Checkup routine.

Detailed Description

Multi-precision integer library.

Definition in file bignum.h.

Typedef Documentation

typedef struct mbedtls_mpi mbedtls_mpi

MPI structure.

Enumeration Type Documentation

enum mbedtls_mpi_gen_prime_flag_t

Flags for mbedtls_mpi_gen_prime()

Each of these flags is a constraint on the result X returned by mbedtls_mpi_gen_prime().

Enumerator:

MBEDTLS_MPI_GEN_PRIME_FLAG_DH	(X-1)/2 is prime too
MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR	lower error rate from 2^-80 to 2^-128

Definition at line 958 of file bignum.h.

Function Documentation

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

Perform an unsigned addition of MPIs: X = |A| + |B|.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
A	The first summand. This must point to an initialized MPI.
B	The second summand. This must point to an initialized MPI.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 1171 of file bignum.c.

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

Perform a signed addition of an MPI and an integer: X = A + b.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
A	The first summand. This must point to an initialized MPI.
b	The second summand.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 1367 of file bignum.c.

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

Perform a signed addition of MPIs: X = A + B.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
A	The first summand. This must point to an initialized MPI.
B	The second summand. This must point to an initialized MPI.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 1297 of file bignum.c.

size_t mbedtls_mpi_bitlen ( const mbedtls_mpi * X )

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

*

Note:: This is same as the one-based index of the most significant bit of value 1.

Parameters:

X	The MPI to query. This must point to an initialized MPI.

Returns:: The number of bits up to and including the most significant bit of value 1.

Definition at line 414 of file bignum.c.

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

Compare the absolute values of two MPIs.

Parameters:

X	The left-hand MPI. This must point to an initialized MPI.
Y	The right-hand MPI. This must point to an initialized MPI.

Returns:: 1 if `|X|` is greater than `|Y|`.; -1 if `|X|` is lesser than `|Y|`.; 0 if `|X|` is equal to `|Y|`.

Definition at line 1087 of file bignum.c.

int mbedtls_mpi_cmp_int	(	const mbedtls_mpi *	X,
		mbedtls_mpi_sint	z
	)

Compare an MPI with an integer.

Parameters:

X	The left-hand MPI. This must point to an initialized MPI.
z	The integer value to compare `X` to.

Returns:: 1 if X is greater than z.; -1 if X is lesser than z.; 0 if X is equal to z.

Definition at line 1154 of file bignum.c.

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

Compare two MPIs.

Parameters:

X	The left-hand MPI. This must point to an initialized MPI.
Y	The right-hand MPI. This must point to an initialized MPI.

Returns:: 1 if X is greater than Y.; -1 if X is lesser than Y.; 0 if X is equal to Y.

Definition at line 1119 of file bignum.c.

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

Make a copy of an MPI.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
Y	The source MPI. This must point to an initialized MPI.

Note:: The limb-buffer in the destination MPI is enlarged if necessary to hold the value in the source MPI.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.; Another negative error code on other kinds of failure.

Definition at line 191 of file bignum.c.

int mbedtls_mpi_div_int	(	mbedtls_mpi *	Q,
		mbedtls_mpi *	R,
		const mbedtls_mpi *	A,
		mbedtls_mpi_sint	b
	)

Perform a division with remainder of an MPI by an integer: A = Q * b + R.

Parameters:

Q	The destination MPI for the quotient. This may be `NULL` if the value of the quotient is not needed.
R	The destination MPI for the remainder value. This may be `NULL` if the value of the remainder is not needed.
A	The dividend. This must point to an initialized MPi.
b	The divisor.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.; MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b equals zero.; Another negative error code on different kinds of failure.

Definition at line 1747 of file bignum.c.

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

Perform a division with remainder of two MPIs: A = Q * B + R.

