A new public key cryptography using $M_{q}$ matrix

Document Type : Research Article

Authors

1 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran & Center of Excellence for Mathematical Modeling Optimization and Combinatorial Computing (MMOCC), University of Guilan, Rasht, Iran

3 Department of Computer Engineering, University of Guilan, Rasht, Iran

Abstract

We consider a new class of square Fibonacci $(q+1)\times(q+1)$-matrices in public key cryptography. This extends previous cryptography using generalized Fibonacci matrices. For a given integer $q$, a $(q+1)\times(q+1)$ binary matrix $M_{q}$ is a matrix which nonzero entries are located either on the super diagonal or on the last row of the matrix. In this article, we have proposed a modified public key cryptography using such matrices as key in Hill cipher and key agreement for encryption-decryption of terms of $M_{q}$-matrix. In this scheme, instead of exchanging the whole key matrix, only a pair of numbers needed to be exchanged, which reduces the time complexity as well as the space complexity of the transmission and has a large key space.

Keywords

Journal of Mathematical Modeling
Volume 11, Issue 4
December 2023
Pages 681-693

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