Estimation of the computational cost of the CSIDH algorithm on supersingular twisted and quadratic Edwards curves

Бессалов, Анатолій Володимирович and Циганкова, Оксана Валентиновна and Абрамов, Сергій Вадимович (2021) Estimation of the computational cost of the CSIDH algorithm on supersingular twisted and quadratic Edwards curves Радіотехника (207). pp. 40-51. ISSN 0485-8972

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Abstract

The properties of twisted and quadratic supersingular Edwards curves that form pairs of quadratic torsion with order over a prime field are considered. A modification of the CSIDH algorithm based on the isogenies of these curves instead of the traditional arithmetic of curves in the Montgomery form is presented. The parameters of these two classes of supersingular Edwards curves are calculated and tabulated for , on the isogenies of which an example of the implementation of the CSIDH algorithm as a non-interactive secret sharing scheme based on the secret and public keys of Alice and Bob is given..It is shown that the sequence of parameters of chains of isogenies for quadratic and twisted supersingular Edwards curves, respectively, has a reverse character on the period of the sequence. A recurrent algorithm for calculating the coordinates of points that form the kernels of isogenies of odd degrees is proposed, and its implementation in various coordinate systems is considered. A comparative analysis of the cost of calculating the parameter of the isogenic curve using the Farashakhi-Hosseini -coordinates and classical projective coordinates is given(X:Y:Z)is given.

Item Type: Article
Additional Information: DOI:10.30837/rt.2021.4.207.03
Uncontrolled Keywords: curve in generalized Edwards form; complete Edwards curve; twisted Edwards curve; quadratic Edwards curve; curve order; point order; isomorphism; isogeny; W-coordinates; square; non-rsquare
Subjects: Статті у наукометричних базах > Index Copernicus
Статті у журналах > Фахові (входять до переліку фахових, затверджений МОН)
Divisions: Факультет інформаційних технологій та математики > Кафедра інформаційної та кібернетичної безпеки імені професора Володимира Бурячка
Depositing User: професор Анатолій Володимирович Бессалов
Date Deposited: 08 Nov 2022 08:06
Last Modified: 08 Nov 2022 08:06
URI: https://elibrary.kubg.edu.ua/id/eprint/42383

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