Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves-Reference-Cited by-同舟云学术

Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves

Published:2024-08-27 Issue:3 Volume:8 Page:38
ISSN:2410-387X
Container-title:Cryptography
language:en
Short-container-title:Cryptography

Author:

Bessalov Anatoly¹,Sokolov Volodymyr¹^ORCID,Abramov Serhii¹

Affiliation:

1. Department of Information and Cyber Security, Borys Grinchenko Kyiv Metropolitan University, 18/2 Bulvarno-Kudriavska str., 04053 Kyiv, Ukraine

Abstract

The article presents the author’s works in the field of modifications and modeling of the Post-Quantum Cryptography (PQC) Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) algorithm on non-cyclic supersingular Edwards curves and its predecessor Couveignes-Rostovtsev-Stolbunov (CRS) scheme on ordinary non-cyclic Edwards curves are reviewed. Lower estimates of the computational speed gains of the modified algorithms over the original ones are obtained. The most significant results were obtained by choosing classes of non-cyclic Edwards curves connected as quadratic twist pairs instead of cyclic complete Edwards curves, as well as the method of algorithm randomization as an alternative to “constant time CSIDH”. It is shown that in the CSIDH and Commutative Supersingular Isogeny Key Encapsulation (CSIKE) algorithms, there are two independent cryptosystems with the possibility of parallel computation, eliminating the threat of side-channel attacks. There are four such cryptosystems for the CRS scheme. Integral lower bound estimates of the performance gain of the modified CSIDH algorithm are obtained at 1.5 × 29, and for the CRS scheme are 3 × 29.

Publisher

MDPI AG

Link

https://www.mdpi.com/2410-387X/8/3/38/pdf

Reference24 articles.

1. Raimondo, G.M., and Locascio, L.E. (2023). Module-Lattice-Based Key-Encapsulation Mechanism Standard. Initial Public Draft (Standard No. FIPS 203).

2. Raimondo, G.M., and Locascio, L.E. (2023). Module-Lattice-Based Digital Signature Standard. Initial Public Draft (Standard No. FIPS 204).

3. Raimondo, G.M., and Locascio, L.E. (2023). Stateless Hash-Based Digital Signature Standard. Initial Public Draft (Standard No. FIPS 205).

4. Castryck, W., Lange, T., Martindale, C., Panny, L., and Renes, J. (2018, January 2–6). CSIDH: An efficient post-quantum commutative group action. Proceedings of the 24th International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT), Brisbane, QLD, Australia.

5. Rostovtsev, A., and Stolbunov, A. (2024, August 04). Public-Key Cryptosystem Based on Isogenies. Cryptology ePrint Archive, Paper 2006/145, 2006 (Preprint). Available online: https://eprint.iacr.org/2006/145.