Novel weakness multivariate quadratic structures detected within Macaulay Matrix
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 weakn...
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| Format: | Article |
| Language: | English |
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Semarak Ilmu Publishing
2025
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| Online Access: | http://psasir.upm.edu.my/id/eprint/118515/ http://psasir.upm.edu.my/id/eprint/118515/1/118515.pdf |
| _version_ | 1848867533423116288 |
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| author | Abdullah, Kamilah Kamel Ariffin, Muhammad Rezal Abdul Jamal, Nurul Amiera Sakinah |
| author_facet | Abdullah, Kamilah Kamel Ariffin, Muhammad Rezal Abdul Jamal, Nurul Amiera Sakinah |
| author_sort | Abdullah, Kamilah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T14:38:01Z |
| format | Article |
| id | upm-118515 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:38:01Z |
| publishDate | 2025 |
| publisher | Semarak Ilmu Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1185152025-07-15T06:57:25Z http://psasir.upm.edu.my/id/eprint/118515/ Novel weakness multivariate quadratic structures detected within Macaulay Matrix Abdullah, Kamilah Kamel Ariffin, Muhammad Rezal Abdul Jamal, Nurul Amiera Sakinah 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. Semarak Ilmu Publishing 2025-07 Article PeerReviewed text en cc_by_nc_4 http://psasir.upm.edu.my/id/eprint/118515/1/118515.pdf 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 https://semarakilmu.com.my/journals/index.php/applied_sciences_eng_tech/article/view/4685 10.37934/araset.49.2.149159 |
| spellingShingle | Abdullah, Kamilah Kamel Ariffin, Muhammad Rezal Abdul Jamal, Nurul Amiera Sakinah Novel weakness multivariate quadratic structures detected within Macaulay Matrix |
| title | Novel weakness multivariate quadratic structures detected within Macaulay Matrix |
| title_full | Novel weakness multivariate quadratic structures detected within Macaulay Matrix |
| title_fullStr | Novel weakness multivariate quadratic structures detected within Macaulay Matrix |
| title_full_unstemmed | Novel weakness multivariate quadratic structures detected within Macaulay Matrix |
| title_short | Novel weakness multivariate quadratic structures detected within Macaulay Matrix |
| title_sort | novel weakness multivariate quadratic structures detected within macaulay matrix |
| url | http://psasir.upm.edu.my/id/eprint/118515/ http://psasir.upm.edu.my/id/eprint/118515/ http://psasir.upm.edu.my/id/eprint/118515/ http://psasir.upm.edu.my/id/eprint/118515/1/118515.pdf |