Conference Paper

Serhii Abramov , Anatoly Bessalov , Volodymyr Sokolov

Some properties of isogenies of non-cyclic supersingular Edwards curves, which are used in the implementation of the CSIDH algorithm, are considered. This article continues the consideration of properties using the example of these classes of supersingular Edwards curves from previous work. All isogeny calculations are performed using one parameter of the curve equation d. Isogeny properties are modeled on an isogeny graph and are considered graph properties. Recommendations are given for selecting some cryptosystem parameters. It is shown which parameters d are prohibited for use in CSIDH algorithms and that the transition from one isogeny to another is not always possible.

commutative supersingular isogeny Diffie-Hellman algorithm; curve in generalized Edwards form; curve order; graph of isogeny; non-cyclic Edwards curve; point order; Post-quantum cryptography

Elliptic Curve; Scalar Multiplication; Public-Key Cryptography

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2023 Cybersecurity Providing in Information and Telecommunication Systems II (CPITS-II)

26 October 2023 Kyiv, Ukraine

First Online: 16 November 2023

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• ISSN: 1613-0073

• EID: 2-s2.0-85178378792

• URN: urn:nbn:de:0074-3550-0

• DBLP: conf/cpits/AbramovBS23

• KUBG: 47363

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Abramov, S., Bessalov, A., & Sokolov, V. (2023). Properties of Isogeny Graph of Non-Cyclic Edwards Curves. In Cybersecurity Providing in Information and Telecommunication Systems II (Vol. 3550, pp. 234–239).

S. Abramov, A. Bessalov, and V. Sokolov, “Properties of Isogeny Graph of Non-Cyclic Edwards Curves,” Cybersecurity Providing in Information and Telecommunication Systems II, vol. 3550, pp. 234–239, 2023.

S. Abramov, A. Bessalov, V. Sokolov, Properties of Isogeny Graph of Non-Cyclic Edwards Curves, in: Cybersecurity Providing in Information and Telecommunication Systems, vol. 3550 (2023) 234–239.