Package org.bouncycastle.pqc.legacy.math.linearalgebra

Class PolynomialGF2mSmallM

java.lang.Object
org.bouncycastle.pqc.legacy.math.linearalgebra.PolynomialGF2mSmallM
public class PolynomialGF2mSmallM extends Object
This class describes operations with polynomials from the ring R = GF(2^m)[X], where 2 <= m <=31.
See Also:

  • Field Details

  • Constructor Details

    • 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, 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 Details

    • 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:
      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:
      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(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 Object
      Parameters:
      other - object
      Returns:
      true or false

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object
      Returns:
      the hash code of this polynomial

    • toString

      public String toString()
      Returns a human readable form of the polynomial.
      Overrides:
      toString in class Object
      Returns:
      a human readable form of the polynomial.