Parameters:

Q	The destination MPI for the quotient. This may be `NULL` if the value of the quotient is not needed.
R	The destination MPI for the remainder value. This may be `NULL` if the value of the remainder is not needed.
A	The dividend. This must point to an initialized MPi.
B	The divisor. This must point to an initialized MPI.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.; MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B equals zero.; Another negative error code on different kinds of failure.

Definition at line 1629 of file bignum.c.

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

Perform a sliding-window exponentiation: X = A^E mod N.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
A	The base of the exponentiation. This must point to an initialized MPI.
E	The exponent MPI. This must point to an initialized MPI.
N	The base for the modular reduction. This must point to an initialized MPI.
_RR	A helper MPI depending solely on `N` which can be used to speed-up multiple modular exponentiations for the same value of `N`. This may be `NULL`. If it is not `NULL`, it must point to an initialized MPI. If it hasn't been used after the call to mbedtls_mpi_init(), this function will compute the helper value and store it in `_RR` for reuse on subsequent calls to this function. Otherwise, the function will assume that `_RR` holds the helper value set by a previous call to mbedtls_mpi_exp_mod(), and reuse it.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or even, or if E is negative.; Another negative error code on different kinds of failures.

Definition at line 1926 of file bignum.c.

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 with a number of random bytes.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
size	The number of random bytes to generate.
f_rng	The RNG function to use. This must not be `NULL`.
p_rng	The RNG parameter to be passed to `f_rng`. This may be `NULL` if `f_rng` doesn't need a context argument.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on failure.

Note:: The bytes obtained from the RNG are interpreted as a big-endian representation of an MPI; this can be relevant in applications like deterministic ECDSA.

Definition at line 2203 of file bignum.c.

void mbedtls_mpi_free ( mbedtls_mpi * X )

This function frees the components of an MPI context.

Parameters:

X	The MPI context to be cleared. This may be `NULL`, in which case this function is a no-op. If it is not `NULL`, it must point to an initialized MPI.

Definition at line 101 of file bignum.c.

int mbedtls_mpi_gcd	(	mbedtls_mpi *	G,
		const mbedtls_mpi *	A,
		const mbedtls_mpi *	B
	)

Compute the greatest common divisor: G = gcd(A, B)

Parameters:

G	The destination MPI. This must point to an initialized MPI.
A	The first operand. This must point to an initialized MPI.
B	The second operand. This must point to an initialized MPI.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 2143 of file bignum.c.

int mbedtls_mpi_gen_prime	(	mbedtls_mpi *	X,
		size_t	nbits,
		int	flags,
		int()(void , unsigned char *, size_t)	f_rng,
		void *	p_rng
	)

Generate a prime number.

Parameters:

X	The destination MPI to store the generated prime in. This must point to an initialized MPi.
nbits	The required size of the destination MPI in bits. This must be between `3` and MBEDTLS_MPI_MAX_BITS.
flags	A mask of flags of type mbedtls_mpi_gen_prime_flag_t.
f_rng	The RNG function to use. This must not be `NULL`.
p_rng	The RNG parameter to be passed to `f_rng`. This may be `NULL` if `f_rng` doesn't use a context parameter.

Returns:: 0 if successful, in which case X holds a probably prime number.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between 3 and MBEDTLS_MPI_MAX_BITS.

Definition at line 2545 of file bignum.c.

int mbedtls_mpi_get_bit	(	const mbedtls_mpi *	X,
		size_t	pos
	)

Get a specific bit from an MPI.

Parameters:

X	The MPI to query. This must be initialized.
pos	Zero-based index of the bit to query.

Returns:: 0 or 1 on success, depending on whether bit pos of X is unset or set.; A negative error code on failure.

Definition at line 334 of file bignum.c.

int mbedtls_mpi_grow	(	mbedtls_mpi *	X,
		size_t	nblimbs
	)

Enlarge an MPI to the specified number of limbs.

Note:: This function does nothing if the MPI is already large enough.

Parameters:

X	The MPI to grow. It must be initialized.
nblimbs	The target number of limbs.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.; Another negative error code on other kinds of failure.

