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PolynomialMod2 Class Reference

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

#include <gf2n.h>

List of all members.

ENUMS, EXCEPTIONS, and TYPEDEFS
typedef unsigned int	RandomizationParameter
CREATORS
	PolynomialMod2 ()
	creates the zero polynomial. More...
	PolynomialMod2 (const PolynomialMod2 &t)
	copy constructor. More...
	PolynomialMod2 (word value,unsigned int bitLength=WORD_BITS)
	convert from word. More...
	PolynomialMod2 (const byte *encodedPoly,unsigned int byteCount)
	convert from big-endian byte array. More...
	PolynomialMod2 (BufferedTransformation &encodedPoly,unsigned int byteCount)
	convert from big-endian form stored in a BufferedTransformation. More...
	PolynomialMod2 (RandomNumberGenerator &rng,unsigned int bitcount)
	create a random polynomial uniformly distributed over all polynomials with degree less than bitcount. More...
PolynomialMod2	Monomial (unsigned i)
	return x^i. More...
PolynomialMod2	Trinomial (unsigned t0,unsigned t1,unsigned t2)
	return x^t0 + x^t1 + x^t2. More...
PolynomialMod2	Pentanomial (unsigned t0,unsigned t1,unsigned t2,unsigned int t3,unsigned int t4)
	return x^t0 + x^t1 + x^t2 + x^t3 + x^t4. More...
PolynomialMod2	AllOnes (unsigned n)
	return x^(n-1) + ... + x + 1. More...
const PolynomialMod2&	Zero ()
const PolynomialMod2&	One ()
ENCODE/DECODE
unsigned int	MinEncodedSize ()const
	minimum number of bytes to encode this polynomial. More...
unsigned int	Encode (byte *output,unsigned int outputLen)const
	encode in big-endian format. More...
unsigned int	Encode (BufferedTransformation &bt,unsigned int outputLen)const
void	Decode (const byte *input,unsigned int inputLen)
void	Decode (BufferedTransformation &bt,unsigned int inputLen)
void	DEREncodeAsOctetString (BufferedTransformation &bt,unsigned int length)const
	encode value as big-endian octet string. More...
void	BERDecodeAsOctetString (BufferedTransformation &bt,unsigned int 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 (unsigned int n)const
	return the n-th bit, n=0 being the least significant bit. More...
byte	GetByte (unsigned int 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 (unsigned int 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,unsigned int bitcount)
void	SetBit (unsigned int i,int value=1)
void	SetByte (unsigned int n,byte value)
	set the n-th byte to value. More...
void	SetCoefficient (unsigned int 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.
PolynomialMod2	Gcd (const PolynomialMod2 &a,const PolynomialMod2 &n)
	greatest common divisor. More...
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)). More...
INPUT/OUTPUT
class	operator<<
Friends
class	GF2NT

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Detailed Description

Polynomial with Coefficients in GF(2).

Definition at line 16 of file gf2n.h.

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Member Typedef Documentation

typedef unsigned int PolynomialMod2::RandomizationParameter

Definition at line 28 of file gf2n.h.

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Constructor & Destructor Documentation

PolynomialMod2::PolynomialMod2 ( )

creates the zero polynomial. Definition at line 17 of file gf2n.cpp.

PolynomialMod2::PolynomialMod2 ( const PolynomialMod2 & t )

copy constructor. Definition at line 33 of file gf2n.cpp.

PolynomialMod2::PolynomialMod2 ( word value, unsigned int bitLength = WORD_BITS )

convert from 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 21 of file gf2n.cpp.

PolynomialMod2::PolynomialMod2 ( const byte * encodedPoly, unsigned int byteCount ) [inline]

convert from big-endian byte array. Definition at line 46 of file gf2n.h.

PolynomialMod2::PolynomialMod2 ( BufferedTransformation & encodedPoly, unsigned int byteCount ) [inline]

convert from big-endian form stored in a BufferedTransformation. Definition at line 50 of file gf2n.h.

