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

Fields
Modifier and Type	Field	Description
`static char`	`RANDOM_IRREDUCIBLE_POLYNOMIAL`	Constant used for polynomial construction (see constructor `PolynomialGF2mSmallM(GF2mField, int, char, SecureRandom)`).

Constructor Summary

Constructors
Constructor	Description
`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

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`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.

Class PolynomialGF2mSmallM

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

RANDOM_IRREDUCIBLE_POLYNOMIAL

Constructor Detail

PolynomialGF2mSmallM

PolynomialGF2mSmallM

PolynomialGF2mSmallM

PolynomialGF2mSmallM

PolynomialGF2mSmallM

PolynomialGF2mSmallM

PolynomialGF2mSmallM

Method Detail

getDegree

getHeadCoefficient

getCoefficient

getEncoded

evaluateAt

add

addToThis

addMonomial

multWithElement

multThisWithElement

multWithMonomial

div

gcd

multiply

mod

modMultiply

modSquareMatrix

modSquareRoot

modSquareRootMatrix

modDiv

modInverse

modPolynomialToFracton

equals

hashCode

toString