Computing the number of points on an elliptic curve over a finite field: algorithmic aspects
type: Item
instance of: scholarly article
title: Computing the number of points on an elliptic curve over a finite field: algorithmic aspects
zbMATH Open document ID: 0843.11030
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1996-03-24T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/229174
full work available at URL: jtnb7-1.html
review text: The author describes in some detail his implementation of Schoof's algorithm to compute the number of rational points on an elliptic curve over a prime field. His algorithm depends on the practical improvements of Atkin and Elkies. The author explains how to compute convenient equations of certain modular curves and how to find factors of the division polynomials. He illustrates his efficient program by computing the number of points on an elliptic curve modulo the 500 digit prime \(p= 10^{499}+ 153\).
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11Y16
zbMATH DE Number: 858027
zbMATH Keywords: factors of division polynomials
zbMATH Keywords: Schoof's algorithm
zbMATH Keywords: number of rational points
zbMATH Keywords: elliptic curve
zbMATH Keywords: prime field
zbMATH Keywords: modular curves
author: François Morain
reviewed by: René Schoof
MaRDI profile type: Publication
OpenAlex ID: W2067361453
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DOI: 10.5802/JTNB.143
description: scientific article; zbMATH DE number 858027