Given a monic polynomial f over finite fields F, (i.e. the coefficents of f are in the field F), we will factor f into product of irreducible monic polynomials. (a polynomial is irreducible if it is ...

We describe algorithms for polynomial factorization over the binary field F2, and their implementation. They allow polynomials of degree up to 250 000 to be factored in about one day of CPU time, ...

I have been talking to Thomas Sturm at ACA today and together we had the following idea, which we should discuss, since it opens up a fully new field of applications for the MWS stystem. The ...

Abstract: In this paper we show that the problem of deterministically factoring multivariate polynomials reduces to the problem of deterministic polynomial identity testing. Specifically, we show that ...

We consider polynomials of bi-degree (n, 1) over the skew field of quaternions where the indeterminates commute with each other and with all coefficients. Polynomials of this type do not generally ...

Abstract: A method is presented for polynomial factorization using a search method. The method used is to search for real parts of roots by iteratively applying the Routh test to a shifted polynomial.

We show that the binary expansions of algebraic numbers do not form secure pseudorandom sequences; given sufficiently many initial bits of an algebraic number, its minimal polynomial can be ...

ABSTRACT: Substitution boxes or S-boxes play a significant role in encryption and de-cryption of bit level plaintext and cipher-text respectively. Irreducible Poly-nomials (IPs) have been used to ...