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

Abstract

In this paper we present and analyse a construction of irreducible polynomials over odd prime fields via the transforms which take any polynomial $f\in {\mathbf{F}}_p[x]$ of positive degree $n$ to ${\left(\frac{x}{k}\right)}^n\cdot f(k(x+x^{-1}))$, for some specific values of the odd prime $p$ and $k\in {\mathbf{F}}_p$.

9 pages. Exposition revised. References updated

References in corpus (2)

• On the iterations of certain maps $x\mapsto k\cdot (x+x^{-1})$ over finite fields of odd characteristic
• Sequences of irreducible polynomials without prescribed coefficients over odd prime fields

Cited by in corpus (1)

• On the construction of irreducible polynomials over finite fields via prime degree endomorphisms of elliptic curves