On Encryption by Stirling Polynomial Matrices

Year 2025, Volume: 38 Issue: 3, 1404 - 1418, 01.09.2025

Hatice Kayhan , Serpil Halıcı

https://doi.org/10.35378/gujs.1602943

Abstract

In this article, by examining Stirling numbers, a new matrix type containing these numbers is defined and this matrix is called Stirling matrix. Based on the fact that the use of matrices is very common and convenient in the field of encryption, we used the newly defined Stirling matrix to perform AES type encryption. Inspired by the properties of integer sequences, a new recurrence relation that gives Stirling polynomials is defined. The Stirling polynomials used in our study are associated with k-order generalized matrices. LU decomposition of this generalized matrix is performed and examined. The L matrix obtained with the help of this decomposition is used in AES-like encryption methods. In our study, the examination and verification of this algorithm are given with an application.

Keywords

Stirling polynomials , Galois field , Coding- decoding

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