Chapter

Algorithmic Number Theory

Volume 877 of the series Lecture Notes in Computer Science pp 60-70

Date:

Counting the number of points on elliptic curves over finite fields of characteristic greater than three

  • Frank LehmannAffiliated withFB Informatik, Universität des Saarlandes
  • , Markus MaurerAffiliated withFB Informatik, Universität des Saarlandes
  • , Volker MüllerAffiliated withFB Informatik, Universität des Saarlandes
  • , Victor ShoupAffiliated withFB Informatik, Universität des Saarlandes

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Abstract

We present a variant of an algorithm of Oliver Atkin for counting the number of points on an elliptic curve over a finite field. We describe an implementation of this algorithm for prime fields. We report on the use of this implementation to count the number of points on a curve over \(\mathbb{F}\) p, where p is a 375-digit prime.