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

#include <gf2n.h>

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

ENUMS, EXCEPTIONS, and TYPEDEFS
typedef unsigned int	RandomizationParameter

INPUT/OUTPUT
class	GF2NT

class	GF2NT233

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

CREATORS
	PolynomialMod2 ()
	Construct the zero polynomial.

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

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

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

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

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

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

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

static PolynomialMod2	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.

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

static const PolynomialMod2 &	Zero ()
	The Zero polinomial.

static const PolynomialMod2 &	One ()
	The One polinomial.

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

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

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

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

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

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

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

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

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

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

unsigned int	CoefficientCount () const
	degree + 1

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

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

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

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

bool	IsIrreducible () const
	check for irreducibility

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

PolynomialMod2	Squared () const

bool	IsUnit () const
	only 1 is a unit

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

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

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

static void	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))

Detailed Description

Polynomial with Coefficients in GF(2)

Definition at line 26 of file gf2n.h.

Member Typedef Documentation

◆ RandomizationParameter

typedef unsigned int PolynomialMod2::RandomizationParameter

Definition at line 38 of file gf2n.h.

Constructor & Destructor Documentation

◆ PolynomialMod2() [1/4]

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

◆ PolynomialMod2() [2/4]

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

inline

Construct a PolynomialMod2 from big-endian byte array.

Definition at line 55 of file gf2n.h.

◆ PolynomialMod2() [3/4]

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

inline

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

Definition at line 59 of file gf2n.h.

◆ PolynomialMod2() [4/4]

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 64 of file gf2n.h.

Member Function Documentation

◆ Monomial()

static PolynomialMod2 PolynomialMod2::Monomial ( size_t i )

static

Provides x^i.

Returns: x^i

◆ Trinomial()

static 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

Precondition

The coefficients should be provided in descending order. That is,

t0 > t1 > t2.

◆ Pentanomial()

static 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

Precondition

The coefficients should be provided in descending order. That is,

t0 > t1 > t2 > t3 > t4.

◆ AllOnes()

static PolynomialMod2 PolynomialMod2::AllOnes ( size_t n )

static

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

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

◆ Zero()

static const PolynomialMod2 & PolynomialMod2::Zero ( )

static

The Zero polinomial.

Returns: the zero polynomial

◆ One()

static const PolynomialMod2 & PolynomialMod2::One ( )

static

The One polinomial.

Returns: the one polynomial

◆ MinEncodedSize()

unsigned int PolynomialMod2::MinEncodedSize ( ) const

inline

minimum number of bytes to encode this polynomial

MinEncodedSize of 0 is 1

Definition at line 94 of file gf2n.h.

◆ Encode()

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

◆ GetBit()

bool PolynomialMod2::GetBit ( size_t n ) const

inline

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

Definition at line 125 of file gf2n.h.

◆ Degree()

signed int PolynomialMod2::Degree ( ) const

inline

the zero polynomial will return a degree of -1

Definition at line 130 of file gf2n.h.

◆ CoefficientCount()

unsigned int PolynomialMod2::CoefficientCount ( ) const

inline

degree + 1

Definition at line 132 of file gf2n.h.

◆ GetCoefficient()

int PolynomialMod2::GetCoefficient ( size_t i ) const

inline

return coefficient for x^i

Definition at line 134 of file gf2n.h.

◆ operator[]()

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

inline

return coefficient for x^i

Definition at line 137 of file gf2n.h.

◆ IsZero()

bool PolynomialMod2::IsZero ( ) const

inline

Definition at line 140 of file gf2n.h.

◆ operator+=()

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

inline

Definition at line 154 of file gf2n.h.

◆ operator-=()

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

inline

Definition at line 156 of file gf2n.h.

◆ SetCoefficient()

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

inline

Definition at line 177 of file gf2n.h.

◆ swap()

void PolynomialMod2::swap ( PolynomialMod2 & a )

inline

Definition at line 180 of file gf2n.h.

◆ operator+()

PolynomialMod2 PolynomialMod2::operator+ ( ) const

inline

Definition at line 188 of file gf2n.h.

◆ operator-()

PolynomialMod2 PolynomialMod2::operator- ( ) const

inline

Definition at line 190 of file gf2n.h.

◆ Plus()

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

inline

Definition at line 200 of file gf2n.h.

◆ Minus()

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

inline

Definition at line 202 of file gf2n.h.

◆ Doubled()

PolynomialMod2 PolynomialMod2::Doubled ( ) const

inline

is always zero since we're working modulo 2

Definition at line 225 of file gf2n.h.

◆ IsUnit()

bool PolynomialMod2::IsUnit ( ) const

inline

only 1 is a unit

Definition at line 230 of file gf2n.h.

◆ MultiplicativeInverse()

PolynomialMod2 PolynomialMod2::MultiplicativeInverse ( ) const

inline

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

Definition at line 232 of file gf2n.h.

Friends And Related Symbol Documentation

◆ GF2NT

friend class GF2NT

friend

Definition at line 250 of file gf2n.h.

◆ GF2NT233

friend class GF2NT233

friend

Definition at line 251 of file gf2n.h.

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

gf2n.h

Classes

ENUMS, EXCEPTIONS, and TYPEDEFS

INPUT/OUTPUT

CREATORS

ENCODE/DECODE

ACCESSORS

MANIPULATORS

UNARY OPERATORS

BINARY OPERATORS

OTHER ARITHMETIC FUNCTIONS

Detailed Description

Member Typedef Documentation

◆ RandomizationParameter

Constructor & Destructor Documentation

◆ PolynomialMod2() [1/4]

◆ PolynomialMod2() [2/4]

◆ PolynomialMod2() [3/4]

◆ PolynomialMod2() [4/4]

Member Function Documentation

◆ Monomial()

◆ Trinomial()

◆ Pentanomial()

◆ AllOnes()

◆ Zero()

◆ One()

◆ MinEncodedSize()

◆ Encode()

◆ GetBit()

◆ Degree()

◆ CoefficientCount()

◆ GetCoefficient()

◆ operator[]()

◆ IsZero()

◆ operator+=()

◆ operator-=()

◆ SetCoefficient()

◆ swap()

◆ operator+()

◆ operator-()

◆ Plus()

◆ Minus()

◆ Doubled()

◆ IsUnit()

◆ MultiplicativeInverse()

Friends And Related Symbol Documentation

◆ GF2NT

◆ GF2NT233