org.bouncycastle.pqc.math.linearalgebra
Class PolynomialGF2mSmallM

java.lang.Object
  org.bouncycastle.pqc.math.linearalgebra.PolynomialGF2mSmallM

public class PolynomialGF2mSmallM
extends java.lang.Object

This class describes operations with polynomials from the ring R = GF(2^m)[X], where 2 <= m <=31.

See Also:

GF2mField, PolynomialRingGF2m

Field Summary

static char

RANDOM_IRREDUCIBLE_POLYNOMIAL Constant used for polynomial construction (see constructor PolynomialGF2mSmallM(GF2mField, int, char, SecureRandom)).

Constructor Summary

PolynomialGF2mSmallM(GF2mField field)
Construct the zero polynomial over the finite field GF(2^m).

PolynomialGF2mSmallM(GF2mField field, byte[] enc)
Create a polynomial over the finite field GF(2^m).

PolynomialGF2mSmallM(GF2mField field, int degree)
Construct a monomial of the given degree over the finite field GF(2^m).

PolynomialGF2mSmallM(GF2mField field, int[] coeffs)
Construct the polynomial over the given finite field GF(2^m) from the given coefficient vector.

PolynomialGF2mSmallM(GF2mField field, int deg, char typeOfPolynomial, java.security.SecureRandom sr)
Construct a polynomial over the finite field GF(2^m).

PolynomialGF2mSmallM(GF2mVector vect)
Create a polynomial over the finite field GF(2^m) out of the given coefficient vector.

PolynomialGF2mSmallM(PolynomialGF2mSmallM other)
Copy constructor.

Method Summary

PolynomialGF2mSmallM	add(PolynomialGF2mSmallM addend) Compute the sum of this polynomial and the given polynomial.
PolynomialGF2mSmallM	addMonomial(int degree) Compute the sum of this polynomial and the monomial of the given degree.
void	addToThis(PolynomialGF2mSmallM addend) Add the given polynomial to this polynomial (overwrite this).
PolynomialGF2mSmallM[]	div(PolynomialGF2mSmallM f) Divide this polynomial by the given polynomial.
boolean	equals(java.lang.Object other) checks if given object is equal to this polynomial.
int	evaluateAt(int e) Evaluate this polynomial p at a value e (in GF(2^m)) with the Horner scheme.
PolynomialGF2mSmallM	gcd(PolynomialGF2mSmallM f) Return the greatest common divisor of this and a polynomial f
int	getCoefficient(int index) Return the coefficient with the given index.
int	getDegree() Return the degree of this polynomial
byte[]	getEncoded() Returns encoded polynomial, i.e., this polynomial in byte array form
int	getHeadCoefficient()
int	hashCode()
PolynomialGF2mSmallM	mod(PolynomialGF2mSmallM f) Reduce this polynomial modulo another polynomial.
PolynomialGF2mSmallM	modDiv(PolynomialGF2mSmallM divisor, PolynomialGF2mSmallM modulus) Compute the result of the division of this polynomial by another polynomial modulo a third polynomial.
PolynomialGF2mSmallM	modInverse(PolynomialGF2mSmallM a) Compute the inverse of this polynomial modulo the given polynomial.
PolynomialGF2mSmallM	modMultiply(PolynomialGF2mSmallM a, PolynomialGF2mSmallM b) Compute the product of this polynomial and another polynomial modulo a third polynomial.
PolynomialGF2mSmallM[]	modPolynomialToFracton(PolynomialGF2mSmallM g) Compute a polynomial pair (a,b) from this polynomial and the given polynomial g with the property b*this = a mod g and deg(a)<=deg(g)/2.
PolynomialGF2mSmallM	modSquareMatrix(PolynomialGF2mSmallM[] matrix) Square this polynomial using a squaring matrix.
PolynomialGF2mSmallM	modSquareRoot(PolynomialGF2mSmallM a) Compute the square root of this polynomial modulo the given polynomial.
PolynomialGF2mSmallM	modSquareRootMatrix(PolynomialGF2mSmallM[] matrix) Compute the square root of this polynomial using a square root matrix.
PolynomialGF2mSmallM	multiply(PolynomialGF2mSmallM factor) Compute the product of this polynomial and the given factor using a Karatzuba like scheme.
void	multThisWithElement(int element) Multiply this polynomial with an element from GF(2^m).
PolynomialGF2mSmallM	multWithElement(int element) Compute the product of this polynomial with an element from GF(2^m).
PolynomialGF2mSmallM	multWithMonomial(int k) Compute the product of this polynomial with a monomial X^k.
java.lang.String	toString() Returns a human readable form of the polynomial.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

