bignum.c File Reference

#include "polarssl/config.h"
#include "polarssl/bignum.h"
#include "polarssl/bn_mul.h"
#include <stdlib.h>

Include dependency graph for bignum.c:

Defines
#define	polarssl_malloc malloc
#define	polarssl_free free
#define	ciL (sizeof(t_uint))
#define	biL (ciL << 3)
#define	biH (ciL << 2)
#define	BITS_TO_LIMBS(i) (((i) + biL - 1) / biL)
#define	CHARS_TO_LIMBS(i) (((i) + ciL - 1) / ciL)
#define	GCD_PAIR_COUNT 3
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 (const mpi *X, size_t pos)
	Get a specific bit from X.
int	mpi_set_bit (mpi *X, size_t pos, unsigned char val)
	Set a bit of X to a specific value of 0 or 1.
size_t	mpi_lsb (const mpi *X)
	Return the number of zero-bits before the least significant '1' bit.
size_t	mpi_msb (const mpi *X)
	Return the number of bits up to and including the most significant '1' bit'.
size_t	mpi_size (const mpi *X)
	Return the total size in bytes.
static int	mpi_get_digit (t_uint *d, int radix, char c)
int	mpi_read_string (mpi X, int radix, const char s)
	Import from an ASCII string.
static int	mpi_write_hlp (mpi X, int radix, char *p)
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)
int	mpi_write_file (const char p, const mpi X, int radix, FILE *fout)
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\|.
static void	mpi_sub_hlp (size_t n, t_uint s, t_uint d)
int	mpi_sub_abs (mpi X, const mpi A, const mpi *B)
	Unsigned subtraction: 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 subtraction: 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 subtraction: X = A - b.
static void	mpi_mul_hlp (size_t i, t_uint s, t_uint d, t_uint 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.
static void	mpi_montg_init (t_uint mm, const mpi N)
static void	mpi_montmul (mpi A, const mpi B, const mpi N, t_uint mm, const mpi T)
static void	mpi_montred (mpi A, const mpi N, t_uint mm, const mpi *T)
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_gcd (mpi G, const mpi A, const mpi *B)
	Greatest common divisor: G = gcd(A, B).
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_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.
Variables
static const int	small_prime []
static const int	gcd_pairs [GCD_PAIR_COUNT][3]

Define Documentation

#define biH (ciL << 2)

Definition at line 51 of file bignum.c.

Referenced by mpi_div_mpi(), and mpi_mod_int().

#define biL (ciL << 3)

Definition at line 50 of file bignum.c.

Referenced by mpi_div_mpi(), mpi_exp_mod(), mpi_get_bit(), mpi_lsb(), mpi_montg_init(), mpi_msb(), mpi_set_bit(), mpi_shift_l(), and mpi_shift_r().

#define BITS_TO_LIMBS ( i ) (((i) + biL - 1) / biL)

Definition at line 56 of file bignum.c.

Referenced by mpi_gen_prime(), mpi_read_string(), and mpi_shift_l().

#define CHARS_TO_LIMBS ( i ) (((i) + ciL - 1) / ciL)

Definition at line 57 of file bignum.c.

Referenced by mpi_fill_random(), and mpi_read_binary().

#define ciL (sizeof(t_uint))

Definition at line 49 of file bignum.c.

Referenced by mpi_copy(), mpi_free(), mpi_gen_prime(), mpi_grow(), mpi_is_prime(), mpi_lset(), mpi_montmul(), mpi_read_binary(), mpi_read_string(), mpi_write_binary(), and mpi_write_string().

#define GCD_PAIR_COUNT 3

Definition at line 1989 of file bignum.c.

Referenced by mpi_self_test().

#define polarssl_free free

Definition at line 44 of file bignum.c.

#define polarssl_malloc malloc

Definition at line 43 of file bignum.c.

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

Definition at line 741 of file bignum.c.

References MPI_CHK, mpi_copy(), mpi_grow(), mpi::n, mpi::p, and mpi::s.

Referenced by ecp_mod_p521(), mpi_add_mpi(), and mpi_sub_mpi().

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

Definition at line 919 of file bignum.c.

References mpi_add_mpi(), mpi::n, mpi::p, and mpi::s.

Referenced by ecp_group_read_string(), ecp_mul(), mpi_gen_prime(), and mpi_read_string().

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

Definition at line 857 of file bignum.c.

References mpi_add_abs(), MPI_CHK, mpi_cmp_abs(), mpi_sub_abs(), and mpi::s.