PolynomialMod2::PolynomialMod2 ( RandomNumberGenerator & rng, unsigned int bitcount ) [inline]

create a random polynomial uniformly distributed over all polynomials with degree less than bitcount. Definition at line 54 of file gf2n.h.

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Member Function Documentation

PolynomialMod2 PolynomialMod2::AllOnes ( unsigned n ) [static]

return x^(n-1) + ... + x + 1. Definition at line 48 of file gf2n.cpp.

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

Definition at line 235 of file gf2n.cpp.

void PolynomialMod2::BERDecodeAsOctetString ( BufferedTransformation & bt, unsigned int length )

decode value as big-endian octet string. Definition at line 163 of file gf2n.cpp.

unsigned int PolynomialMod2::BitCount ( ) const

number of significant bits = Degree() + 1. Definition at line 186 of file gf2n.cpp. Referenced by CoefficientCount(), Degree(), and Divide().

unsigned int PolynomialMod2::ByteCount ( ) const

number of significant bytes = ceiling(BitCount()/8). Definition at line 177 of file gf2n.cpp. Referenced by MinEncodedSize().

unsigned int PolynomialMod2::CoefficientCount ( ) const [inline]

degree + 1. Definition at line 115 of file gf2n.h.

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

encode value as big-endian octet string. Definition at line 156 of file gf2n.cpp.

void PolynomialMod2::Decode ( BufferedTransformation & bt, unsigned int inputLen )

Definition at line 137 of file gf2n.cpp.

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

Definition at line 125 of file gf2n.cpp.

signed int PolynomialMod2::Degree ( ) const [inline]

the zero polynomial will return a degree of -1. Definition at line 113 of file gf2n.h. Referenced by Divide(), and IsIrreducible().

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 275 of file gf2n.cpp.

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

Definition at line 300 of file gf2n.cpp.

PolynomialMod2 PolynomialMod2::Doubled ( ) const [inline]

is always zero since we're working modulo 2. Definition at line 208 of file gf2n.h.

unsigned int PolynomialMod2::Encode ( BufferedTransformation & bt, unsigned int outputLen ) const

Definition at line 149 of file gf2n.cpp.

unsigned int PolynomialMod2::Encode ( byte * output, unsigned int 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 131 of file gf2n.cpp. Referenced by DEREncodeAsOctetString().

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

Definition at line 433 of file gf2n.cpp.

PolynomialMod2 PolynomialMod2::Gcd ( const PolynomialMod2 & a, const PolynomialMod2 & n ) [static]

greatest common divisor. Definition at line 498 of file gf2n.cpp. Referenced by IsIrreducible().

bool PolynomialMod2::GetBit ( unsigned int n ) const [inline]

return the n-th bit, n=0 being the least significant bit. Definition at line 108 of file gf2n.h.

byte PolynomialMod2::GetByte ( unsigned int n ) const

return the n-th byte. Definition at line 71 of file gf2n.cpp.

int PolynomialMod2::GetCoefficient ( unsigned int i ) const [inline]

return coefficient for x^i. Definition at line 117 of file gf2n.h. Referenced by GetBit(), and operator[]().

bool PolynomialMod2::IsIrreducible ( ) const

check for irreducibility. Definition at line 503 of file gf2n.cpp.

bool PolynomialMod2::IsUnit ( ) const [inline]

only 1 is a unit. Definition at line 213 of file gf2n.h. Referenced by IsIrreducible(), and MultiplicativeInverse().

bool PolynomialMod2::IsZero ( ) const [inline]

Definition at line 123 of file gf2n.h.

unsigned int PolynomialMod2::MinEncodedSize ( ) const [inline]

minimum number of bytes to encode this polynomial. MinEncodedSize of 0 is 1 Definition at line 76 of file gf2n.h.

PolynomialMod2 PolynomialMod2::Minus ( const PolynomialMod2 & b ) const [inline]

Definition at line 185 of file gf2n.h.

