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Elliptic Divisibility Sequences over Finite Fields

Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim

Abstract:

In this work, we study elliptic divisibility sequences over finite fields. Morgan Ward in [14], [15] gave arithmetic theory of elliptic divisibility sequences and formulas for elliptic divisibility sequences with rank two over finite field Fp. We study elliptic divisibility sequences with rank three, four and five over a finite field Fp, where p > 3 is a prime and give general terms of these sequences and then we determine elliptic and singular curves associated with these sequences.

Keywords: Elliptic divisibility sequences, singular elliptic divisibilitysequences, elliptic curves, singular curves.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334960

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