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Novel weakness multivariate quadratic structures detected within Macaulay Matrix


Citation

Abdullah, Kamilah and Kamel Ariffin, Muhammad Rezal and Abdul Jamal, Nurul Amiera Sakinah (2025) Novel weakness multivariate quadratic structures detected within Macaulay Matrix. Journal of Advanced Research in Applied Sciences and Engineering Technology, 49 (2). pp. 149-159. ISSN 2462-1943; eISSN: 2462-1943

Abstract

The security of a Multivariate Public-Key Cryptosystem (MPKC) is based on the hard mathematical problem of solving Multivariate Quadratic (MQ) equations over finite fields, also known as the MQ problem. An MPKC has the potential to be a post-quantum cryptosystem. In this paper, we identify new weaknesses in the Macaulay matrix identified via Wang's technique, which was initially designed for solving multivariate quadratic equation systems. This new weakness occurs in the case of random coefficients in any column vector for different variables of monomials and random coefficients are assigned to other monomials. The weakness is exposed through the use of Gaussian elimination to obtain a univariate equation. We illustrate our findings using a random example.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.37934/araset.49.2.149159
Publisher: Semarak Ilmu Publishing
Keywords: Gaussian elimination; Macaulay matrix; Multivariate Public-Key Cryptosystem; Multivariate Quadratic problem
Depositing User: Mohamad Jefri Mohamed Fauzi
Date Deposited: 15 Jul 2025 06:57
Last Modified: 15 Jul 2025 06:57
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.37934/araset.49.2.149159
URI: http://psasir.upm.edu.my/id/eprint/118515
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