Resultant of a polynomial with x^n–1

Question

Resultant of a polynomial with x^n–1 (mod p)

I am implementing the NTRUSign algorithm as described in http://grouper.ieee.org/groups/1363/lattPK/submissions/EESS1v2.pdf , section 2.2.7.1 which involves computing the resultant of a polynomial. I keep getting a zero vector for the resultant which is obviously incorrect.

private static CompResResult compResMod(IntegerPolynomial f, int p) {
    int N = f.coeffs.length;
    IntegerPolynomial a = new IntegerPolynomial(N);
    a.coeffs[0] = -1;
    a.coeffs[N-1] = 1;
    IntegerPolynomial b = new IntegerPolynomial(f.coeffs);
    IntegerPolynomial v1 = new IntegerPolynomial(N);
    IntegerPolynomial v2 = new IntegerPolynomial(N);
    v2.coeffs[0] = 1;
    int da = a.degree();
    int db = b.degree();
    int ta = da;
    int c = 0;
    int r = 1;
    while (db > 0) {
        c = invert(b.coeffs[db], p);
        c = (c * a.coeffs[da]) % p;

        IntegerPolynomial cb = b.clone();
        cb.mult(c);
        cb.shift(da - db);
        a.sub(cb, p);

        IntegerPolynomial v2c = v2.clone();
        v2c.mult(c);
        v2c.shift(da - db);
        v1.sub(v2c, p);

        if (a.degree() < db) {
            r *= (int)Math.pow(b.coeffs[db], ta-a.degree());
            r %= p;
            if (ta%2==1 && db%2==1)
                r = (-r) % p;
            IntegerPolynomial temp = a;
            a = b;
            b = temp;
            temp = v1;
            v1 = v2;
            v2 = temp;
            ta = db;
        }
        da = a.degree();
        db = b.degree();
    }
    r *= (int)Math.pow(b.coeffs[0], da);
    r %= p;
    c = invert(b.coeffs[0], p);
    v2.mult(c);
    v2.mult(r);
    v2.mod(p);
    return new CompResResult(v2, r);
}

There is pseudocode in http://www.crypto.rub.de/imperia/md/content/texte/theses/da_driessen.pdf which looks very similar.

Why is my code not working? Are there any intermediate results I can check?

I am not posting the IntegerPolynomial code because it isn't too interesting and I have unit tests for it that pass. CompResResult is just a simple "Java struct".

Answer 1

As an alternative, consider the JScience class Polynomial<R extends Ring<R>>. As the class is generic, Polynomial<Integer> might simplify the implementation. This example uses Polynomial<Complex> for convenience in testing.

Answer 2

My guess is that (int)Math.pow(b.coeffs[0], da) is evaluating to 0. Have you tried to step through this code with a debugger, it should show you why your values is zero each time.