Referenced by ecdsa_sign(), ecp_check_pubkey(), ecp_double_jac(), ecp_modp(), mpi_add_int(), mpi_div_mpi(), mpi_exp_mod(), mpi_inv_mod(), mpi_mod_mpi(), and rsa_private().

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|

Definition at line 662 of file bignum.c.

References mpi::n, and mpi::p.

Referenced by mpi_add_mpi(), mpi_div_mpi(), mpi_montmul(), mpi_sub_abs(), and mpi_sub_mpi().

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

Definition at line 725 of file bignum.c.

References mpi_cmp_mpi(), mpi::n, mpi::p, and mpi::s.

Referenced by dhm_make_params(), dhm_make_public(), dhm_update_blinding(), ecdsa_sign(), ecdsa_verify(), ecp_add_mixed(), ecp_check_privkey(), ecp_check_pubkey(), ecp_gen_keypair(), ecp_is_zero(), ecp_modp(), ecp_mul(), ecp_normalize(), ecp_point_write_binary(), ecp_randomize_coordinates(), ecp_w_naf_fixed(), mpi_div_mpi(), mpi_exp_mod(), mpi_gcd(), mpi_inv_mod(), mpi_is_prime(), mpi_mod_mpi(), mpi_self_test(), mpi_write_hlp(), rsa_check_privkey(), rsa_gen_key(), and rsa_prepare_blinding().

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

Definition at line 692 of file bignum.c.

References mpi::n, mpi::p, and mpi::s.

Referenced by dhm_check_range(), dhm_make_params(), dhm_make_public(), dhm_update_blinding(), ecdsa_verify(), ecp_check_privkey(), ecp_check_pubkey(), ecp_gen_keypair(), ecp_modp(), ecp_mul(), ecp_randomize_coordinates(), mpi_cmp_int(), mpi_div_mpi(), mpi_exp_mod(), mpi_gcd(), mpi_inv_mod(), mpi_is_prime(), mpi_mod_mpi(), mpi_self_test(), rsa_check_privkey(), rsa_gen_key(), rsa_private(), and rsa_public().

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

Definition at line 125 of file bignum.c.

References ciL, MPI_CHK, mpi_free(), mpi_grow(), mpi::n, mpi::p, and mpi::s.

Referenced by dhm_calc_secret(), dhm_update_blinding(), ecdh_compute_shared(), ecdsa_from_keypair(), ecp_add_mixed(), ecp_copy(), ecp_double_jac(), ecp_mul(), ecp_normalize_many(), ecp_w_naf_fixed(), mpi_add_abs(), mpi_div_mpi(), mpi_exp_mod(), mpi_gcd(), mpi_inv_mod(), mpi_is_prime(), mpi_mul_mpi(), mpi_sub_abs(), mpi_write_string(), rsa_copy(), rsa_prepare_blinding(), ssl_set_dh_param_ctx(), ssl_write_server_key_exchange(), and x509write_crt_set_serial().

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.

Definition at line 1240 of file bignum.c.

References mpi_div_mpi(), mpi::n, mpi::p, and mpi::s.

Referenced by mpi_write_hlp().

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.

Definition at line 1076 of file bignum.c.

References biH, biL, mpi_add_mpi(), MPI_CHK, mpi_cmp_abs(), mpi_cmp_int(), mpi_cmp_mpi(), mpi_copy(), mpi_free(), mpi_grow(), mpi_init(), mpi_lset(), mpi_msb(), mpi_mul_int(), mpi_shift_l(), mpi_shift_r(), mpi_sub_mpi(), mpi::n, mpi::p, POLARSSL_ERR_MPI_DIVISION_BY_ZERO, and mpi::s.

Referenced by mpi_div_int(), mpi_mod_mpi(), mpi_self_test(), and rsa_check_privkey().

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 or if E is negative

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.

Definition at line 1405 of file bignum.c.

References biL, mpi_add_mpi(), MPI_CHK, mpi_cmp_int(), mpi_cmp_mpi(), mpi_copy(), mpi_free(), mpi_grow(), mpi_init(), mpi_lset(), mpi_mod_mpi(), mpi_montg_init(), mpi_montmul(), mpi_montred(), mpi_msb(), mpi_shift_l(), mpi::n, mpi::p, POLARSSL_ERR_MPI_BAD_INPUT_DATA, POLARSSL_MPI_WINDOW_SIZE, and mpi::s.

