Polynomial with Coefficients in GF(2) More...

#include <gf2n.h>

Collaboration diagram for PolynomialMod2:

Classes
class	DivideByZero
	Excpetion thrown when divide by zero is encountered. More...

Private Attributes
SecWordBlock	reg

Friends
class	GF2NT

ENUMS, EXCEPTIONS, and TYPEDEFS
typedef unsigned int	RandomizationParameter

CREATORS
	PolynomialMod2 ()
	Construct the zero polynomial. More...

	PolynomialMod2 (const PolynomialMod2 &t)
	Copy construct a PolynomialMod2. More...

	PolynomialMod2 (word value, size_t bitLength=WORD_BITS)
	Construct a PolynomialMod2 from a word. More...

	PolynomialMod2 (const byte *encodedPoly, size_t byteCount)
	Construct a PolynomialMod2 from big-endian byte array. More...

	PolynomialMod2 (BufferedTransformation &encodedPoly, size_t byteCount)
	Construct a PolynomialMod2 from big-endian form stored in a BufferedTransformation. More...

	PolynomialMod2 (RandomNumberGenerator &rng, size_t bitcount)
	Create a uniformly distributed random polynomial. More...

static PolynomialMod2 CRYPTOPP_API	Monomial (size_t i)
	Provides x^i. More...

static PolynomialMod2 CRYPTOPP_API	Trinomial (size_t t0, size_t t1, size_t t2)
	Provides x^t0 + x^t1 + x^t2. More...

static PolynomialMod2 CRYPTOPP_API	Pentanomial (size_t t0, size_t t1, size_t t2, size_t t3, size_t t4)
	Provides x^t0 + x^t1 + x^t2 + x^t3 + x^t4. More...

static PolynomialMod2 CRYPTOPP_API	AllOnes (size_t n)
	Provides x^(n-1) + ... More...

static const PolynomialMod2 &CRYPTOPP_API	Zero ()
	The Zero polinomial. More...

static const PolynomialMod2 &CRYPTOPP_API	One ()
	The One polinomial. More...

ENCODE/DECODE
unsigned int	MinEncodedSize () const
	minimum number of bytes to encode this polynomial More...

void	Encode (byte *output, size_t outputLen) const
	encode in big-endian format More...

void	Encode (BufferedTransformation &bt, size_t outputLen) const

void	Decode (const byte *input, size_t inputLen)

void	Decode (BufferedTransformation &bt, size_t inputLen)

void	DEREncodeAsOctetString (BufferedTransformation &bt, size_t length) const
	encode value as big-endian octet string More...

void	BERDecodeAsOctetString (BufferedTransformation &bt, size_t length)
	decode value as big-endian octet string More...

ACCESSORS
unsigned int	BitCount () const
	number of significant bits = Degree() + 1 More...

unsigned int	ByteCount () const
	number of significant bytes = ceiling(BitCount()/8) More...

unsigned int	WordCount () const
	number of significant words = ceiling(ByteCount()/sizeof(word)) More...

bool	GetBit (size_t n) const
	return the n-th bit, n=0 being the least significant bit More...

byte	GetByte (size_t n) const
	return the n-th byte More...

signed int	Degree () const
	the zero polynomial will return a degree of -1 More...

unsigned int	CoefficientCount () const
	degree + 1 More...

int	GetCoefficient (size_t i) const
	return coefficient for x^i More...

int	operator[] (unsigned int i) const
	return coefficient for x^i More...

bool	IsZero () const

bool	Equals (const PolynomialMod2 &rhs) const

MANIPULATORS
PolynomialMod2 &	operator= (const PolynomialMod2 &t)

PolynomialMod2 &	operator&= (const PolynomialMod2 &t)

PolynomialMod2 &	operator^= (const PolynomialMod2 &t)

PolynomialMod2 &	operator+= (const PolynomialMod2 &t)

PolynomialMod2 &	operator-= (const PolynomialMod2 &t)

PolynomialMod2 &	operator*= (const PolynomialMod2 &t)

PolynomialMod2 &	operator/= (const PolynomialMod2 &t)

PolynomialMod2 &	operator%= (const PolynomialMod2 &t)

PolynomialMod2 &	operator<<= (unsigned int)

PolynomialMod2 &	operator>>= (unsigned int)

void	Randomize (RandomNumberGenerator &rng, size_t bitcount)

void	SetBit (size_t i, int value=1)

void	SetByte (size_t n, byte value)
	set the n-th byte to value More...

void	SetCoefficient (size_t i, int value)

void	swap (PolynomialMod2 &a)