Definition at line 120 of file bignum.c.

void mbedtls_mpi_init ( mbedtls_mpi * X )

Initialize an MPI context.

This makes the MPI ready to be set or freed, but does not define a value for the MPI.

Parameters:

X	The MPI context to initialize. This must not be `NULL`.

Definition at line 89 of file bignum.c.

int mbedtls_mpi_inv_mod	(	mbedtls_mpi *	X,
		const mbedtls_mpi *	A,
		const mbedtls_mpi *	N
	)

Compute the modular inverse: X = A^-1 mod N.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
A	The MPI to calculate the modular inverse of. This must point to an initialized MPI.
N	The base of the modular inversion. This must point to an initialized MPI.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is less than or equal to one.; MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if has no modular inverse with respect to N.

Definition at line 2236 of file bignum.c.

MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime	(	const mbedtls_mpi *	X,
		int()(void , unsigned char *, size_t)	f_rng,
		void *	p_rng
	)

Perform a Miller-Rabin primality test with error probability of 2^-80.

Parameters:

X	The MPI to check for primality. This must point to an initialized MPI.
f_rng	The RNG function to use. This must not be `NULL`.
p_rng	The RNG parameter to be passed to `f_rng`. This may be `NULL` if `f_rng` doesn't use a context parameter.

Returns:: 0 if successful, i.e. X is probably prime.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime.; Another negative error code on other kinds of failure.

Definition at line 2522 of file bignum.c.

int mbedtls_mpi_is_prime_ext	(	const mbedtls_mpi *	X,
		int	rounds,
		int()(void , unsigned char *, size_t)	f_rng,
		void *	p_rng
	)

Miller-Rabin primality test.

Warning:: If X is potentially generated by an adversary, for example when validating cryptographic parameters that you didn't generate yourself and that are supposed to be prime, then rounds should be at least the half of the security strength of the cryptographic algorithm. On the other hand, if X is chosen uniformly or non-adversially (as is the case when mbedtls_mpi_gen_prime calls this function), then rounds can be much lower.

Parameters:

X	The MPI to check for primality. This must point to an initialized MPI.
rounds	The number of bases to perform the Miller-Rabin primality test for. The probability of returning 0 on a composite is at most 2^-2*rounds.
f_rng	The RNG function to use. This must not be `NULL`.
p_rng	The RNG parameter to be passed to `f_rng`. This may be `NULL` if `f_rng` doesn't use a context parameter.

Returns:: 0 if successful, i.e. X is probably prime.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime.; Another negative error code on other kinds of failure.

Definition at line 2487 of file bignum.c.

size_t mbedtls_mpi_lsb ( const mbedtls_mpi * X )

Return the number of bits of value 0 before the least significant bit of value 1.

Note:: This is the same as the zero-based index of the least significant bit of value 1.

Parameters:

X	The MPI to query.

Returns:: The number of bits of value 0 before the least significant bit of value 1 in X.

Definition at line 380 of file bignum.c.

int mbedtls_mpi_lset	(	mbedtls_mpi *	X,
		mbedtls_mpi_sint	z
	)

Store integer value in MPI.

Parameters:

X	The MPI to set. This must be initialized.
z	The value to use.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.; Another negative error code on other kinds of failure.

Definition at line 315 of file bignum.c.

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

Perform a modular reduction with respect to an integer.

r = A mod b

Parameters:

r	The address at which to store the residue. This must not be `NULL`.
A	The MPI to compute the residue of. This must point to an initialized MPi.
b	The integer base of the modular reduction.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b equals zero.; MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b is negative.; Another negative error code on different kinds of failure.

Definition at line 1792 of file bignum.c.

int mbedtls_mpi_mod_mpi	(	mbedtls_mpi *	R,
		const mbedtls_mpi *	A,
		const mbedtls_mpi *	B
	)

Perform a modular reduction.

