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PQC CSIKE Algorithm on Non-Cyclic Edwards Curves

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Cybernetics and Systems Analysis Aims and scope

Abstract

An original CSIKE post-quantum cryptography algorithm is proposed as a modification of the CSIDH algorithm but with one public key instead of two. The conditions for its implementation on two classes of non-cyclic Edwards curves are substantiated. The properties of quadratic and twisted supersingular Edwards curves that form pairs of quadratic twist of order p + 1 ≡ 0 mod 8 over a prime field Fp are considered. A modification of the CSIDH algorithm and the CSIKE algorithm are presented, which are generated on the isogenies of these curves instead of the traditional arithmetic of curves in the Montgomery form. For isogenies of degrees 3, 5, and 7, the parameters of isogenic chains of non-cyclic supersingular Edwards curves are calculated and tabulated for p = 839. The implementation of the key encapsulation scheme with its encryption by Alice with Bob’s public key is considered. A new randomized CSIKE algorithm with random equiprobable selection of the curve from two classes at each step of the isogeny chain is proposed. The probability of a successful side-channel attack in a randomized algorithm is estimated. It is proposed to abandon the calculation of the isogenic function ϕ(R) of a random point R, which significantly speeds up the algorithm.

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  1. Borys Grinchenko Kyiv University, Kyiv, Ukraine

    A. V. Bessalov & S. V. Abramov

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  1. A. V. Bessalov
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  2. S. V. Abramov
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Correspondence to A. V. Bessalov.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2023, pp. 3–18.

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Bessalov, A.V., Abramov, S.V. PQC CSIKE Algorithm on Non-Cyclic Edwards Curves. Cybern Syst Anal 59, 867–879 (2023). https://doi.org/10.1007/s10559-023-00622-x

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