Background material on α-shift radix systems and α-CNS polynomials is collected. Symmetric CNS trinomials of the shape Xd + bX + c (d > 2) are characterized, thereby extending known results on quadratic symmetric CNS polynomials.

This paper proposes an algorithm for generating irreducible cubic trinomials in the form x + ax + b, b ∈ Fp, where a is a certain fixed non-zero element in the prime field Fp. The proposed algorithm needs a certain irreducible cubic trinomial over Fp to be previously given as a generator; however, the proposed algorithm can generate irreducible cubic polynomials one after another by changing a ...

In this paper we introduce so-called redundant trinomials to represent elements of nite elds of characteristic 2. The concept is in fact similar to almost irreducible trinomials introduced by Brent and Zimmermann in the context of random numbers generators in [BZ ]. See also [BZ]. In fact, Blake et al. [BGL , BGL ] and Tromp et al. [TZZ ] explored also similar ideas some years a...