RANDOM_IRREDUCIBLE_POLYNOMIAL

public static final char RANDOM_IRREDUCIBLE_POLYNOMIAL

Constant used for polynomial construction (see constructor PolynomialGF2mSmallM(GF2mField, int, char, SecureRandom)).

See Also:

Constant Field Values

Constructor Detail

PolynomialGF2mSmallM

public PolynomialGF2mSmallM(GF2mField field)

Construct the zero polynomial over the finite field GF(2^m).

Parameters:

field - the finite field GF(2^m)

PolynomialGF2mSmallM

public PolynomialGF2mSmallM(GF2mField field,
                            int deg,
                            char typeOfPolynomial,
                            java.security.SecureRandom sr)

Construct a polynomial over the finite field GF(2^m).

Parameters:

field - the finite field GF(2^m)

deg - degree of polynomial

typeOfPolynomial - type of polynomial

sr - PRNG

PolynomialGF2mSmallM

public PolynomialGF2mSmallM(GF2mField field,
                            int degree)

Construct a monomial of the given degree over the finite field GF(2^m).

Parameters:

field - the finite field GF(2^m)

degree - the degree of the monomial

PolynomialGF2mSmallM

public PolynomialGF2mSmallM(GF2mField field,
                            int[] coeffs)

Construct the polynomial over the given finite field GF(2^m) from the given coefficient vector.

Parameters:

field - finite field GF2m

coeffs - the coefficient vector

PolynomialGF2mSmallM

public PolynomialGF2mSmallM(GF2mField field,
                            byte[] enc)

Create a polynomial over the finite field GF(2^m).

Parameters:

field - the finite field GF(2^m)

enc - byte[] polynomial in byte array form

PolynomialGF2mSmallM

public PolynomialGF2mSmallM(PolynomialGF2mSmallM other)

Copy constructor.

Parameters:

other - another PolynomialGF2mSmallM

PolynomialGF2mSmallM

public PolynomialGF2mSmallM(GF2mVector vect)

Create a polynomial over the finite field GF(2^m) out of the given coefficient vector. The finite field is also obtained from the GF2mVector.

Parameters:

vect - the coefficient vector

Method Detail

getDegree

public int getDegree()

Return the degree of this polynomial

Returns:

int degree of this polynomial if this is zero polynomial return -1

getHeadCoefficient

public int getHeadCoefficient()

Returns:

the head coefficient of this polynomial

getCoefficient

public int getCoefficient(int index)

Return the coefficient with the given index.

Parameters:

index - the index

Returns:

the coefficient with the given index

getEncoded

public byte[] getEncoded()

Returns encoded polynomial, i.e., this polynomial in byte array form

Returns:

the encoded polynomial

evaluateAt

public int evaluateAt(int e)

Evaluate this polynomial p at a value e (in GF(2^m)) with the Horner scheme.

Parameters:

e - the element of the finite field GF(2^m)

Returns:

this(e)

add

public PolynomialGF2mSmallM add(PolynomialGF2mSmallM addend)

Compute the sum of this polynomial and the given polynomial.

Parameters:

addend - the addend

Returns:

this + a (newly created)

addToThis

public void addToThis(PolynomialGF2mSmallM addend)

Add the given polynomial to this polynomial (overwrite this).

Parameters:

addend - the addend

addMonomial

public PolynomialGF2mSmallM addMonomial(int degree)

Compute the sum of this polynomial and the monomial of the given degree.

Parameters:

degree - the degree of the monomial

Returns:

this + X^k

multWithElement

public PolynomialGF2mSmallM multWithElement(int element)

Compute the product of this polynomial with an element from GF(2^m).

Parameters:

element - an element of the finite field GF(2^m)

Returns:

this * element (newly created)

Throws:

java.lang.ArithmeticException - if element is not an element of the finite field this polynomial is defined over.

multThisWithElement

public void multThisWithElement(int element)

Multiply this polynomial with an element from GF(2^m).

