XOR count and block circulant MDS matrices over finite commutative rings
Document Type
Article
Publication Date
1-1-2024
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.
Keywords
MDS matrix, finite commutative ring, circulant matrix, block circulant matrix, XOR count, diffusion layer
Divisions
MathematicalSciences
Funders
Princess Nourah bint Abdulrahman University (PNU) , Riyadh, Saudi Arabia (PNURSP2024R231),University Grants Commission, India (221610203798)
Publication Title
AIMS Mathematics
Volume
9
Issue
11
Publisher
AIMS Press
Publisher Location
PO BOX 2604, SPRINGFIELD, MO 65801-2604, UNITED STATES