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Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

Quantum-resilient cryptographic schemes using multivariate polynomial lattices

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pp. 2489–2497Vol. 28Issue 6September 2025DOI: 10.47974/JDMSC-2334 Crossmark XML
Received:
06 Mar 2024
Published Online:
09 Jul 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2334
Pages:
2489–2497

Abstract

In the changing field of post-quantum cryptography, making digital communications immune to quantum attacks is a footstone. This paper proposes a new cryptographic platform called Multivariate Polynomial Lattices (MPL) which combines the structural hardness of lattice-based cryptography with the algebraic hardness of multivariate polynomial systems. MPL uses discrete mathematics to develop strong cryptographic primitives that are secure against classical and quantum attacks. The introduced scheme extends (beyond) currently Multivariate Polynomial Cryptography (MPC3 (d) where it involves lattice into polynomial forms, thus making attacks more difficult if not impossible for anybody but the parities of the scheme. Our method is not only immune to attacks based on algebraic and Grobner basis but also has practical performance so that it can be practically deployed and used in the real world. A full proof that MPL is secure and a full analysis of its performance are presented to show the viability and security of MPL for post-quantum cryptographic schemes. This paper emphasizes the essential nature of lattice structures based polynomial cryptography for the development of this field for securing the digital communications in the future.

Keywords

Subject Classifications

81P94

References

[1] A. Aydeger, E. Zeydan, A. K. Yadav, K. T. Hemachandra, and M. Liyanage, “Towards a quantum-resilient future: Strategies for transitioning to post-quantum cryptography,” in Proc. 2024 15th Int. Conf. Network of the Future (NoF), pp. 195–203 (2024).
[2] B. Halak, T. Gibson, M. Henley, C. B. Botea, B. Heath, and S. Khan, “Evaluation of performance, energy, and computation costs of quantum-attack resilient encryption algorithms for embedded devices,” IEEE Access (2024).
[3] M. Singh, S. K. Singh, S. Kumar, M. Preet, V. Arya, and B. B. Gupta, “Quantum-resilient cryptographic primitives: An innovative modular hash learning algorithm to enhanced security in the quantum era,” unpublished (2024).
[4] A. Pedrouzo-Ulloa, J. R. Troncoso-Pastoriza, N. Gama, M. Georgieva, and F. Pérez-González, “Revisiting multivariate ring learning with errors and its applications on lattice-based cryptography,” Mathematics, vol. 9, no. 8 (2021).
[5] R. Cools, F. Y. Kuo, D. Nuyens, and I. H. Sloan, “Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters,” in 75 Years of Mathematics of Computation, vol. 754, Contemp. Math., Amer. Math. Soc., pp. 93–113 (2020), doi: 10.1090/conm/754/15150.
[6] M. Buchacher and M. Kauers, “On the problem of separating variables in multivariate polynomial ideals,” in Proc. 2024 Int. Symp. Symbolic Algebraic Comput. (2024).
[7] H. Bandara, Y. Herath, T. Weerasundara, and J. Alawatugoda, “On advances of lattice-based cryptographic schemes and their implementations,” Cryptography, vol. 6, no. 4 (2022).
[8] W. Yang, “ECC, RSA, and DSA analogies in applied mathematics,” in Int. Conf. Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), vol. 12163, SPIE (2022).
[9] S. Chavan and P. Mulay, “Define, refined and re-defined concepts of quantum machine learning: A review,” J. Inf. Optim. Sci., vol. 45, no. 5, pp. 1229–1262 (2024), doi: 10.47974/JIOS-1320.
[10] A. Akhileshwari and J. Majumdar, “Exploring the untapped potential of digital lending through the power of quantum computing,” J. Inf. Optim. Sci., vol. 46, no. 3, pp. 851–860 (2025), doi: 10.47974/JIOS-1942.
[11] D. Sudarshan, C. Khandelwal, L. Gowda, K. K. Bijjaragi, and R. SS, “Resource centric analysis of RSA and ECC algorithms on FPGA,” ITM Web Conf., vol. 56 (2023).

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