Referenced by dhm_calc_secret(), dhm_make_params(), dhm_make_public(), dhm_update_blinding(), mpi_is_prime(), mpi_self_test(), rsa_prepare_blinding(), rsa_private(), and rsa_public().

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

Definition at line 1662 of file bignum.c.

References CHARS_TO_LIMBS, MPI_CHK, mpi_grow(), mpi_lset(), and mpi::p.

Referenced by dhm_make_params(), dhm_make_public(), dhm_update_blinding(), ecp_gen_keypair(), ecp_randomize_coordinates(), mpi_gen_prime(), mpi_is_prime(), and rsa_prepare_blinding().

void mpi_free ( mpi * X )

Unallocate one MPI.

Parameters:

X

One MPI to unallocate.

Definition at line 75 of file bignum.c.

References ciL, mpi::n, mpi::p, polarssl_free, and mpi::s.

Referenced by dhm_calc_secret(), dhm_check_range(), dhm_free(), ecdh_free(), ecdsa_free(), ecdsa_sign(), ecdsa_verify(), ecp_add_mixed(), ecp_check_pubkey(), ecp_double_jac(), ecp_group_free(), ecp_keypair_free(), ecp_mul(), ecp_normalize(), ecp_normalize_many(), ecp_point_free(), ecp_randomize_coordinates(), ecp_self_test(), ecp_w_naf_fixed(), mpi_copy(), mpi_div_mpi(), mpi_exp_mod(), mpi_gcd(), mpi_gen_prime(), mpi_inv_mod(), mpi_is_prime(), mpi_mul_mpi(), mpi_read_string(), mpi_self_test(), mpi_sub_abs(), mpi_write_string(), rsa_check_privkey(), rsa_free(), rsa_gen_key(), rsa_private(), rsa_public(), ssl_free(), and x509write_crt_free().

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

Definition at line 1613 of file bignum.c.

References MPI_CHK, mpi_cmp_int(), mpi_cmp_mpi(), mpi_copy(), mpi_free(), mpi_init(), mpi_lsb(), mpi_shift_l(), mpi_shift_r(), mpi_sub_abs(), and mpi::s.

Referenced by mpi_inv_mod(), mpi_self_test(), rsa_check_privkey(), rsa_gen_key(), and rsa_prepare_blinding().

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

Definition at line 1920 of file bignum.c.

References BITS_TO_LIMBS, ciL, mpi_add_int(), MPI_CHK, mpi_fill_random(), mpi_free(), mpi_init(), mpi_is_prime(), mpi_msb(), mpi_shift_l(), mpi_shift_r(), mpi_sub_int(), mpi::p, POLARSSL_ERR_MPI_BAD_INPUT_DATA, POLARSSL_ERR_MPI_NOT_ACCEPTABLE, and POLARSSL_MPI_MAX_BITS.

Referenced by rsa_gen_key().

int mpi_get_bit	(	const 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

Definition at line 189 of file bignum.c.

References biL, mpi::n, and mpi::p.

Referenced by ecp_mul(), and ecp_point_write_binary().

static int mpi_get_digit	(	t_uint *	d,
		int	radix,
		char	c
	)			`[static]`

Definition at line 268 of file bignum.c.

References POLARSSL_ERR_MPI_INVALID_CHARACTER.

Referenced by mpi_read_file(), and mpi_read_string().

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

Definition at line 94 of file bignum.c.

References ciL, mpi::n, mpi::p, POLARSSL_ERR_MPI_MALLOC_FAILED, polarssl_free, polarssl_malloc, and POLARSSL_MPI_MAX_LIMBS.

Referenced by ecp_mod_p192(), mpi_add_abs(), mpi_copy(), mpi_div_mpi(), mpi_exp_mod(), mpi_fill_random(), mpi_lset(), mpi_mul_mpi(), mpi_read_binary(), mpi_read_string(), mpi_set_bit(), and mpi_shift_l().

void mpi_init ( mpi * X )

Initialize one MPI.

Parameters:

X

One MPI to initialize.

Definition at line 62 of file bignum.c.

References mpi::n, mpi::p, and mpi::s.

