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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.5 and up.
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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;
    }

}