UNARY OPERATORS
bool	operator! () const

PolynomialMod2	operator+ () const

PolynomialMod2	operator- () const

BINARY OPERATORS
PolynomialMod2	And (const PolynomialMod2 &b) const

PolynomialMod2	Xor (const PolynomialMod2 &b) const

PolynomialMod2	Plus (const PolynomialMod2 &b) const

PolynomialMod2	Minus (const PolynomialMod2 &b) const

PolynomialMod2	Times (const PolynomialMod2 &b) const

PolynomialMod2	DividedBy (const PolynomialMod2 &b) const

PolynomialMod2	Modulo (const PolynomialMod2 &b) const

PolynomialMod2	operator>> (unsigned int n) const

PolynomialMod2	operator<< (unsigned int n) const

OTHER ARITHMETIC FUNCTIONS
unsigned int	Parity () const
	sum modulo 2 of all coefficients More...

bool	IsIrreducible () const
	check for irreducibility More...

PolynomialMod2	Doubled () const
	is always zero since we're working modulo 2 More...

PolynomialMod2	Squared () const

bool	IsUnit () const
	only 1 is a unit More...

PolynomialMod2	MultiplicativeInverse () const
	return inverse if *this is a unit, otherwise return 0 More...

PolynomialMod2	InverseMod (const PolynomialMod2 &) const
	calculate multiplicative inverse of *this mod n More...

static PolynomialMod2 CRYPTOPP_API	Gcd (const PolynomialMod2 &a, const PolynomialMod2 &n)
	greatest common divisor More...

static void CRYPTOPP_API	Divide (PolynomialMod2 &r, PolynomialMod2 &q, const PolynomialMod2 &a, const PolynomialMod2 &d)
	calculate r and q such that (a == d*q + r) && (deg(r) < deg(d)) More...

INPUT/OUTPUT
std::ostream &	operator<< (std::ostream &out, const PolynomialMod2 &a)

Detailed Description

Polynomial with Coefficients in GF(2)

Definition at line 21 of file gf2n.h.

Member Typedef Documentation

typedef unsigned int PolynomialMod2::RandomizationParameter

Definition at line 33 of file gf2n.h.

Constructor & Destructor Documentation

PolynomialMod2::PolynomialMod2 ( )

Construct the zero polynomial.

Definition at line 29 of file gf2n.cpp.

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PolynomialMod2::PolynomialMod2 ( const PolynomialMod2 & t )

Copy construct a PolynomialMod2.

Definition at line 45 of file gf2n.cpp.

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PolynomialMod2::PolynomialMod2	(	word	value,
		size_t	bitLength = `WORD_BITS`
	)

Construct a PolynomialMod2 from a word.

value should be encoded with the least significant bit as coefficient to x^0 and most significant bit as coefficient to x^(WORD_BITS-1) bitLength denotes how much memory to allocate initially

Definition at line 33 of file gf2n.cpp.

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PolynomialMod2::PolynomialMod2	(	const byte *	encodedPoly,
		size_t	byteCount
	)

inline

Construct a PolynomialMod2 from big-endian byte array.

Definition at line 50 of file gf2n.h.

PolynomialMod2::PolynomialMod2	(	BufferedTransformation &	encodedPoly,
		size_t	byteCount
	)

inline

Construct a PolynomialMod2 from big-endian form stored in a BufferedTransformation.

Definition at line 54 of file gf2n.h.

PolynomialMod2::PolynomialMod2	(	RandomNumberGenerator &	rng,
		size_t	bitcount
	)

inline

Create a uniformly distributed random polynomial.

Create a random polynomial uniformly distributed over all polynomials with degree less than bitcount

Definition at line 59 of file gf2n.h.

Member Function Documentation

PolynomialMod2 PolynomialMod2::AllOnes ( size_t n )

static

Provides x^(n-1) + ...

x + 1
Returns
x^(n-1) + ... + x + 1

Definition at line 60 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::And ( const PolynomialMod2 & b ) const

Definition at line 253 of file gf2n.cpp.

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void PolynomialMod2::BERDecodeAsOctetString	(	BufferedTransformation &	bt,
		size_t	length
	)

decode value as big-endian octet string

Definition at line 181 of file gf2n.cpp.

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unsigned int PolynomialMod2::BitCount ( ) const

number of significant bits = Degree() + 1

Definition at line 204 of file gf2n.cpp.

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unsigned int PolynomialMod2::ByteCount ( ) const

number of significant bytes = ceiling(BitCount()/8)

Definition at line 195 of file gf2n.cpp.

