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package org.bouncycastle.pqc.math.linearalgebra;
/**
* This class describes operations with polynomials over finite field GF(2), i e
* polynomial ring R = GF(2)[X]. All operations are defined only for polynomials
* with degree <=32. For the polynomial representation the map f: R->Z,
* poly(X)->poly(2) is used, where integers have the binary representation. For
* example: X^7+X^3+X+1 -> (00...0010001011)=139 Also for polynomials type
* Integer is used.
*
* @see GF2mField
*/
public final class PolynomialRingGF2
{
/**
* Default constructor (private).
*/
private PolynomialRingGF2()
{
// empty
}
/**
* Return sum of two polyomials
*
* @param p polynomial
* @param q polynomial
* @return p+q
*/
public static int add(int p, int q)
{
return p ^ q;
}
/**
* Return product of two polynomials
*
* @param p polynomial
* @param q polynomial
* @return p*q
*/
public static long multiply(int p, int q)
{
long result = 0;
if (q != 0)
{
long q1 = q & 0x00000000ffffffffL;
while (p != 0)
{
byte b = (byte)(p & 0x01);
if (b == 1)
{
result ^= q1;
}
p >>>= 1;
q1 <<= 1;
}
}
return result;
}
/**
* Compute the product of two polynomials modulo a third polynomial.
*
* @param a the first polynomial
* @param b the second polynomial
* @param r the reduction polynomial
* @return a * b mod r
*/
public static int modMultiply(int a, int b, int r)
{
int result = 0;
int p = remainder(a, r);
int q = remainder(b, r);
if (q != 0)
{
int d = 1 << degree(r);
while (p != 0)
{
byte pMod2 = (byte)(p & 0x01);
if (pMod2 == 1)
{
result ^= q;
}
p >>>= 1;
q <<= 1;
if (q >= d)
{
q ^= r;
}
}
}
return result;
}
/**
* Return the degree of a polynomial
*
* @param p polynomial p
* @return degree(p)
*/
public static int degree(int p)
{
int result = -1;
while (p != 0)
{
result++;
p >>>= 1;
}
return result;
}
/**
* Return the degree of a polynomial
*
* @param p polynomial p
* @return degree(p)
*/
public static int degree(long p)
{
int result = 0;
while (p != 0)
{
result++;
p >>>= 1;
}
return result - 1;
}
/**
* Return the remainder of a polynomial division of two polynomials.
*
* @param p dividend
* @param q divisor
* @return p mod q
*/
public static int remainder(int p, int q)
{
int result = p;
if (q == 0)
{
System.err.println("Error: to be divided by 0");
return 0;
}
while (degree(result) >= degree(q))
{
result ^= q << (degree(result) - degree(q));
}
return result;
}
/**
* Return the rest of devision two polynomials
*
* @param p polinomial
* @param q polinomial
* @return p mod q
*/
public static int rest(long p, int q)
{
long p1 = p;
if (q == 0)
{
System.err.println("Error: to be divided by 0");
return 0;
}
long q1 = q & 0x00000000ffffffffL;
while ((p1 >>> 32) != 0)
{
p1 ^= q1 << (degree(p1) - degree(q1));
}
int result = (int)(p1 & 0xffffffff);
while (degree(result) >= degree(q))
{
result ^= q << (degree(result) - degree(q));
}
return result;
}
/**
* Return the greatest common divisor of two polynomials
*
* @param p polinomial
* @param q polinomial
* @return GCD(p, q)
*/
public static int gcd(int p, int q)
{
int a, b, c;
a = p;
b = q;
while (b != 0)
{
c = remainder(a, b);
a = b;
b = c;
}
return a;
}
/**
* Checking polynomial for irreducibility
*
* @param p polinomial
* @return true if p is irreducible and false otherwise
*/
public static boolean isIrreducible(int p)
{
if (p == 0)
{
return false;
}
int d = degree(p) >>> 1;
int u = 2;
for (int i = 0; i < d; i++)
{
u = modMultiply(u, u, p);
if (gcd(u ^ 2, p) != 1)
{
return false;
}
}
return true;
}
/**
* Creates irreducible polynomial with degree d
*
* @param deg polynomial degree
* @return irreducible polynomial p
*/
public static int getIrreduciblePolynomial(int deg)
{
if (deg < 0)
{
System.err.println("The Degree is negative");
return 0;
}
if (deg > 31)
{
System.err.println("The Degree is more then 31");
return 0;
}
if (deg == 0)
{
return 1;
}
int a = 1 << deg;
a++;
int b = 1 << (deg + 1);
for (int i = a; i < b; i += 2)
{
if (isIrreducible(i))
{
return i;
}
}
return 0;
}
}