Edwards Form Elliptic Curves and Cryptography

Бессалов, Анатолій Володимирович (2017) Edwards Form Elliptic Curves and Cryptography Одноосібна. ІВЦ «Видавництво «Політехника»», Київ.

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Abstract

The properties of a new class of elliptic curves in the Edwards form, which is useful for solving of asymmetric cryptography problems are investigated. The new classification has been substantiated, in consolidated Edwards curves form over a finite field of odd characteristic with splitting them into three disjoint classes depending on the properties of parameters a and d. The analysis of properties of complete Edwards curves and noncyclic twisted Edwards curves over a prime field is given, and the 12 theorems about new properties of these curves are proven. On the basis of the properties of the points halfing an original method of finding points order is proposed, hundreds of times more powerful than the standard method. The comparative analysis of scalar multiplication of points for curves in the Edwards form of and Weierstrass form, and first win at 1.5-1.6 times. Calculated and tabulated cryptographic system-parameters of complete Edwards curves over a prime field and extensions of small prime fields and twisted Edward curves over prime fields. For students, postgraduates, programmers and scientists specializing in asymmetric cryptography and information security.

Item Type: Monograph (Одноосібна)
Uncontrolled Keywords: Elliptic curve; Weerschtrasse form; Edwards form; curves order; points order; addition law; isomorphism
Subjects: Монографії > Видані в Україні
Divisions: Факультети > Факультет інформаційних технологій та управління > Кафедра інформаційних технологій і математичних дисциплін
Depositing User: професор Анатолій Володимирович Бессалов
Date Deposited: 20 Dec 2017 07:38
Last Modified: 20 Nov 2018 08:17
URI: http://elibrary.kubg.edu.ua/id/eprint/21879

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