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Mathematics > Number Theory

arXiv:1601.03227 (math)
[Submitted on 13 Jan 2016 (v1), last revised 25 Jul 2017 (this version, v2)]

Title:Elliptic Gauß sums and Schoof's algorithm

Authors:Christian J. Berghoff
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Abstract:We present a new approach to handling the case of Atkin primes in Schoof's algorithm for counting points on elliptic curves over finite fields. Our approach is based on the theory of polynomially cyclic algebras, which we recall as far as necessary. We then proceed to describe our method, which essentially relies on transferring costly computations in extensions of $\mathbb{F}_p$ to isomorphic ones endowed with a special structure allowing to reduce run-time. We analyse the new run-time and conclude this procedure yields some improvement as compared to the classical approaches.
Comments: 16 pages, revised version
Subjects: Number Theory (math.NT)
MSC classes: 11Y40
Cite as: arXiv:1601.03227 [math.NT]
  (or arXiv:1601.03227v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1601.03227

Submission history

From: Christian Berghoff [view email]
[v1] Wed, 13 Jan 2016 13:16:00 UTC (17 KB)
[v2] Tue, 25 Jul 2017 15:54:05 UTC (17 KB)
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