A new approuch to calculation of exact number of Edwards curve over prime field

Бессалов, Анатолій Володимирович and Третьяков, Дмитрий Борисович and Цыганкова, Оксана Валентиновна (2014) A new approuch to calculation of exact number of Edwards curve over prime field Сучасний захист інформації (3). pp. 11-15.

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Abstract

New properties of the cryptoresistant Edwards curves over prime fields accepted for cryptographic appendices are considered. The conditions of existence of curves in an initial form of y2 = x3 + ax + b isomorphic to Edwards's curves are found. Dependence of parameter d of Edwards curve x2 + y2 = 1 + d x2 y2 from parameters a and b of an elliptic curve in an initial form is determined. The new proof of exact formulas of calculation of number of curves of Edwards, isomorphic to initial curves with nonzero parameters a and b is provided. It differs from the proof provided in the previous work

Item Type: Article
Uncontrolled Keywords: cryptosystem, initial form of an elliptic curve, Edwards's curve, torsion curve, curve parameters, isomorphism, square, not square.
Subjects: Articles in journals > Збірники наукових праць
Divisions: Institutes > Institute of Society > Chair of Information Technologies and Mathematics > Chair of Computer Science
Depositing User: професор Анатолій Володимирович Бессалов
Date Deposited: 08 Jun 2015 05:22
Last Modified: 15 Dec 2017 11:37
URI: http://elibrary.kubg.edu.ua/id/eprint/9835

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