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

Class GF2mField

java.lang.Object
org.bouncycastle.pqc.legacy.math.linearalgebra.GF2mField
public class GF2mField extends Object
This class describes operations with elements from the finite field F = GF(2^m). ( GF(2^m)= GF(2)[A] where A is a root of irreducible polynomial with degree m, each field element B has a polynomial basis representation, i.e. it is represented by a different binary polynomial of degree less than m, B = poly(A) ) All operations are defined only for field with 1< m <32. For the representation of field elements the map f: F->Z, poly(A)->poly(2) is used, where integers have the binary representation. For example: A^7+A^3+A+1 -> (00...0010001011)=139 Also for elements type Integer is used.
See Also:

  • Constructor Details

    • GF2mField

      public GF2mField(int degree)
      create a finite field GF(2^m)
      Parameters:
      degree - the degree of the field

    • GF2mField

      public GF2mField(int degree, int poly)
      create a finite field GF(2^m) with the fixed field polynomial
      Parameters:
      degree - the degree of the field
      poly - the field polynomial

    • GF2mField

      public GF2mField(byte[] enc)

    • GF2mField

      public GF2mField(GF2mField field)

  • Method Details

    • getDegree

      public int getDegree()
      return degree of the field
      Returns:
      degree of the field

    • getPolynomial

      public int getPolynomial()
      return the field polynomial
      Returns:
      the field polynomial

    • getEncoded

      public byte[] getEncoded()
      return the encoded form of this field
      Returns:
      the field in byte array form

    • add

      public int add(int a, int b)
      Return sum of two elements
      Parameters:
      a -
      b -
      Returns:
      a+b

    • mult

      public int mult(int a, int b)
      Return product of two elements
      Parameters:
      a -
      b -
      Returns:
      a*b

    • exp

      public int exp(int a, int k)
      compute exponentiation a^k
      Parameters:
      a - a field element a
      k - k degree
      Returns:
      a^k

    • inverse

      public int inverse(int a)
      compute the multiplicative inverse of a
      Parameters:
      a - a field element a
      Returns:
      a-1

    • sqRoot

      public int sqRoot(int a)
      compute the square root of an integer
      Parameters:
      a - a field element a
      Returns:
      a1/2

    • getRandomElement

      public int getRandomElement(SecureRandom sr)
      create a random field element using PRNG sr
      Parameters:
      sr - SecureRandom
      Returns:
      a random element

    • getRandomNonZeroElement

      public int getRandomNonZeroElement()
      create a random non-zero field element
      Returns:
      a random element

    • getRandomNonZeroElement

      public int getRandomNonZeroElement(SecureRandom sr)
      create a random non-zero field element using PRNG sr
      Parameters:
      sr - SecureRandom
      Returns:
      a random non-zero element

    • isElementOfThisField

      public boolean isElementOfThisField(int e)
      Returns:
      true if e is encoded element of this field and false otherwise

    • elementToStr

      public String elementToStr(int a)

    • equals

      public boolean equals(Object other)
      checks if given object is equal to this field.

      The method returns false whenever the given object is not GF2m.

      Overrides:
      equals in class Object
      Parameters:
      other - object
      Returns:
      true or false

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object

    • toString

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