Referenced by dhm_calc_secret(), dhm_check_range(), ecdsa_init(), ecdsa_sign(), ecdsa_verify(), ecp_add_mixed(), ecp_check_pubkey(), ecp_double_jac(), ecp_keypair_init(), ecp_mul(), ecp_normalize(), ecp_normalize_many(), ecp_point_init(), ecp_randomize_coordinates(), ecp_self_test(), ecp_w_naf_fixed(), mpi_div_mpi(), mpi_exp_mod(), mpi_gcd(), mpi_gen_prime(), mpi_inv_mod(), mpi_is_prime(), mpi_mul_mpi(), mpi_read_string(), mpi_self_test(), mpi_sub_abs(), mpi_write_string(), rsa_check_privkey(), rsa_gen_key(), rsa_private(), rsa_public(), and x509write_crt_init().

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

Definition at line 1680 of file bignum.c.

References mpi_add_mpi(), MPI_CHK, mpi_cmp_int(), mpi_cmp_mpi(), mpi_copy(), mpi_free(), mpi_gcd(), mpi_init(), mpi_lset(), mpi_mod_mpi(), mpi_shift_r(), mpi_sub_mpi(), mpi::p, POLARSSL_ERR_MPI_BAD_INPUT_DATA, and POLARSSL_ERR_MPI_NOT_ACCEPTABLE.

Referenced by dhm_update_blinding(), ecdsa_sign(), ecdsa_verify(), ecp_normalize(), ecp_normalize_many(), mpi_self_test(), rsa_check_privkey(), rsa_gen_key(), and rsa_prepare_blinding().

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

Definition at line 1802 of file bignum.c.

References A, ciL, MPI_CHK, mpi_cmp_int(), mpi_cmp_mpi(), mpi_copy(), mpi_exp_mod(), mpi_fill_random(), mpi_free(), mpi_init(), mpi_lsb(), mpi_mod_int(), mpi_mod_mpi(), mpi_msb(), mpi_mul_mpi(), mpi_shift_r(), mpi_sub_int(), mpi::n, mpi::p, POLARSSL_ERR_MPI_NOT_ACCEPTABLE, R, and mpi::s.

Referenced by mpi_gen_prime().

size_t mpi_lsb ( const 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

Definition at line 227 of file bignum.c.

References biL, mpi::n, and mpi::p.

Referenced by mpi_gcd(), and mpi_is_prime().

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

Definition at line 171 of file bignum.c.

References ciL, MPI_CHK, mpi_grow(), mpi::n, mpi::p, and mpi::s.

Referenced by dhm_check_range(), dhm_update_blinding(), ecp_normalize(), ecp_normalize_many(), ecp_point_read_binary(), ecp_point_read_string(), ecp_self_test(), ecp_set_zero(), mpi_div_mpi(), mpi_exp_mod(), mpi_fill_random(), mpi_inv_mod(), mpi_mul_mpi(), mpi_read_binary(), mpi_read_string(), mpi_self_test(), mpi_shift_r(), and rsa_gen_key().

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

Definition at line 1279 of file bignum.c.

References biH, mpi::n, mpi::p, POLARSSL_ERR_MPI_DIVISION_BY_ZERO, POLARSSL_ERR_MPI_NEGATIVE_VALUE, and mpi::s.

Referenced by mpi_is_prime(), and mpi_write_hlp().

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

Definition at line 1256 of file bignum.c.

References mpi_add_mpi(), MPI_CHK, mpi_cmp_int(), mpi_cmp_mpi(), mpi_div_mpi(), mpi_sub_mpi(), and POLARSSL_ERR_MPI_NEGATIVE_VALUE.

Referenced by dhm_calc_secret(), dhm_update_blinding(), ecdsa_sign(), ecdsa_verify(), ecp_modp(), mpi_exp_mod(), mpi_inv_mod(), mpi_is_prime(), rsa_check_privkey(), rsa_gen_key(), rsa_prepare_blinding(), and rsa_private().

static void mpi_montg_init	(	t_uint *	mm,
		const mpi *	N
	)			`[static]`

Definition at line 1336 of file bignum.c.

References biL, and mpi::p.

Referenced by mpi_exp_mod().

static void mpi_montmul	(	mpi *	A,
		const mpi *	B,
		const mpi *	N,
		t_uint	mm,
		const mpi *	T
	)			`[static]`

Definition at line 1354 of file bignum.c.

References ciL, mpi_cmp_abs(), mpi_mul_hlp(), mpi_sub_hlp(), mpi::n, and mpi::p.

Referenced by mpi_exp_mod(), and mpi_montred().

static void mpi_montred	(	mpi *	A,
		const mpi *	N,
		t_uint	mm,
		const mpi *	T
	)			`[static]`

Definition at line 1391 of file bignum.c.

References mpi_montmul(), mpi::n, mpi::p, and mpi::s.

Referenced by mpi_exp_mod().

size_t mpi_msb ( const 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

Definition at line 242 of file bignum.c.

References biL, mpi::n, and mpi::p.

Referenced by d2i_RSA_PUBKEY(), ecp_group_read_string_gen(), ecp_modp(), ecp_mul(), mpi_div_mpi(), mpi_exp_mod(), mpi_gen_prime(), mpi_is_prime(), mpi_shift_l(), mpi_size(), mpi_write_string(), rsa_check_pubkey(), rsa_gen_key(), rsa_rsassa_pss_sign(), and rsa_rsassa_pss_verify().

static void mpi_mul_hlp	(	size_t	i,
		t_uint *	s,
		t_uint *	d,
		t_uint	b
	)			`[static]`

Definition at line 959 of file bignum.c.

References MULADDC_CORE, MULADDC_INIT, and MULADDC_STOP.

Referenced by mpi_montmul(), and mpi_mul_mpi().

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

Definition at line 1060 of file bignum.c.

References mpi_mul_mpi(), mpi::n, mpi::p, and mpi::s.

Referenced by ecp_add_mixed(), ecp_double_jac(), mpi_div_mpi(), and mpi_read_string().

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

Definition at line 1023 of file bignum.c.

References MPI_CHK, mpi_copy(), mpi_free(), mpi_grow(), mpi_init(), mpi_lset(), mpi_mul_hlp(), mpi::n, mpi::p, and mpi::s.

Referenced by dhm_calc_secret(), dhm_update_blinding(), ecdsa_sign(), ecdsa_verify(), ecp_add_mixed(), ecp_check_pubkey(), ecp_double_jac(), ecp_normalize(), ecp_normalize_many(), ecp_randomize_coordinates(), mpi_is_prime(), mpi_mul_int(), mpi_self_test(), rsa_check_privkey(), rsa_gen_key(), rsa_prepare_blinding(), and rsa_private().

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

Definition at line 526 of file bignum.c.

References CHARS_TO_LIMBS, ciL, MPI_CHK, mpi_grow(), mpi_lset(), and mpi::p.

Referenced by asn1_get_mpi(), d2i_RSA_PUBKEY(), derive_mpi(), dhm_read_bignum(), dhm_read_public(), ecp_point_read_binary(), pk_parse_key_sec1_der(), rsa_private(), and rsa_public().

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

Definition at line 452 of file bignum.c.

References mpi_get_digit(), mpi_read_string(), POLARSSL_ERR_MPI_BUFFER_TOO_SMALL, POLARSSL_ERR_MPI_FILE_IO_ERROR, POLARSSL_MPI_RW_BUFFER_SIZE, and slen.

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

Definition at line 285 of file bignum.c.

References BITS_TO_LIMBS, ciL, mpi_add_int(), MPI_CHK, mpi_free(), mpi_get_digit(), mpi_grow(), mpi_init(), mpi_lset(), mpi_mul_int(), mpi_sub_int(), mpi::p, POLARSSL_ERR_MPI_BAD_INPUT_DATA, mpi::s, and slen.

Referenced by ecp_group_read_string_gen(), ecp_point_read_string(), ecp_self_test(), mpi_read_file(), mpi_self_test(), rsa_self_test(), ssl_init(), and ssl_set_dh_param().

int mpi_self_test ( int verbose )

Checkup routine.

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

Definition at line 2001 of file bignum.c.

References A, GCD_PAIR_COUNT, MPI_CHK, mpi_cmp_int(), mpi_cmp_mpi(), mpi_div_mpi(), mpi_exp_mod(), mpi_free(), mpi_gcd(), mpi_init(), mpi_inv_mod(), mpi_lset(), mpi_mul_mpi(), and mpi_read_string().

int mpi_set_bit	(	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, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, POLARSSL_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1

Definition at line 200 of file bignum.c.

References biL, MPI_CHK, mpi_grow(), mpi::n, mpi::p, and POLARSSL_ERR_MPI_BAD_INPUT_DATA.

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

Definition at line 569 of file bignum.c.

References biL, BITS_TO_LIMBS, MPI_CHK, mpi_grow(), mpi_msb(), mpi::n, and mpi::p.

Referenced by mpi_div_mpi(), mpi_exp_mod(), mpi_gcd(), and mpi_gen_prime().

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

Definition at line 619 of file bignum.c.

