org.bouncycastle.pqc.math.linearalgebra.GF2mField Maven / Gradle / Ivy
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package org.bouncycastle.pqc.math.linearalgebra;
import java.security.SecureRandom;
/**
* 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 PolynomialRingGF2
*/
public class GF2mField
{
/*
* degree - degree of the field polynomial - the field polynomial ring -
* polynomial ring over the finite field GF(2)
*/
private int degree = 0;
private int polynomial;
/**
* create a finite field GF(2^m)
*
* @param degree the degree of the field
*/
public GF2mField(int degree)
{
if (degree >= 32)
{
throw new IllegalArgumentException(
" Error: the degree of field is too large ");
}
if (degree < 1)
{
throw new IllegalArgumentException(
" Error: the degree of field is non-positive ");
}
this.degree = degree;
polynomial = PolynomialRingGF2.getIrreduciblePolynomial(degree);
}
/**
* create a finite field GF(2^m) with the fixed field polynomial
*
* @param degree the degree of the field
* @param poly the field polynomial
*/
public GF2mField(int degree, int poly)
{
if (degree != PolynomialRingGF2.degree(poly))
{
throw new IllegalArgumentException(
" Error: the degree is not correct");
}
if (!PolynomialRingGF2.isIrreducible(poly))
{
throw new IllegalArgumentException(
" Error: given polynomial is reducible");
}
this.degree = degree;
polynomial = poly;
}
public GF2mField(byte[] enc)
{
if (enc.length != 4)
{
throw new IllegalArgumentException(
"byte array is not an encoded finite field");
}
polynomial = LittleEndianConversions.OS2IP(enc);
if (!PolynomialRingGF2.isIrreducible(polynomial))
{
throw new IllegalArgumentException(
"byte array is not an encoded finite field");
}
degree = PolynomialRingGF2.degree(polynomial);
}
public GF2mField(GF2mField field)
{
degree = field.degree;
polynomial = field.polynomial;
}
/**
* return degree of the field
*
* @return degree of the field
*/
public int getDegree()
{
return degree;
}
/**
* return the field polynomial
*
* @return the field polynomial
*/
public int getPolynomial()
{
return polynomial;
}
/**
* return the encoded form of this field
*
* @return the field in byte array form
*/
public byte[] getEncoded()
{
return LittleEndianConversions.I2OSP(polynomial);
}
/**
* Return sum of two elements
*
* @param a
* @param b
* @return a+b
*/
public int add(int a, int b)
{
return a ^ b;
}
/**
* Return product of two elements
*
* @param a
* @param b
* @return a*b
*/
public int mult(int a, int b)
{
return PolynomialRingGF2.modMultiply(a, b, polynomial);
}
/**
* compute exponentiation a^k
*
* @param a a field element a
* @param k k degree
* @return a^k
*/
public int exp(int a, int k)
{
if (k == 0)
{
return 1;
}
if (a == 0)
{
return 0;
}
if (a == 1)
{
return 1;
}
int result = 1;
if (k < 0)
{
a = inverse(a);
k = -k;
}
while (k != 0)
{
if ((k & 1) == 1)
{
result = mult(result, a);
}
a = mult(a, a);
k >>>= 1;
}
return result;
}
/**
* compute the multiplicative inverse of a
*
* @param a a field element a
* @return a-1
*/
public int inverse(int a)
{
int d = (1 << degree) - 2;
return exp(a, d);
}
/**
* compute the square root of an integer
*
* @param a a field element a
* @return a1/2
*/
public int sqRoot(int a)
{
for (int i = 1; i < degree; i++)
{
a = mult(a, a);
}
return a;
}
/**
* create a random field element using PRNG sr
*
* @param sr SecureRandom
* @return a random element
*/
public int getRandomElement(SecureRandom sr)
{
int result = RandUtils.nextInt(sr, 1 << degree);
return result;
}
/**
* create a random non-zero field element
*
* @return a random element
*/
public int getRandomNonZeroElement()
{
return getRandomNonZeroElement(new SecureRandom());
}
/**
* create a random non-zero field element using PRNG sr
*
* @param sr SecureRandom
* @return a random non-zero element
*/
public int getRandomNonZeroElement(SecureRandom sr)
{
int controltime = 1 << 20;
int count = 0;
int result = RandUtils.nextInt(sr, 1 << degree);
while ((result == 0) && (count < controltime))
{
result = RandUtils.nextInt(sr, 1 << degree);
count++;
}
if (count == controltime)
{
result = 1;
}
return result;
}
/**
* @return true if e is encoded element of this field and false otherwise
*/
public boolean isElementOfThisField(int e)
{
// e is encoded element of this field iff 0<= e < |2^m|
if (degree == 31)
{
return e >= 0;
}
return e >= 0 && e < (1 << degree);
}
/*
* help method for visual control
*/
public String elementToStr(int a)
{
String s = "";
for (int i = 0; i < degree; i++)
{
if (((byte)a & 0x01) == 0)
{
s = "0" + s;
}
else
{
s = "1" + s;
}
a >>>= 1;
}
return s;
}
/**
* checks if given object is equal to this field.
*
* The method returns false whenever the given object is not GF2m.
*
* @param other object
* @return true or false
*/
public boolean equals(Object other)
{
if ((other == null) || !(other instanceof GF2mField))
{
return false;
}
GF2mField otherField = (GF2mField)other;
if ((degree == otherField.degree)
&& (polynomial == otherField.polynomial))
{
return true;
}
return false;
}
public int hashCode()
{
return polynomial;
}
/**
* Returns a human readable form of this field.
*
* @return a human readable form of this field.
*/
public String toString()
{
String str = "Finite Field GF(2^" + degree + ") = " + "GF(2)[X]/<"
+ polyToString(polynomial) + "> ";
return str;
}
private static String polyToString(int p)
{
String str = "";
if (p == 0)
{
str = "0";
}
else
{
byte b = (byte)(p & 0x01);
if (b == 1)
{
str = "1";
}
p >>>= 1;
int i = 1;
while (p != 0)
{
b = (byte)(p & 0x01);
if (b == 1)
{
str = str + "+x^" + i;
}
p >>>= 1;
i++;
}
}
return str;
}
}