bignum.h File Reference


Detailed Description

Copyright (C) 2006-2009, Paul Bakker <polarssl_maintainer at polarssl.org> All rights reserved.

Joined copyright on original XySSL code with: Christophe Devine

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

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

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

Definition in file bignum.h.

#include <stdio.h>

Go to the source code of this file.

Data Structures

struct  mpi
 MPI structure. More...

Defines

#define MPI_CHK(f)   if( ( ret = f ) != 0 ) goto cleanup
#define POLARSSL_ERR_MPI_BAD_INPUT_DATA   0x0004
#define POLARSSL_ERR_MPI_BUFFER_TOO_SMALL   0x0008
#define POLARSSL_ERR_MPI_DIVISION_BY_ZERO   0x000C
#define POLARSSL_ERR_MPI_FILE_IO_ERROR   0x0002
#define POLARSSL_ERR_MPI_INVALID_CHARACTER   0x0006
#define POLARSSL_ERR_MPI_NEGATIVE_VALUE   0x000A
#define POLARSSL_ERR_MPI_NOT_ACCEPTABLE   0x000E

Typedefs

typedef unsigned long t_int

Functions

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


Define Documentation

#define MPI_CHK (  )     if( ( ret = f ) != 0 ) goto cleanup

Definition at line 36 of file bignum.h.

#define POLARSSL_ERR_MPI_BAD_INPUT_DATA   0x0004

Definition at line 29 of file bignum.h.

#define POLARSSL_ERR_MPI_BUFFER_TOO_SMALL   0x0008

Definition at line 31 of file bignum.h.

#define POLARSSL_ERR_MPI_DIVISION_BY_ZERO   0x000C

Definition at line 33 of file bignum.h.

#define POLARSSL_ERR_MPI_FILE_IO_ERROR   0x0002

Definition at line 28 of file bignum.h.

#define POLARSSL_ERR_MPI_INVALID_CHARACTER   0x0006

Definition at line 30 of file bignum.h.

#define POLARSSL_ERR_MPI_NEGATIVE_VALUE   0x000A

Definition at line 32 of file bignum.h.

#define POLARSSL_ERR_MPI_NOT_ACCEPTABLE   0x000E

Definition at line 34 of file bignum.h.


Typedef Documentation

typedef unsigned long t_int

Definition at line 49 of file bignum.h.


Function Documentation

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

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

Parameters:
X Destination MPI
A Left-hand MPI
B Right-hand MPI
Returns:
0 if successful, 1 if memory allocation failed

int mpi_add_int ( mpi X,
mpi A,
int  b 
)

Signed addition: X = A + b.

Parameters:
X Destination MPI
A Left-hand MPI
b The integer value to add
Returns:
0 if successful, 1 if memory allocation failed

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

Signed addition: X = A + B.

Parameters:
X Destination MPI
A Left-hand MPI
B Right-hand MPI
Returns:
0 if successful, 1 if memory allocation failed

int mpi_cmp_abs ( mpi X,
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|

int mpi_cmp_int ( mpi X,
int  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

int mpi_cmp_mpi ( mpi X,
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

int mpi_copy ( mpi X,
mpi Y 
)

Copy the contents of Y into X.

Parameters:
X Destination MPI
Y Source MPI
Returns:
0 if successful, 1 if memory allocation failed

int mpi_div_int ( mpi Q,
mpi R,
mpi A,
int  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, 1 if memory allocation failed, POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0
Note:
Either Q or R can be NULL.

int mpi_div_mpi ( mpi Q,
mpi R,
mpi A,
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, 1 if memory allocation failed, POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0
Note:
Either Q or R can be NULL.

int mpi_exp_mod ( mpi X,
mpi A,
mpi E,
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, 1 if memory allocation failed, POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or even
Note:
_RR is used to avoid re-computing R*R mod N across multiple calls, which speeds up things a bit. It can be set to NULL if the extra performance is unneeded.

void mpi_free ( mpi X,
  ... 
)

Unallocate one or more mpi.

int mpi_gcd ( mpi G,
mpi A,
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, 1 if memory allocation failed

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

Prime number generation.

Parameters:
X Destination MPI
nbits Required size of X in 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), 1 if memory allocation failed, POLARSSL_ERR_MPI_BAD_INPUT_DATA if nbits is < 3

int mpi_grow ( mpi X,
int  nblimbs 
)

Enlarge to the specified number of limbs.

