Sequences of irreducible polynomials over odd prime fields via elliptic curve endomorphisms, II

Abstract

In this paper we extend a previous investigation by us regarding an iterative construction of irreducible polynomials over finite fields of odd characteristic. In particular, we show how it is possible to iteratively construct irreducible polynomials by means of two families of transforms, which we call the $Q_k$ and $\hat{Q}_k$-transforms, related to certain degree two isogenies over elliptic curves, which split the multiplication-by-$2$ map.