Value sets of Lattes maps over finite fields

Kucuksakalli O.

JOURNAL OF NUMBER THEORY, vol.143, pp.262-278, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 143
  • Publication Date: 2014
  • Doi Number: 10.1016/j.jnt.2014.04.014
  • Journal Name: JOURNAL OF NUMBER THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.262-278
  • Keywords: Dickson polynomial, Lattes map, Elliptic curve, Complex multiplication, Permutation
  • Middle East Technical University Affiliated: Yes

Abstract

We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication. (C) 2014 Elsevier Inc. All rights reserved.