Fq-primitive points on elliptic curves over finite prime fields

Abstract

This article is about a new kind of point on elliptic curves over finite fields, double generators. These points are Fp -primitive points on an elliptic curve E over Fp which are also a generators of the group of Fp-rational points, E(Fp). The article discusses results and tests conjectures of Cohen et. al (2022, “The existence of Fq-primitive points on curves using freeness”) and obtains results about what double generators are and how often and under what conditions these points exist.