Modeling CSIKE Algorithm on Non-Cyclic Edwards Curves

Bessalov, Anatoly and Sokolov, Volodymyr and Skladannyi, Pavlo and Abramov, Serhii and Zhyltsov, Oleksii (2022) Modeling CSIKE Algorithm on Non-Cyclic Edwards Curves Cybersecurity Providing in Information and Telecommunication Systems 2022, 3288 (1). pp. 1-10. ISSN 1613-0073

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Abstract

An original key encapsulation scheme is proposed as a modification of the CSIDH algorithm built on the isogenies of non-cyclic Edwards curves. The corresponding CSIKE algorithm uses only one public key of the recipient. A brief review of the properties of non-cyclic quadratic and twisted supersingular Edwards curves is given. We use a new scheme for modeling the CSIKE algorithm on isogenies of 4 degrees 3, 5, 7, 11 for p = 9239. In contrast to the CSIDH models of previous works, this scheme does not use precomputations and tabulation of the parameters of isogenic chains, but uses one known supersingular starting curve Ed with the parameter d = 2. Examples of calculations of isogenic chains by Alice and Bob at three stages of CSIKE operation using a randomized algorithm are given. It also proposes to abandon the calculation of the isogenic function ϕ(R) of a random point R, which significantly speeds up the algorithm.

Item Type:	Article
Uncontrolled Keywords:	Curve in generalized Edwards form; complete Edwards curve; twisted Edwards curve; quadratic Edwards curve; curve order; point order; isomorphism; isogeny; randomization; w-oordinates
Subjects:	Це архівна тематика Київського університету імені Бориса Грінченка > Статті у наукометричних базах > Scopus
Divisions:	Це архівні підрозділи Київського університету імені Бориса Грінченка > Факультет інформаційних технологій та математики > Кафедра інформаційної та кібернетичної безпеки імені професора Володимира Бурячка
Depositing User:	Павло Миколайович Складанний
Date Deposited:	20 Dec 2022 16:42
Last Modified:	20 Dec 2022 16:42
URI:	https://elibrary.kubg.edu.ua/id/eprint/43188

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