Abramov S. Models and Methods for Improving the Performance of the CSIDH Algorithm based on Supersingular Twisted Edwards Curves

Українська версія

Thesis for the degree of Doctor of Philosophy (PhD)

State registration number

0825U000720

Thesis Registration Form

0825U000720.pdf

Applicant for

Specialization

  • 125 - Кібербезпека та захист інформації

15-04-2025

Specialized Academic Board

PhD 7894

Borys Grinchenko Kyiv Metropolitan University

Essay

The dissertation is devoted to solving an urgent scientific problem, the essence of which is to increase the security and performance of cryptosystems based on the Commutative Supersingular Isogeny Diffie-Hellman, which is one of the leaders in asymmetric post-quantum cryptosystems, in post-quantum conditions. The algorithm is proposed to be built based on isogenies of noncyclic supersingular Edwards curves as pairs of quadratic torsion. The use of elliptic Edwards curves significantly increases the security of the cryptoalgorithm, but it increases the complexity of the algorithm’s computation and, accordingly, reduces its performance. Therefore, the problem of improving performance by modifying this algorithm is relevant.

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Research papers

Bessalov, A., Kovalchuk, L., & Abramov, S. (2022). Randomization of CSIDH Algorithm on Quadratic and Twisted Edwards Curves. Electronic Professional Scientific Journal “Cybersecurity: Education, Science, Technique”, 1(17), 128–144. https://doi.org/10.28925/2663-4023.2022.17.128144.

Bessalov, A., & Abramov, S. (2022). Special Properties of the Point Addition Law for Non-Cyclic Edwards Curves. Cybernetics and Systems Analysis, 58(683), 851–861. https://doi.org/10.1007/s10559-023-00518-w (Scopus Q3).

Bessalov, V., & Abramov, S. (2023). PQC CSIKE Algorithm on Non-Cyclic Edwards Curves. Cybernetics and Systems Analysis, 59(6), 867–879. https://doi.org/10.1007/s10559-023-00622-x (Scopus Q3).

Bessalov, A., Sokolov, V., & Abramov, S. (2024). Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves. Cryptography, 8(3), 1–17. https://doi.org/10.3390/cryptography8030038 (Scopus Q2, WoS Q2).

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Files

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