Ali, Shakir and Alali, Amal S. and Khan, Atif Ahmad and Wijayanti, Indah Emilia and Wong, Kok Bin (2024) XOR count and block circulant MDS matrices over finite commutative rings. AIMS Mathematics, 9 (11). pp. 30529-30547. ISSN 2473-6988, DOI https://doi.org/10.3934/math.20241474.
Full text not available from this repository.Abstract
Block circulant MDS matrices are used in the design of linear diffusion layers for lightweight cryptographic applications. Most of the work on construction of block circulant MDS matrices focused either on finite fields or GL(m, F2). The main objective of this paper is to extend the above study of block circulant MDS matrices to finite commutative rings. Additionally, we examine the behavior of the XOR count distribution under different reducible polynomials of equal degree over F2. We show that the determinant of a block circulant matrix over a ring can be expressed in a simple form. We construct 4 x 4 and 8 x 8 block circulant matrices over a ring. Furthermore, for non-negative integer f (x) is an irreducible polynomial of degree m. To facilitate efficient implementation, we analyze XOR distinct XOR distributions when utilizing two reducible polynomials of equal degree, with XOR count distributions 776 and 764, respectively. However, when using irreducible polynomials of the same in lightweight cryptography.
| Item Type: | Article |
|---|---|
| Funders: | Princess Nourah bint Abdulrahman University (PNU) , Riyadh, Saudi Arabia (PNURSP2024R231), University Grants Commission, India (221610203798) |
| Uncontrolled Keywords: | MDS matrix; finite commutative ring; circulant matrix; block circulant matrix; XOR count; diffusion layer |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms. Juhaida Abd Rahim |
| Date Deposited: | 20 Jan 2025 02:56 |
| Last Modified: | 20 Jan 2025 02:56 |
| URI: | http://eprints.um.edu.my/id/eprint/47626 |
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