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# PolynomialMod2 Class Reference

`#include <gf2n.h>`

List of all members.

## Detailed Description

Polynomial with Coefficients in GF(2).

Definition at line 17 of file gf2n.h.

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

## Constructor & Destructor Documentation

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 22 of file gf2n.cpp. References SecBlock< word >::size().

## Member Function Documentation

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

| minimum number of bytes to encode this polynomial MinEncodedSize of 0 is 1 Definition at line 77 of file gf2n.h.

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 132 of file gf2n.cpp. Referenced by DEREncodeAsOctetString().

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

- gf2n.h
- gf2n.cpp