R = A mod B

Parameters:

R	The destination MPI for the residue value. This must point to an initialized MPI.
A	The MPI to compute the residue of. This must point to an initialized MPI.
B	The base of the modular reduction. This must point to an initialized MPI.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B equals zero.; MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is negative.; Another negative error code on different kinds of failure.

Definition at line 1766 of file bignum.c.

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

Perform a multiplication of an MPI with an unsigned integer: X = A * b.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
A	The first factor. This must point to an initialized MPI.
b	The second factor.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 1515 of file bignum.c.

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

Perform a multiplication of two MPIs: X = A * B.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
A	The first factor. This must point to an initialized MPI.
B	The second factor. This must point to an initialized MPI.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 1475 of file bignum.c.

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

Import an MPI from unsigned big endian binary data.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
buf	The input buffer. This must be a readable buffer of length `buflen` Bytes.
buflen	The length of the input buffer `p` in Bytes.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 865 of file bignum.c.

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

Import X from unsigned binary data, little endian.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
buf	The input buffer. This must be a readable buffer of length `buflen` Bytes.
buflen	The length of the input buffer `p` in Bytes.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 832 of file bignum.c.

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

Read an MPI from a line in an opened file.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
radix	The numeric base of the string representation used in the source line.
fin	The input file handle to use. This must not be `NULL`.

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.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer is too small.; Another negative error code on failure.

Definition at line 659 of file bignum.c.

int mbedtls_mpi_read_string	(	mbedtls_mpi *	X,
		int	radix,
		const char *	s
	)

Import an MPI from an ASCII string.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
radix	The numeric base of the input string.
s	Null-terminated string buffer.

Returns:: 0 if successful.; A negative error code on failure.

Definition at line 458 of file bignum.c.

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

Perform a safe conditional copy of MPI which doesn't reveal whether the condition was true or not.

Parameters:

X	The MPI to conditionally assign to. This must point to an initialized MPI.
Y	The MPI to be assigned from. This must point to an initialized MPI.
assign	The condition deciding whether to perform the assignment or not. Possible values: * `1`: Perform the assignment `X = Y`. * `0`: Keep the original value of `X`.

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).

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.; Another negative error code on other kinds of failure.

Definition at line 249 of file bignum.c.

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

Perform a safe conditional swap which doesn't reveal whether the condition was true or not.

Parameters:

X	The first MPI. This must be initialized.
Y	The second MPI. This must be initialized.
assign	The condition deciding whether to perform the swap or not. Possible values: * `1`: Swap the values of `X` and `Y`. * `0`: Keep the original values of `X` and `Y`.

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).

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.; Another negative error code on other kinds of failure.

Definition at line 279 of file bignum.c.

int mbedtls_mpi_self_test ( int verbose )

Checkup routine.

Returns:: 0 if successful, or 1 if the test failed

Definition at line 2681 of file bignum.c.

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

Modify a specific bit in an MPI.

Note:: This function will grow the target MPI if necessary to set a bit to 1 in a not yet existing limb. It will not grow if the bit should be set to 0.

Parameters:

X	The MPI to modify. This must be initialized.
pos	Zero-based index of the bit to modify.
val	The desired value of bit `pos:` `0` or `1`.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.; Another negative error code on other kinds of failure.

Definition at line 351 of file bignum.c.

int mbedtls_mpi_shift_l	(	mbedtls_mpi *	X,
		size_t	count
	)

Perform a left-shift on an MPI: X <<= count.

Parameters:

X	The MPI to shift. This must point to an initialized MPI.
count	The number of bits to shift by.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 992 of file bignum.c.

int mbedtls_mpi_shift_r	(	mbedtls_mpi *	X,
		size_t	count
	)

Perform a right-shift on an MPI: X >>= count.

Parameters:

X	The MPI to shift. This must point to an initialized MPI.
count	The number of bits to shift by.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 1043 of file bignum.c.

int mbedtls_mpi_shrink	(	mbedtls_mpi *	X,
		size_t	nblimbs
	)

This function resizes an MPI downwards, keeping at least the specified number of limbs.