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

Definition at line 307 of file gf2n.cpp.

PolynomialMod2 PolynomialMod2::Monomial ( unsigned i ) [static]

return x^i. Definition at line 86 of file gf2n.cpp.

PolynomialMod2 PolynomialMod2::MultiplicativeInverse ( ) const [inline]

return inverse if *this is a unit, otherwise return 0. Definition at line 215 of file gf2n.h.

const PolynomialMod2 & PolynomialMod2::One ( ) [static]

Definition at line 119 of file gf2n.cpp.

unsigned int PolynomialMod2::Parity ( ) const

sum modulo 2 of all coefficients. Definition at line 195 of file gf2n.cpp.

PolynomialMod2 PolynomialMod2::Pentanomial ( unsigned t0, unsigned t1, unsigned t2, unsigned int t3, unsigned int t4 ) [static]

return x^t0 + x^t1 + x^t2 + x^t3 + x^t4. Definition at line 102 of file gf2n.cpp.

PolynomialMod2 PolynomialMod2::Plus ( const PolynomialMod2 & b ) const [inline]

Definition at line 183 of file gf2n.h.

void PolynomialMod2::Randomize ( RandomNumberGenerator & rng, unsigned int bitcount )

Definition at line 39 of file gf2n.cpp.

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

Definition at line 57 of file gf2n.cpp.

void PolynomialMod2::SetByte ( unsigned int n, byte value )

set the n-th byte to value. Definition at line 79 of file gf2n.cpp.

void PolynomialMod2::SetCoefficient ( unsigned int i, int value ) [inline]

Definition at line 160 of file gf2n.h.

PolynomialMod2 PolynomialMod2::Squared ( ) const

Definition at line 255 of file gf2n.cpp.

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

Definition at line 242 of file gf2n.cpp.

PolynomialMod2 PolynomialMod2::Trinomial ( unsigned t0, unsigned t1, unsigned t2 ) [static]

return x^t0 + x^t1 + x^t2. Definition at line 93 of file gf2n.cpp.

unsigned int PolynomialMod2::WordCount ( ) const

number of significant words = ceiling(ByteCount()/sizeof(word)). Definition at line 172 of file gf2n.cpp. Referenced by BitCount(), and ByteCount().

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

Definition at line 217 of file gf2n.cpp.

const PolynomialMod2 & PolynomialMod2::Zero ( ) [static]

Definition at line 113 of file gf2n.cpp.

bool PolynomialMod2::operator! ( ) const

Definition at line 426 of file gf2n.cpp.

PolynomialMod2 PolynomialMod2::operator+ ( ) const [inline]

Definition at line 171 of file gf2n.h.

PolynomialMod2 & PolynomialMod2::operator+= ( const PolynomialMod2 & t ) [inline]

Definition at line 137 of file gf2n.h.

PolynomialMod2 PolynomialMod2::operator- ( ) const [inline]

Definition at line 173 of file gf2n.h.

PolynomialMod2 & PolynomialMod2::operator-= ( const PolynomialMod2 & t ) [inline]

Definition at line 139 of file gf2n.h.

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

Definition at line 414 of file gf2n.cpp.

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

Definition at line 314 of file gf2n.cpp.

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

Definition at line 204 of file gf2n.cpp.

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

Definition at line 420 of file gf2n.cpp.

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

Definition at line 378 of file gf2n.cpp.

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

return coefficient for x^i. Definition at line 120 of file gf2n.h.

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

Definition at line 210 of file gf2n.cpp.

void PolynomialMod2::swap ( PolynomialMod2 & a ) [inline]

Definition at line 163 of file gf2n.h.

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Friends And Related Function Documentation

class GF2NT [friend]

Definition at line 233 of file gf2n.h.

ostream & operator<< ( ::ostream & out, const PolynomialMod2 & a ) [friend]

Definition at line 449 of file gf2n.cpp.

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

• gf2n.h
• gf2n.cpp

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