References biL, mpi_lset(), mpi::n, and mpi::p.

Referenced by dhm_make_params(), dhm_make_public(), dhm_update_blinding(), ecp_gen_keypair(), ecp_mod_p521(), ecp_randomize_coordinates(), ecp_w_naf_fixed(), mpi_div_mpi(), mpi_gcd(), mpi_gen_prime(), mpi_inv_mod(), and mpi_is_prime().

size_t mpi_size ( const mpi * X )

Return the total size in bytes.

Parameters:

X

MPI to use

Definition at line 260 of file bignum.c.

References mpi_msb().

Referenced by asn1_write_mpi(), dhm_calc_secret(), dhm_make_params(), dhm_read_params(), dhm_update_blinding(), ecdh_calc_secret(), ecp_point_read_binary(), ecp_point_write_binary(), mpi_write_binary(), pk_get_rsapubkey(), pk_parse_key_pkcs1_der(), ssl_parse_client_key_exchange(), ssl_write_client_key_exchange(), and ssl_write_server_key_exchange().

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

Unsigned subtraction: 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

Definition at line 814 of file bignum.c.

References MPI_CHK, mpi_cmp_abs(), mpi_copy(), mpi_free(), mpi_init(), mpi_sub_hlp(), mpi::n, mpi::p, POLARSSL_ERR_MPI_NEGATIVE_VALUE, and mpi::s.

Referenced by ecp_modp(), fix_negative(), mpi_add_mpi(), mpi_gcd(), and mpi_sub_mpi().

static void mpi_sub_hlp	(	size_t	n,
		t_uint *	s,
		t_uint *	d
	)			`[static]`

Definition at line 793 of file bignum.c.

Referenced by mpi_montmul(), and mpi_sub_abs().

int mpi_sub_int	(	mpi *	X,
		const mpi *	A,
		t_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, POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

Definition at line 935 of file bignum.c.

References mpi_sub_mpi(), mpi::n, mpi::p, and mpi::s.

Referenced by dhm_check_range(), mpi_gen_prime(), mpi_is_prime(), mpi_read_string(), rsa_check_privkey(), and rsa_gen_key().

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

Signed subtraction: 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

Definition at line 888 of file bignum.c.

References mpi_add_abs(), MPI_CHK, mpi_cmp_abs(), mpi_sub_abs(), and mpi::s.

Referenced by ecp_add_mixed(), ecp_double_jac(), mpi_div_mpi(), mpi_inv_mod(), mpi_mod_mpi(), mpi_sub_int(), and rsa_private().

void mpi_swap	(	mpi *	X,
		mpi *	Y
	)

Swap the contents of X and Y.

Parameters:

	X	First MPI value
	Y	Second MPI value

Definition at line 159 of file bignum.c.

Referenced by rsa_gen_key().

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

Definition at line 549 of file bignum.c.

References ciL, mpi_size(), mpi::p, and POLARSSL_ERR_MPI_BUFFER_TOO_SMALL.

Referenced by asn1_write_mpi(), dhm_calc_secret(), dhm_make_public(), ecdh_calc_secret(), ecp_point_write_binary(), rsa_private(), and rsa_public().

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

Definition at line 485 of file bignum.c.

References MPI_CHK, mpi_write_string(), plen, POLARSSL_ERR_MPI_FILE_IO_ERROR, POLARSSL_MPI_RW_BUFFER_SIZE, and slen.

static int mpi_write_hlp	(	mpi *	X,
		int	radix,
		char **	p
	)			`[static]`

Definition at line 354 of file bignum.c.

References MPI_CHK, mpi_cmp_int(), mpi_div_int(), mpi_mod_int(), and POLARSSL_ERR_MPI_BAD_INPUT_DATA.

Referenced by mpi_write_string().

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.

Definition at line 381 of file bignum.c.

References ciL, MPI_CHK, mpi_copy(), mpi_free(), mpi_init(), mpi_msb(), mpi_write_hlp(), mpi::n, mpi::p, POLARSSL_ERR_MPI_BAD_INPUT_DATA, POLARSSL_ERR_MPI_BUFFER_TOO_SMALL, and mpi::s.

Referenced by mpi_write_file().

Variable Documentation

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

Initial value:

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

Definition at line 1991 of file bignum.c.

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
}

Definition at line 1774 of file bignum.c.

bignum.c File Reference

Defines

Functions

Variables

Define Documentation

Function Documentation

Variable Documentation