Algorithms and estimates of calculation complexity of 3- and 5-isogenes of supersingular Edwards curves

Бессалов, Анатолій Володимирович (2020) Algorithms and estimates of calculation complexity of 3- and 5-isogenes of supersingular Edwards curves Радіотехника, 200. pp. 37-50. ISSN 0485-8972

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Abstract

The analysis of properties and conditions of existence of 3- and 5-isogenies of complete and quadratic supersingular Edwards curves is given. For the problem of key distribution based on the SIDH algorithm, it is proposed to use isogeny of minimum odd degrees 3 and 5, which allows us to bypass the problem of singular points of the 2nd and 4th orders, which is typical for 2-isogenies. An overview of the main properties of the classes of Edwards curves is given. Formulas are obtained for estimating the complexity of isogenies of odd degrees 3 and 5 in the classes of complete and quadratic Edwards curves in projective coordinates. Algorithms for computing 3- and 5-isogenies of Edwards curves are constructed.

Item Type: Article
Uncontrolled Keywords: generalized Edwards curve; complete Edwards curve; twisted Edwards curve; quadratic Edwards curve; curve order; point order; isomorphism; isogeny; degree of isogeny; kernel of isogeny; quadratic residue; quadratic non-residue.
Subjects: Статті у журналах > Наукові (входять до інших наукометричних баз, крім перерахованих, мають ISSN, DOI, індекс цитування)
Divisions: Факультети > Факультет інформаційних технологій та управління > Кафедра інформаційної та кібернетичної безпеки імені професора Володимира Бурячка
Depositing User: професор Анатолій Володимирович Бессалов
Date Deposited: 23 Oct 2020 05:59
Last Modified: 23 Oct 2020 05:59
URI: https://elibrary.kubg.edu.ua/id/eprint/32298

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