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API Documentation (Doxygen generated)

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bignum.h File Reference

Multi-precision integer library. More...

#include "config.h"
#include <stddef.h>
#include <stdint.h>
#include <stdio.h>
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Data Structures

struct  mbedtls_mpi
 MPI structure. More...
 

Macros

#define MBEDTLS_ERR_MPI_FILE_IO_ERROR   -0x0002
 An error occurred while reading from or writing to a file. More...
 
#define MBEDTLS_ERR_MPI_BAD_INPUT_DATA   -0x0004
 Bad input parameters to function. More...
 
#define MBEDTLS_ERR_MPI_INVALID_CHARACTER   -0x0006
 There is an invalid character in the digit string. More...
 
#define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL   -0x0008
 The buffer is too small to write to. More...
 
#define MBEDTLS_ERR_MPI_NEGATIVE_VALUE   -0x000A
 The input arguments are negative or result in illegal output. More...
 
#define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO   -0x000C
 The input argument for division is zero, which is not allowed. More...
 
#define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE   -0x000E
 The input arguments are not acceptable. More...
 
#define MBEDTLS_ERR_MPI_ALLOC_FAILED   -0x0010
 Memory allocation failed. More...
 
#define MBEDTLS_MPI_CHK(f)   do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 )
 
#define MBEDTLS_MPI_MAX_LIMBS   10000
 
#define MBEDTLS_MPI_WINDOW_SIZE   6
 Maximum windows size used. More...
 
#define MBEDTLS_MPI_MAX_SIZE   1024
 Maximum number of bytes for usable MPIs. More...
 
#define MBEDTLS_MPI_MAX_BITS   ( 8 * MBEDTLS_MPI_MAX_SIZE )
 Maximum number of bits for usable MPIs. More...
 
#define MBEDTLS_MPI_MAX_BITS_SCALE100   ( 100 * MBEDTLS_MPI_MAX_BITS )
 
#define MBEDTLS_LN_2_DIV_LN_10_SCALE100   332
 
#define MBEDTLS_MPI_RW_BUFFER_SIZE   ( ((MBEDTLS_MPI_MAX_BITS_SCALE100 + MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6 )
 
#define MBEDTLS_HAVE_INT32
 
#define MBEDTLS_HAVE_UDBL
 
#define MBEDTLS_DEPRECATED
 

Typedefs

typedef int32_t mbedtls_mpi_sint
 
typedef uint32_t mbedtls_mpi_uint
 
typedef uint64_t mbedtls_t_udbl
 
typedef struct mbedtls_mpi mbedtls_mpi
 MPI structure. More...
 

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. More...
 
void mbedtls_mpi_free (mbedtls_mpi *X)
 This function frees the components of an MPI context. More...
 
int mbedtls_mpi_grow (mbedtls_mpi *X, size_t nblimbs)
 Enlarge an MPI to the specified number of limbs. More...
 
int mbedtls_mpi_shrink (mbedtls_mpi *X, size_t nblimbs)
 This function resizes an MPI downwards, keeping at least the specified number of limbs. More...
 
int mbedtls_mpi_copy (mbedtls_mpi *X, const mbedtls_mpi *Y)
 Make a copy of an MPI. More...
 
void mbedtls_mpi_swap (mbedtls_mpi *X, mbedtls_mpi *Y)
 Swap the contents of two MPIs. More...
 
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. More...
 
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. More...
 
int mbedtls_mpi_lset (mbedtls_mpi *X, mbedtls_mpi_sint z)
 Store integer value in MPI. More...
 
int mbedtls_mpi_get_bit (const mbedtls_mpi *X, size_t pos)
 Get a specific bit from an MPI. More...
 
int mbedtls_mpi_set_bit (mbedtls_mpi *X, size_t pos, unsigned char val)
 Modify a specific bit in an MPI. More...
 
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. More...
 
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. More...
 
size_t mbedtls_mpi_size (const mbedtls_mpi *X)
 Return the total size of an MPI value in bytes. More...
 
int mbedtls_mpi_read_string (mbedtls_mpi *X, int radix, const char *s)
 Import an MPI from an ASCII string. More...
 
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. More...
 
int mbedtls_mpi_read_file (mbedtls_mpi *X, int radix, FILE *fin)
 Read an 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)
 Export an MPI into an opened file. More...
 
int mbedtls_mpi_read_binary (mbedtls_mpi *X, const unsigned char *buf, size_t buflen)
 Import an MPI from unsigned big endian binary data. More...
 
int mbedtls_mpi_write_binary (const mbedtls_mpi *X, unsigned char *buf, size_t buflen)
 Export an MPI into unsigned big endian binary data of fixed size. More...
 
int mbedtls_mpi_shift_l (mbedtls_mpi *X, size_t count)
 Perform a left-shift on an MPI: X <<= count. More...
 
int mbedtls_mpi_shift_r (mbedtls_mpi *X, size_t count)
 Perform a right-shift on an MPI: X >>= count. More...
 
int mbedtls_mpi_cmp_abs (const mbedtls_mpi *X, const mbedtls_mpi *Y)
 Compare the absolute values of two MPIs. More...
 
int mbedtls_mpi_cmp_mpi (const mbedtls_mpi *X, const mbedtls_mpi *Y)
 Compare two MPIs. More...
 
int mbedtls_mpi_cmp_int (const mbedtls_mpi *X, mbedtls_mpi_sint z)
 Compare an MPI with an integer. More...
 
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|. More...
 
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|. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
int mbedtls_mpi_mod_mpi (mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B)
 Perform a modular reduction. More...
 
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. More...
 
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. 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 with a number of random bytes. More...
 
int mbedtls_mpi_gcd (mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B)
 Compute the greatest common divisor: G = gcd(A, B) More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
int mbedtls_mpi_self_test (int verbose)
 Checkup routine. More...
 

Detailed Description

Multi-precision integer library.

Definition in file bignum.h.

Macro Definition Documentation

#define MBEDTLS_DEPRECATED

Definition at line 855 of file bignum.h.

#define MBEDTLS_ERR_MPI_ALLOC_FAILED   -0x0010

Memory allocation failed.

Definition at line 47 of file bignum.h.

#define MBEDTLS_ERR_MPI_BAD_INPUT_DATA   -0x0004

Bad input parameters to function.

Definition at line 41 of file bignum.h.

#define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL   -0x0008

The buffer is too small to write to.

Definition at line 43 of file bignum.h.

#define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO   -0x000C

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

Definition at line 45 of file bignum.h.

#define MBEDTLS_ERR_MPI_FILE_IO_ERROR   -0x0002

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

Definition at line 40 of file bignum.h.

#define MBEDTLS_ERR_MPI_INVALID_CHARACTER   -0x0006

There is an invalid character in the digit string.

Definition at line 42 of file bignum.h.

#define MBEDTLS_ERR_MPI_NEGATIVE_VALUE   -0x000A

The input arguments are negative or result in illegal output.

Definition at line 44 of file bignum.h.

#define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE   -0x000E

The input arguments are not acceptable.

Definition at line 46 of file bignum.h.

#define MBEDTLS_HAVE_INT32

Definition at line 163 of file bignum.h.

#define MBEDTLS_HAVE_UDBL

Definition at line 169 of file bignum.h.

#define MBEDTLS_LN_2_DIV_LN_10_SCALE100   332

Definition at line 101 of file bignum.h.

#define MBEDTLS_MPI_CHK (   f)    do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 )

Definition at line 49 of file bignum.h.

#define MBEDTLS_MPI_MAX_BITS   ( 8 * MBEDTLS_MPI_MAX_SIZE )

Maximum number of bits for usable MPIs.

Definition at line 80 of file bignum.h.

#define MBEDTLS_MPI_MAX_BITS_SCALE100   ( 100 * MBEDTLS_MPI_MAX_BITS )

Definition at line 100 of file bignum.h.

#define MBEDTLS_MPI_MAX_LIMBS   10000

Definition at line 54 of file bignum.h.

#define MBEDTLS_MPI_MAX_SIZE   1024

Maximum number of bytes for usable MPIs.

Definition at line 77 of file bignum.h.

#define MBEDTLS_MPI_RW_BUFFER_SIZE   ( ((MBEDTLS_MPI_MAX_BITS_SCALE100 + MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6 )

Definition at line 102 of file bignum.h.

#define MBEDTLS_MPI_WINDOW_SIZE   6

Maximum windows size used.

Definition at line 66 of file bignum.h.

Typedef Documentation

typedef struct mbedtls_mpi mbedtls_mpi

MPI structure.

typedef int32_t mbedtls_mpi_sint

Definition at line 165 of file bignum.h.

typedef uint32_t mbedtls_mpi_uint

Definition at line 166 of file bignum.h.

typedef uint64_t mbedtls_t_udbl

Definition at line 168 of file bignum.h.

Enumeration Type Documentation

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 918 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
XThe destination MPI. This must point to an initialized MPI.
AThe first summand. This must point to an initialized MPI.
BThe 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.
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
XThe destination MPI. This must point to an initialized MPI.
AThe first summand. This must point to an initialized MPI.
bThe 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.
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
XThe destination MPI. This must point to an initialized MPI.
AThe first summand. This must point to an initialized MPI.
BThe 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.
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
    XThe 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.
int mbedtls_mpi_cmp_abs ( const mbedtls_mpi X,
const mbedtls_mpi Y 
)

Compare the absolute values of two MPIs.

Parameters
XThe left-hand MPI. This must point to an initialized MPI.
YThe 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|.
int mbedtls_mpi_cmp_int ( const mbedtls_mpi X,
mbedtls_mpi_sint  z 
)

Compare an MPI with an integer.

Parameters
XThe left-hand MPI. This must point to an initialized MPI.
zThe 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.
int mbedtls_mpi_cmp_mpi ( const mbedtls_mpi X,
const mbedtls_mpi Y 
)

Compare two MPIs.

Parameters
XThe left-hand MPI. This must point to an initialized MPI.
YThe 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.
int mbedtls_mpi_copy ( mbedtls_mpi X,
const mbedtls_mpi Y 
)

Make a copy of an MPI.

Parameters
XThe destination MPI. This must point to an initialized MPI.
YThe 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.
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
QThe destination MPI for the quotient. This may be NULL if the value of the quotient is not needed.
RThe destination MPI for the remainder value. This may be NULL if the value of the remainder is not needed.
AThe dividend. This must point to an initialized MPi.
bThe 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.
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
QThe destination MPI for the quotient. This may be NULL if the value of the quotient is not needed.
RThe destination MPI for the remainder value. This may be NULL if the value of the remainder is not needed.
AThe dividend. This must point to an initialized MPi.
BThe 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.
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
XThe destination MPI. This must point to an initialized MPI.
AThe base of the exponentiation. This must point to an initialized MPI.
EThe exponent MPI. This must point to an initialized MPI.
NThe base for the modular reduction. This must point to an initialized MPI.
_RRA 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.
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
XThe destination MPI. This must point to an initialized MPI.
sizeThe number of random bytes to generate.
f_rngThe RNG function to use. This must not be NULL.
p_rngThe 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.
void mbedtls_mpi_free ( mbedtls_mpi X)

This function frees the components of an MPI context.

Parameters
XThe 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.
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
GThe destination MPI. This must point to an initialized MPI.
AThe first operand. This must point to an initialized MPI.
BThe 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.
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
XThe destination MPI to store the generated prime in. This must point to an initialized MPi.
nbitsThe required size of the destination MPI in bits. This must be between 3 and MBEDTLS_MPI_MAX_BITS.
flagsA mask of flags of type mbedtls_mpi_gen_prime_flag_t.
f_rngThe RNG function to use. This must not be NULL.
p_rngThe 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.
int mbedtls_mpi_get_bit ( const mbedtls_mpi X,
size_t  pos 
)

Get a specific bit from an MPI.

Parameters
XThe MPI to query. This must be initialized.
posZero-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.
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
XThe MPI to grow. It must be initialized.
nblimbsThe 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.
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
XThe MPI context to initialize. This must not be NULL.
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
XThe destination MPI. This must point to an initialized MPI.
AThe MPI to calculate the modular inverse of. This must point to an initialized MPI.
NThe 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.
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.

Deprecated:
Superseded by mbedtls_mpi_is_prime_ext() which allows specifying the number of Miller-Rabin rounds.
Parameters
XThe MPI to check for primality. This must point to an initialized MPI.
f_rngThe RNG function to use. This must not be NULL.
p_rngThe 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.
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
XThe MPI to check for primality. This must point to an initialized MPI.
roundsThe 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_rngThe RNG function to use. This must not be NULL.
p_rngThe 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.
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
XThe MPI to query.
Returns
The number of bits of value 0 before the least significant bit of value 1 in X.
int mbedtls_mpi_lset ( mbedtls_mpi X,
mbedtls_mpi_sint  z 
)

Store integer value in MPI.

