Development of crypto-code constructions on hyperelliptic curves

Authors

DOI:

https://doi.org/10.15587/1729-4061.2026.356495

Keywords:

post-quantum cryptography, hyperelliptic curve, cryptographic code construction, Rao–Nama scheme, algebraic-geometric code

Abstract

The subject of this study is the algebraic processes of data formation, encoding and syndrome decoding in cryptographic code constructions based on hyperelliptic curves of higher genera over Galois fields. The problem addressed lies in the excessive computational complexity and energy consumption of post-quantum asymmetric cryptosystems, which precludes their use on hardware platforms with resource constraints. The results obtained include the construction of a mathematical model of an algebraic-geometric code in projective coordinates, the development of a point mapping algorithm, and the generation of sparse matrices. The implementation of hyperelliptic structures into the symmetric Rao–Nama scheme has enabled a reduction in energy consumption of 20–60% compared to the asymmetric McElys scheme. The increase in the overall efficiency of the system is explained by the complete elimination of the resource-intensive operation of inverting Galois field elements thanks to an isomorphic transition to projective space, as well as the complete avoidance of solving matrix equations during the process of decrypting cryptograms. The distinctive features of the results obtained, which enabled the solution of the problem under investigation, lie in the fact that the targeted selection of row vectors for the evaluation matrices allowed the Hamming weight of the code to be artificially minimized. At the same time, the synergy of multidimensional algebraic geometry with symmetric architecture ensured an approximation to linear time complexity of decoding. The scope and conditions for the practical application of the results obtained cover the use of synthesized cryptographic code constructs in nodes of modern cyber-physical systems and Internet of Things (IoT) networks under conditions of severe computational resource constraints and autonomous power supply limits.

Author Biographies

Olena Akhiiezer, National Technical University “Kharkiv Polytechnic Institute”

Associate Professor, Head of Department

Department of Computer Mathematics and Data Analysis

Oleksandr Kushnerov, Sumy State University

Doctor of Philosophy (PhD)

Department of Economic Cybernetics

Hanna Nelasa, Zaporizhzhia Polytechnic National University

PhD, Associate Professor

Department of Information Security and Nanoelectronics

Olha Korol, National Technical University “Kharkiv Polytechnic Institute”

PhD, Associate Professor

Department of Cybersecurity

Klym Yamkovyi, National Technical University “Kharkiv Polytechnic Institute”

Doctor of Philosophy (PhD), Senior Lecturer

Department of Computer Mathematics and Data Analysis

Oleksandr Voitko, National Defence University of Ukraine

Doctor of Military Sciences, Head of Center

Educational and Scientific Center of Strategic Communications in the Field of Ensuring National Security and Defense

Vladyslav Sokol, National Technical University “Kharkiv Polytechnic Institute”

PhD

Department of Cybersecurity

Olena Voloshchuk, Kharkiv National University of Radio Electronics

PhD, Associate Professor

Department of Artificial Intelligence

Oleksandr Novoseletskyi, National University of Ostroh Academy

PhD, Associate Professor, Director

Educational and Scientific Institute of Information Technology and Busines

Oleh Nelasyi, Zaporizhzhia Polytechnic National University

PhD Student

Department of Radio engineering and Telecommunications

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Development of crypto-code constructions on hyperelliptic curves

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Published

2026-04-30

How to Cite

Akhiiezer, O., Kushnerov, O., Nelasa, H., Korol, O., Yamkovyi, K., Voitko, O., Sokol, V., Voloshchuk, O., Novoseletskyi, O., & Nelasyi, O. (2026). Development of crypto-code constructions on hyperelliptic curves. Eastern-European Journal of Enterprise Technologies, 2(9 (140), 6–18. https://doi.org/10.15587/1729-4061.2026.356495

Issue

Vol. 2 No. 9 (140) (2026): Information and controlling system

Section

Information and controlling system

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Copyright (c) 2026 Olena Akhiiezer, Oleksandr Kushnerov, Hanna Nelasa, Olha Korol, Klym Yamkovyi, Oleksandr Voitko, Vladyslav Sokol, Olena Voloshchuk, Oleksandr Novoseletskyi, Oleh Nelasyi

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