Parameters:

element - an element of the finite field GF(2^m)

Throws:

java.lang.ArithmeticException - if element is not an element of the finite field this polynomial is defined over.

multWithMonomial

public PolynomialGF2mSmallM multWithMonomial(int k)

Compute the product of this polynomial with a monomial X^k.

Parameters:

k - the degree of the monomial

Returns:

this * X^k

div

public PolynomialGF2mSmallM[] div(PolynomialGF2mSmallM f)

Divide this polynomial by the given polynomial.

Parameters:

f - a polynomial

Returns:

polynomial pair = {q,r} where this = q*f+r and deg(r) < deg(f);

gcd

public PolynomialGF2mSmallM gcd(PolynomialGF2mSmallM f)

Return the greatest common divisor of this and a polynomial f

Parameters:

f - polynomial

Returns:

GCD(this, f)

multiply

public PolynomialGF2mSmallM multiply(PolynomialGF2mSmallM factor)

Compute the product of this polynomial and the given factor using a Karatzuba like scheme.

Parameters:

factor - the polynomial

Returns:

this * factor

mod

public PolynomialGF2mSmallM mod(PolynomialGF2mSmallM f)

Reduce this polynomial modulo another polynomial.

Parameters:

f - the reduction polynomial

Returns:

this mod f

modMultiply

public PolynomialGF2mSmallM modMultiply(PolynomialGF2mSmallM a,
                                        PolynomialGF2mSmallM b)

Compute the product of this polynomial and another polynomial modulo a third polynomial.

Parameters:

a - another polynomial

b - the reduction polynomial

Returns:

this * a mod b

modSquareMatrix

public PolynomialGF2mSmallM modSquareMatrix(PolynomialGF2mSmallM[] matrix)

Square this polynomial using a squaring matrix.

Parameters:

matrix - the squaring matrix

Returns:

this^2 modulo the reduction polynomial implicitly given via the squaring matrix

modSquareRoot

public PolynomialGF2mSmallM modSquareRoot(PolynomialGF2mSmallM a)

Compute the square root of this polynomial modulo the given polynomial.

Parameters:

a - the reduction polynomial

Returns:

this^(1/2) mod a

modSquareRootMatrix

public PolynomialGF2mSmallM modSquareRootMatrix(PolynomialGF2mSmallM[] matrix)

Compute the square root of this polynomial using a square root matrix.

Parameters:

matrix - the matrix for computing square roots in (GF(2^m))^t the polynomial ring defining the square root matrix

Returns:

this^(1/2) modulo the reduction polynomial implicitly given via the square root matrix

modDiv

public PolynomialGF2mSmallM modDiv(PolynomialGF2mSmallM divisor,
                                   PolynomialGF2mSmallM modulus)

Compute the result of the division of this polynomial by another polynomial modulo a third polynomial.

Parameters:

divisor - the divisor

modulus - the reduction polynomial

Returns:

this * divisor^(-1) mod modulus

modInverse

public PolynomialGF2mSmallM modInverse(PolynomialGF2mSmallM a)

Compute the inverse of this polynomial modulo the given polynomial.

Parameters:

a - the reduction polynomial

Returns:

this^(-1) mod a

modPolynomialToFracton

public PolynomialGF2mSmallM[] modPolynomialToFracton(PolynomialGF2mSmallM g)

Compute a polynomial pair (a,b) from this polynomial and the given polynomial g with the property b*this = a mod g and deg(a)<=deg(g)/2.

Parameters:

g - the reduction polynomial

Returns:

PolynomialGF2mSmallM[] {a,b} with b*this = a mod g and deg(a)<= deg(g)/2

equals

public boolean equals(java.lang.Object other)

checks if given object is equal to this polynomial.

The method returns false whenever the given object is not polynomial over GF(2^m).

Overrides:

equals in class java.lang.Object

Parameters:

other - object

Returns:

true or false

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

Returns:

the hash code of this polynomial

toString

public java.lang.String toString()

Returns a human readable form of the polynomial.

Overrides:

toString in class java.lang.Object

Returns:

a human readable form of the polynomial.