Exact Number of Elliptic Curves in the Canonical Form, Which are Isomorphic to Edwards Curves Over Prime Field

Бессалов, Анатолій Володимирович and Ковальчук, Людмила Василівна (2015) Exact Number of Elliptic Curves in the Canonical Form, Which are Isomorphic to Edwards Curves Over Prime Field Кибернетика и системный анализ, 51 (2). pp. 3-12. ISSN 0023-1274

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Abstract

The necessary and sufficient conditions for the parameters of the curve in the canonical form with two points of order 4 are found. It is proved two lemmas about the properties of quadratic residues, using the Gauss scheme for quadratic residues and non-residues. Based on this lemmas the exact formulas for calculating the number of elliptic curves with non-zero parameters a and b and two points of fourth-order that are isomorphic to Edwards curves over the prime field. It is proved that for a large fields proportion of such curves is close to ¼.

Item Type: Article
Uncontrolled Keywords: canonical form of an elliptic curve, Edwards curve, twisted curve, curve parameters, isomorphism, quadratic residue, quadratic non-residue.
Subjects: Статті у наукометричних базах > РИНЦ
Статті у наукометричних базах > Scopus
Статті у наукометричних базах > Web of Science
Divisions: Факультети > Факультет інформаційних технологій та управління > Кафедра інформаційних технологій і математичних дисциплін
Depositing User: професор Анатолій Володимирович Бессалов
Date Deposited: 21 Dec 2017 08:45
Last Modified: 08 Jan 2019 11:57
URI: http://elibrary.kubg.edu.ua/id/eprint/22330

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