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Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

CiteScore 2025: 2.7 (Q1)

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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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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Discrete mathematics for strengthening multivariate polynomial cryptography by addressing vulnerabilities

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pp. 2123–2132Vol. 27Issue 7October 2024DOI: 10.47974/JDMSC-2085 Crossmark XML
Received:
04 Mar 2024
Published Online:
15 Oct 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2085
Pages:
2123–2132

Abstract

Multivariate Polynomial Cryptography (MPC) has emerged as a promising candidate for securing digital communication in the post-quantum era. Despite its potential, existing MPC schemes exhibit vulnerabilities that compromise their effectiveness against both classical and quantum attacks. This paper leverages discrete mathematics to address these vulnerabilities, providing a robust mathematical foundation for enhancing the security and efficiency of MPC schemes. The paper begins by identifying critical weaknesses in current MPC algorithms, such as susceptibility to algebraic attacks and high computational overhead. Using tools from discrete mathematics, particularly in combinatorics and algebra, novel multivariate quadratic equations are proposed, designed to be computationally infeasible for quantum algorithms to solve. The approach involves constructing new cryptographic primitives that improve resistance to known attack vectors while maintaining practical performance levels. This research fills a significant gap in the field by providing a rigorous mathematical framework for the development of more secure MPC schemes. Comprehensive security proofs and performance analyses demonstrate that these enhanced MPC constructions offer a viable path forward for post-quantum cryptography. The findings underscore the critical role of discrete mathematics in advancing the field and ensuring the future security of digital communications.

Keywords

Multivariate polynomial cryptography (MPC)Post-quantum cryptographyDiscrete mathematicsAlgebraic attacksCombinatorial designsBoolean functions

Subject Classifications

94A60

References

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