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unsigned int PolynomialMod2::CoefficientCount ( ) const

inline

degree + 1

Definition at line 125 of file gf2n.h.

void PolynomialMod2::Decode	(	const byte *	input,
		size_t	inputLen
	)

Definition at line 144 of file gf2n.cpp.

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void PolynomialMod2::Decode	(	BufferedTransformation &	bt,
		size_t	inputLen
	)

Definition at line 156 of file gf2n.cpp.

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signed int PolynomialMod2::Degree ( ) const

inline

the zero polynomial will return a degree of -1

Definition at line 123 of file gf2n.h.

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void PolynomialMod2::DEREncodeAsOctetString	(	BufferedTransformation &	bt,
		size_t	length
	)		const

encode value as big-endian octet string

Definition at line 174 of file gf2n.cpp.

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void PolynomialMod2::Divide	(	PolynomialMod2 &	r,
		PolynomialMod2 &	q,
		const PolynomialMod2 &	a,
		const PolynomialMod2 &	d
	)

static

calculate r and q such that (a == d*q + r) && (deg(r) < deg(d))

Definition at line 293 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::DividedBy ( const PolynomialMod2 & b ) const

Definition at line 318 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::Doubled ( ) const

inline

is always zero since we're working modulo 2

Definition at line 218 of file gf2n.h.

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void PolynomialMod2::Encode	(	byte *	output,
		size_t	outputLen
	)		const

encode in big-endian format

if outputLen < MinEncodedSize, the most significant bytes will be dropped if outputLen > MinEncodedSize, the most significant bytes will be padded

Definition at line 150 of file gf2n.cpp.

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void PolynomialMod2::Encode	(	BufferedTransformation &	bt,
		size_t	outputLen
	)		const

Definition at line 168 of file gf2n.cpp.

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bool PolynomialMod2::Equals ( const PolynomialMod2 & rhs ) const

Definition at line 458 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::Gcd	(	const PolynomialMod2 &	a,
		const PolynomialMod2 &	n
	)

static

greatest common divisor

Definition at line 526 of file gf2n.cpp.

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bool PolynomialMod2::GetBit ( size_t n ) const

inline

return the n-th bit, n=0 being the least significant bit

Definition at line 118 of file gf2n.h.

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byte PolynomialMod2::GetByte ( size_t n ) const

return the n-th byte

Definition at line 83 of file gf2n.cpp.

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int PolynomialMod2::GetCoefficient ( size_t i ) const

inline

return coefficient for x^i

Definition at line 127 of file gf2n.h.

PolynomialMod2 PolynomialMod2::InverseMod ( const PolynomialMod2 & modulus ) const

calculate multiplicative inverse of *this mod n

Definition at line 531 of file gf2n.cpp.

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bool PolynomialMod2::IsIrreducible ( ) const

check for irreducibility

Definition at line 537 of file gf2n.cpp.

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bool PolynomialMod2::IsUnit ( ) const

inline

only 1 is a unit

Definition at line 223 of file gf2n.h.

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bool PolynomialMod2::IsZero ( ) const

inline

Definition at line 133 of file gf2n.h.

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unsigned int PolynomialMod2::MinEncodedSize ( ) const

inline

minimum number of bytes to encode this polynomial

MinEncodedSize of 0 is 1

Definition at line 87 of file gf2n.h.

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PolynomialMod2 PolynomialMod2::Minus ( const PolynomialMod2 & b ) const

inline

Definition at line 195 of file gf2n.h.

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PolynomialMod2 PolynomialMod2::Modulo ( const PolynomialMod2 & b ) const

Definition at line 325 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::Monomial ( size_t i )

static

Provides x^i.

Returns: x^i

Definition at line 98 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::MultiplicativeInverse ( ) const

inline

return inverse if *this is a unit, otherwise return 0

Definition at line 225 of file gf2n.h.

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const PolynomialMod2 & PolynomialMod2::One ( )

static

The One polinomial.

Returns: the one polynomial

Definition at line 139 of file gf2n.cpp.

bool PolynomialMod2::operator! ( ) const

Definition at line 451 of file gf2n.cpp.

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PolynomialMod2& PolynomialMod2::operator%= ( const PolynomialMod2 & t )

PolynomialMod2& PolynomialMod2::operator&= ( const PolynomialMod2 & t )

PolynomialMod2& PolynomialMod2::operator*= ( const PolynomialMod2 & t )

PolynomialMod2 PolynomialMod2::operator+ ( ) const

inline

Definition at line 181 of file gf2n.h.