Parameters
XThe MPI to set. This must be initialized.
zThe 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.
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
rThe address at which to store the residue. This must not be NULL.
AThe MPI to compute the residue of. This must point to an initialized MPi.
bThe 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.
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
RThe destination MPI for the residue value. This must point to an initialized MPI.
AThe MPI to compute the residue of. This must point to an initialized MPI.
BThe 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.
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
XThe destination MPI. This must point to an initialized MPI.
AThe first factor. This must point to an initialized MPI.
bThe 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.
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
XThe destination MPI. This must point to an initialized MPI.
AThe first factor. This must point to an initialized MPI.
BThe 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.
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
XThe destination MPI. This must point to an initialized MPI.
bufThe input buffer. This must be a readable buffer of length buflen Bytes.
buflenThe 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.
int mbedtls_mpi_read_file ( mbedtls_mpi X,
int  radix,
FILE *  fin 
)

Read an MPI from a line in an opened file.

Parameters
XThe destination MPI. This must point to an initialized MPI.
radixThe numeric base of the string representation used in the source line.
finThe 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.
int mbedtls_mpi_read_string ( mbedtls_mpi X,
int  radix,
const char *  s 
)

Import an MPI from an ASCII string.

Parameters
XThe destination MPI. This must point to an initialized MPI.
radixThe numeric base of the input string.
sNull-terminated string buffer.
Returns
0 if successful.
A negative error code on failure.
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
XThe MPI to conditionally assign to. This must point to an initialized MPI.
YThe MPI to be assigned from. This must point to an initialized MPI.
assignThe 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.
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
XThe first MPI. This must be initialized.
YThe second MPI. This must be initialized.
assignThe 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.
int mbedtls_mpi_self_test ( int  verbose)

Checkup routine.

Returns
0 if successful, or 1 if the test failed
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
XThe MPI to modify. This must be initialized.
posZero-based index of the bit to modify.
valThe 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.
int mbedtls_mpi_shift_l ( mbedtls_mpi X,
size_t  count 
)

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

Parameters
XThe MPI to shift. This must point to an initialized MPI.
countThe 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.
int mbedtls_mpi_shift_r ( mbedtls_mpi X,
size_t  count 
)

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

Parameters
XThe MPI to shift. This must point to an initialized MPI.
countThe 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.
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
XThe MPI to shrink. This must point to an initialized MPI.
nblimbsThe 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.
size_t mbedtls_mpi_size ( const mbedtls_mpi X)

Return the total size of an MPI value in bytes.

Parameters
XThe 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.
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
XThe destination MPI. This must point to an initialized MPI.
AThe minuend. This must point to an initialized MPI.
BThe 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.
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
XThe destination MPI. This must point to an initialized MPI.
AThe minuend. This must point to an initialized MPI.
bThe subtrahend.
Returns
0 if successful.
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
Another negative error code on different kinds of failure.
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
XThe destination MPI. This must point to an initialized MPI.
AThe minuend. This must point to an initialized MPI.
BThe 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.
void mbedtls_mpi_swap ( mbedtls_mpi X,
mbedtls_mpi Y 
)

Swap the contents of two MPIs.

Parameters
XThe first MPI. It must be initialized.
YThe second MPI. It must be initialized.
int mbedtls_mpi_write_binary ( const mbedtls_mpi X,
unsigned char *  buf,
size_t  buflen 
)

Export an MPI into unsigned big endian binary data of fixed size.

Parameters
XThe source MPI. This must point to an initialized MPI.
bufThe output buffer. This must be a writable buffer of length buflen Bytes.
buflenThe 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.
int mbedtls_mpi_write_file ( const char *  p,
const mbedtls_mpi X,
int  radix,
FILE *  fout 
)

Export an MPI into an opened file.

Parameters
pA 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.
XThe source MPI. This must point to an initialized MPI.
radixThe numeric base to be used in the emitted string.
foutThe 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.
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
XThe source MPI. This must point to an initialized MPI.
radixThe numeric base of the output string.
bufThe buffer to write the string to. This must be writable buffer of length buflen Bytes.
buflenThe available size in Bytes of buf.
olenThe 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.