CSIKE-ENC Combined Encryption Scheme with Optimized Degrees of Isogeny Distribution

Bessalov, Anatoliy and Abramov, Serhii and Sokolov, Volodymyr and Mazur, Nataliia (2023) CSIKE-ENC Combined Encryption Scheme with Optimized Degrees of Isogeny Distribution Cybersecurity Providing in Information and Telecommunication Systems, 3421. pp. 36-45. ISSN 1613-0073

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Abstract

For the PQC CSIDH and CSIKE algorithms, the advantages of two classes of quadratic and twisted supersingular Edwards curves over complete Edwards curves are justified. These classes form pairs of quadratic twist curves with order p + 1 ≡ 0mod8 over the prime field Fp and double the space of all curves in the algorithms. The randomized algorithms CSIDH and CSIKE are presented. An analysis of the degrees lk isogenies distribution is given, and an optimal distribution within the given conditions is proposed with the degree lmax = 397 instead of lmax = 587 while maintaining the number K = 74 of all degrees. A probabilistic analysis of random odd order points R was carried out, probability estimates are obtained, and it is recommended to avoid isogenies with small values of the degrees lk in algorithms. The features of the CSIKE algorithm with one public key of Bob in the problem of encapsulation by Alice of the secret key κ, which Bob calculates at the stage of decapsulation with his secret key, are considered. A CSIKE-ENC scheme for combined encryption of the key κ and message M based on two asymmetric algorithms CSIDH and CSIKE with Alice’s authentication and the well-known symmetric message encryption standard is proposed. The security aspects of the scheme are discussed.

Item Type: Article
Additional Information: EID: 2-s2.0-85163882231
Uncontrolled Keywords: CSIKE; CSIKE-ENC; curve in generalized Edwards form; complete Edwards curve; twisted Edwards curve; quadratic Edwards curve; supersingular Edwards curve; curve order; point order; isogeny; isomorphism; class-group action; w-coordinates;
Subjects: Статті у наукометричних базах > Scopus
Divisions: Факультет інформаційних технологій та математики > Кафедра інформаційної та кібернетичної безпеки імені професора Володимира Бурячка
Depositing User: Volodymyr Sokolov
Date Deposited: 19 Jul 2023 06:44
Last Modified: 19 Jul 2023 06:58
URI: https://elibrary.kubg.edu.ua/id/eprint/45691

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