PolynomialMod2& PolynomialMod2::operator+= ( const PolynomialMod2 & t )

inline

Definition at line 147 of file gf2n.h.

PolynomialMod2 PolynomialMod2::operator- ( ) const

inline

Definition at line 183 of file gf2n.h.

PolynomialMod2& PolynomialMod2::operator-= ( const PolynomialMod2 & t )

inline

Definition at line 149 of file gf2n.h.

PolynomialMod2& PolynomialMod2::operator/= ( const PolynomialMod2 & t )

PolynomialMod2 PolynomialMod2::operator<< ( unsigned int n ) const

Definition at line 439 of file gf2n.cpp.

PolynomialMod2 & PolynomialMod2::operator<<= ( unsigned int n )

Definition at line 332 of file gf2n.cpp.

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PolynomialMod2 & PolynomialMod2::operator= ( const PolynomialMod2 & t )

Definition at line 222 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::operator>> ( unsigned int n ) const

Definition at line 445 of file gf2n.cpp.

PolynomialMod2 & PolynomialMod2::operator>>= ( unsigned int n )

Definition at line 403 of file gf2n.cpp.

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int PolynomialMod2::operator[] ( unsigned int i ) const

inline

return coefficient for x^i

Definition at line 130 of file gf2n.h.

PolynomialMod2 & PolynomialMod2::operator^= ( const PolynomialMod2 & t )

Definition at line 228 of file gf2n.cpp.

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unsigned int PolynomialMod2::Parity ( ) const

sum modulo 2 of all coefficients

Definition at line 213 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::Pentanomial	(	size_t	t0,
		size_t	t1,
		size_t	t2,
		size_t	t3,
		size_t	t4
	)

static

Provides x^t0 + x^t1 + x^t2 + x^t3 + x^t4.

Returns: x^t0 + x^t1 + x^t2 + x^t3 + x^t4

Definition at line 114 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::Plus ( const PolynomialMod2 & b ) const

inline

Definition at line 193 of file gf2n.h.

void PolynomialMod2::Randomize	(	RandomNumberGenerator &	rng,
		size_t	bitcount
	)

Definition at line 51 of file gf2n.cpp.

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void PolynomialMod2::SetBit	(	size_t	i,
		int	value = `1`
	)

Definition at line 69 of file gf2n.cpp.

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void PolynomialMod2::SetByte	(	size_t	n,
		byte	value
	)

set the n-th byte to value

Definition at line 91 of file gf2n.cpp.

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void PolynomialMod2::SetCoefficient	(	size_t	i,
		int	value
	)

inline

Definition at line 170 of file gf2n.h.

PolynomialMod2 PolynomialMod2::Squared ( ) const

Definition at line 273 of file gf2n.cpp.

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void PolynomialMod2::swap ( PolynomialMod2 & a )

inline

Definition at line 173 of file gf2n.h.

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PolynomialMod2 PolynomialMod2::Times ( const PolynomialMod2 & b ) const

Definition at line 260 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::Trinomial	(	size_t	t0,
		size_t	t1,
		size_t	t2
	)

static

Provides x^t0 + x^t1 + x^t2.

Returns: x^t0 + x^t1 + x^t2

Definition at line 105 of file gf2n.cpp.

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unsigned int PolynomialMod2::WordCount ( ) const

number of significant words = ceiling(ByteCount()/sizeof(word))

Definition at line 190 of file gf2n.cpp.

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PolynomialMod2 PolynomialMod2::Xor ( const PolynomialMod2 & b ) const

Definition at line 235 of file gf2n.cpp.

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const PolynomialMod2 & PolynomialMod2::Zero ( )

static

The Zero polinomial.

Returns: the zero polynomial

Definition at line 134 of file gf2n.cpp.

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Friends And Related Function Documentation

friend class GF2NT

friend

Definition at line 243 of file gf2n.h.

std::ostream& operator<<	(	std::ostream &	out,
		const PolynomialMod2 &	a
	)

friend

Definition at line 474 of file gf2n.cpp.

Member Data Documentation

SecWordBlock PolynomialMod2::reg

private

Definition at line 245 of file gf2n.h.

The documentation for this class was generated from the following files:

src/cryptopp/gf2n.h
src/cryptopp/gf2n.cpp

Classes

Private Attributes

Friends

ENUMS, EXCEPTIONS, and TYPEDEFS

CREATORS

ENCODE/DECODE

ACCESSORS

MANIPULATORS

UNARY OPERATORS

BINARY OPERATORS

OTHER ARITHMETIC FUNCTIONS

INPUT/OUTPUT

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation