org.spongycastle.pqc.math.linearalgebra

Class PolynomialRingGF2

java.lang.Object

org.spongycastle.pqc.math.linearalgebra.PolynomialRingGF2

public final class PolynomialRingGF2
extends java.lang.Object

This class describes operations with polynomials over finite field GF(2), i e polynomial ring R = GF(2)[X]. All operations are defined only for polynomials with degree <=32. For the polynomial representation the map f: R->Z, poly(X)->poly(2) is used, where integers have the binary representation. For example: X^7+X^3+X+1 -> (00...0010001011)=139 Also for polynomials type Integer is used.

See Also:

GF2mField

Method Summary

Modifier and Type	Method and Description
static int	add(int p, int q) Return sum of two polyomials
static int	degree(int p) Return the degree of a polynomial
static int	degree(long p) Return the degree of a polynomial
static int	gcd(int p, int q) Return the greatest common divisor of two polynomials
static int	getIrreduciblePolynomial(int deg) Creates irreducible polynomial with degree d
static boolean	isIrreducible(int p) Checking polynomial for irreducibility
static int	modMultiply(int a, int b, int r) Compute the product of two polynomials modulo a third polynomial.
static long	multiply(int p, int q) Return product of two polynomials
static int	remainder(int p, int q) Return the remainder of a polynomial division of two polynomials.
static int	rest(long p, int q) Return the rest of devision two polynomials

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

add

public static int add(int p,
                      int q)

Return sum of two polyomials

Parameters:

p - polynomial

q - polynomial

Returns:

p+q

multiply

public static long multiply(int p,
                            int q)

Return product of two polynomials

Parameters:

p - polynomial

q - polynomial

Returns:

p*q

modMultiply

public static int modMultiply(int a,
                              int b,
                              int r)

Compute the product of two polynomials modulo a third polynomial.

Parameters:

a - the first polynomial

b - the second polynomial

r - the reduction polynomial

Returns:

a * b mod r

degree

public static int degree(int p)

Return the degree of a polynomial

Parameters:

p - polynomial p

Returns:

degree(p)

degree

public static int degree(long p)

Return the degree of a polynomial

Parameters:

p - polynomial p

Returns:

degree(p)

remainder

public static int remainder(int p,
                            int q)

Return the remainder of a polynomial division of two polynomials.

Parameters:

p - dividend

q - divisor

Returns:

p mod q

rest

public static int rest(long p,
                       int q)

Return the rest of devision two polynomials

Parameters:

p - polinomial

q - polinomial

Returns:

p mod q

gcd

public static int gcd(int p,
                      int q)

Return the greatest common divisor of two polynomials

Parameters:

p - polinomial

q - polinomial

Returns:

GCD(p, q)

isIrreducible

public static boolean isIrreducible(int p)

Checking polynomial for irreducibility

Parameters:

p - polinomial

Returns:

true if p is irreducible and false otherwise

getIrreduciblePolynomial

public static int getIrreduciblePolynomial(int deg)

Creates irreducible polynomial with degree d

Parameters:

deg - polynomial degree

Returns:

irreducible polynomial p