If X is smaller than nblimbs, it is resized up instead.

Parameters:

X	The MPI to shrink. This must point to an initialized MPI.
nblimbs	The minimum number of limbs to keep.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed (this can only happen when resizing up).; Another negative error code on other kinds of failure.

Definition at line 151 of file bignum.c.

size_t mbedtls_mpi_size ( const mbedtls_mpi * X )

Return the total size of an MPI value in bytes.

Parameters:

X	The MPI to use. This must point to an initialized MPI.

Note:: The value returned by this function may be less than the number of bytes used to store X internally. This happens if and only if there are trailing bytes of value zero.

Returns:: The least number of bytes capable of storing the absolute value of X.

Definition at line 433 of file bignum.c.

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

Perform an unsigned subtraction of MPIs: X = |A| - |B|.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
A	The minuend. This must point to an initialized MPI.
B	The subtrahend. This must point to an initialized MPI.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A.; Another negative error code on different kinds of failure.

Definition at line 1251 of file bignum.c.

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

Perform a signed subtraction of an MPI and an integer: X = A - b.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
A	The minuend. This must point to an initialized MPI.
b	The subtrahend.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 1385 of file bignum.c.

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

Perform a signed subtraction of MPIs: X = A - B.

Parameters:

X	The destination MPI. This must point to an initialized MPI.
A	The minuend. This must point to an initialized MPI.
B	The subtrahend. This must point to an initialized MPI.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.; Another negative error code on different kinds of failure.

Definition at line 1332 of file bignum.c.

void mbedtls_mpi_swap	(	mbedtls_mpi *	X,
		mbedtls_mpi *	Y
	)

Swap the contents of two MPIs.

Parameters:

X	The first MPI. It must be initialized.
Y	The second MPI. It must be initialized.

Definition at line 233 of file bignum.c.

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	The source MPI. This must point to an initialized MPI.
buf	The output buffer. This must be a writable buffer of length `buflen` Bytes.
buflen	The size of the output buffer `buf` in Bytes.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough to hold the value of X.; Another negative error code on different kinds of failure.

Definition at line 946 of file bignum.c.

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

Export X into unsigned binary data, little endian.

Always fills the whole buffer, which will end with zeros if the number is smaller.

Parameters:

X	The source MPI. This must point to an initialized MPI.
buf	The output buffer. This must be a writable buffer of length `buflen` Bytes.
buflen	The size of the output buffer `buf` in Bytes.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough to hold the value of X.; Another negative error code on different kinds of failure.

Definition at line 907 of file bignum.c.

int mbedtls_mpi_write_file	(	const char *	p,
		const mbedtls_mpi *	X,
		int	radix,
		FILE *	fout
	)

Export an MPI into an opened file.

Parameters:

p	A string prefix to emit prior to the MPI data. For example, this might be a label, or "0x" when printing in base `16`. This may be `NULL` if no prefix is needed.
X	The source MPI. This must point to an initialized MPI.
radix	The numeric base to be used in the emitted string.
fout	The output file handle. This may be `NULL`, in which case the output is written to `stdout`.

Returns:: 0 if successful.; A negative error code on failure.

Definition at line 698 of file bignum.c.

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

Export an MPI to an ASCII string.

Parameters:

X	The source MPI. This must point to an initialized MPI.
radix	The numeric base of the output string.
buf	The buffer to write the string to. This must be writable buffer of length `buflen` Bytes.
buflen	The available size in Bytes of `buf`.
olen	The address at which to store the length of the string written, including the final `NULL` byte. This must not be `NULL`.

Note:: You can call this function with `buflen == 0` to obtain the minimum required buffer size in `*olen`.

Returns:: 0 if successful.; MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer buf is too small to hold the value of X in the desired base. In this case, `*olen` is nonetheless updated to contain the size of buf required for a successful call.; Another negative error code on different kinds of failure.

Definition at line 571 of file bignum.c.

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