Parameters:
X MPI to grow
nblimbs The target number of limbs
Returns:
0 if successful, 1 if memory allocation failed

void mpi_init ( mpi X,
  ... 
)

Initialize one or more mpi.

int mpi_inv_mod ( mpi X,
mpi A,
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, 1 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

int mpi_is_prime ( mpi X,
int(*)(void *)  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), 1 if memory allocation failed, POLARSSL_ERR_MPI_NOT_ACCEPTABLE if X is not prime

int mpi_lsb ( mpi X  ) 

Return the number of least significant bits.

Parameters:
X MPI to use

int mpi_lset ( mpi X,
int  z 
)

Set value from integer.

Parameters:
X MPI to set
z Value to use
Returns:
0 if successful, 1 if memory allocation failed

int mpi_mod_int ( t_int r,
mpi A,
int  b 
)

Modulo: r = A mod b.

Parameters:
r Destination t_int
A Left-hand MPI
b Integer to divide by
Returns:
0 if successful, 1 if memory allocation failed, POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0, POLARSSL_ERR_MPI_NEGATIVE_VALUE if b < 0

int mpi_mod_mpi ( mpi R,
mpi A,
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, 1 if memory allocation failed, POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0, POLARSSL_ERR_MPI_NEGATIVE_VALUE if B < 0

int mpi_msb ( mpi X  ) 

Return the number of most significant bits.

Parameters:
X MPI to use

Referenced by d2i_RSA_PUBKEY().

int mpi_mul_int ( mpi X,
mpi A,
t_int  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, 1 if memory allocation failed

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

Baseline multiplication: X = A * B.

Parameters:
X Destination MPI
A Left-hand MPI
B Right-hand MPI
Returns:
0 if successful, 1 if memory allocation failed

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

Import X from unsigned binary data, big endian.

Parameters:
X Destination MPI
buf Input buffer
buflen Input buffer size
Returns:
0 if successful, 1 if memory allocation failed

Referenced by d2i_RSA_PUBKEY().

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

Read X from an opened file.

Parameters:
X Destination MPI
radix Input numeric base
fin Input file handle
Returns:
0 if successful, or an POLARSSL_ERR_MPI_XXX error code

int mpi_read_string ( mpi X,
int  radix,
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 an POLARSSL_ERR_MPI_XXX error code

int mpi_self_test ( int  verbose  ) 

Checkup routine.

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

Referenced by main().

int mpi_shift_l ( mpi X,
int  count 
)

Left-shift: X <<= count.

Parameters:
X MPI to shift
count Amount to shift
Returns:
0 if successful, 1 if memory allocation failed

int mpi_shift_r ( mpi X,
int  count 
)

Right-shift: X >>= count.

Parameters:
X MPI to shift
count Amount to shift
Returns:
0 if successful, 1 if memory allocation failed

int mpi_size ( mpi X  ) 

Return the total size in bytes.

Parameters:
X MPI to use

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

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

Parameters:
X Destination MPI
A Left-hand MPI
B Right-hand MPI
Returns:
0 if successful, POLARSSL_ERR_MPI_NEGATIVE_VALUE if B is greater than A

int mpi_sub_int ( mpi X,
mpi A,
int  b 
)

Signed substraction: X = A - b.

Parameters:
X Destination MPI
A Left-hand MPI
b The integer value to subtract
Returns:
0 if successful, 1 if memory allocation failed

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

Signed substraction: X = A - B.

Parameters:
X Destination MPI
A Left-hand MPI
B Right-hand MPI
Returns:
0 if successful, 1 if memory allocation failed

void mpi_swap ( mpi X,
mpi Y 
)

Swap the contents of X and Y.

Parameters:
X First MPI value
Y Second MPI value

int mpi_write_binary ( mpi X,
unsigned char *  buf,
int  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

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

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

Parameters:
p Prefix, can be NULL
X Source MPI
radix Output numeric base
fout Output file handle (can be NULL)
Returns:
0 if successful, or an POLARSSL_ERR_MPI_XXX error code
Note:
Set fout == NULL to print X on the console.

int mpi_write_string ( mpi X,
int  radix,
char *  s,
int *  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 an POLARSSL_ERR_MPI_XXX error code
Note:
Call this function with *slen = 0 to obtain the minimum required buffer size in *slen.


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