Conference Paper

Anatoly Bessalov , Serhii Abramov , Volodymyr Sokolov , Nataliia Mazur

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 $$p + 1 ≡ 0 mod 8$$ over the prime field $$F_p$$ and double the space of all curves in the algorithms. The randomized algorithms CSIDH and CSIKE are presented. An analysis of the degrees $$l_k$$ isogenies distribution is given, and an optimal distribution within the given conditions is proposed with the degree $$l_{max} = 397$$ instead of $$l_{max} = 587$$ 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 $$l_k$$ 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.

class-group action; complete Edwards curve; CSIKE; CSIKE-ENC; curve in generalized Edwards form; curve order; isogeny; isomorphism; point order; quadratic Edwards curve; supersingular Edwards curve; twisted Edwards curve; w-coordinates

Elliptic Curve; Scalar Multiplication; Public-Key Cryptography

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2023 Cybersecurity Providing in Information and Telecommunication Systems (CPITS)

28 February 2023 Kyiv, Ukraine

First Online: 16 June 2023

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• ISSN: 1613-0073

• EID: 2-s2.0-85163882231

• URN: urn:nbn:de:0074-3421-9

• DBLP: conf/cpits/BessalovASM23

• KUBG: 45691

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Bessalov, A., Abramov, S., Sokolov, V., & Mazur, N. (2023). CSIKE-ENC Combined Encryption Scheme with Optimized Degrees of Isogeny Distribution. In Cybersecurity Providing in Information and Telecommunication Systems (Vol. 3421, pp. 36–45).

A. Bessalov, S. Abramov, V. Sokolov, and N. Mazur, “CSIKE-ENC Combined Encryption Scheme with Optimized Degrees of Isogeny Distribution,” Cybersecurity Providing in Information and Telecommunication Systems, vol. 3421, pp. 36–45, 2023.

A. Bessalov, et al., CSIKE-ENC Combined Encryption Scheme with Optimized Degrees of Isogeny Distribution, in: Cybersecurity Providing in Information and Telecommunication Systems, vol. 3421 (2023) 36–45.