Document Type : Research Paper

Authors

• Munesh Kumari ¹
• Jagmohan Tanti ²

¹ Department of Mathematics, Central University of Jharkhand, Ranchi, India

² Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow, India

Abstract

In this paper, we propose public key cryptography using recursive block matrices involving generalized Fibonacci numbers over a finite field $\mathbb{Z}_{p}$. For this, we define multinacci block matrices, a kind of upper triangular matrix involving multinacci matrices at diagonal places and give some of its algebraic properties. Moreover, we set up a method for key element agreement at end users, which makes cryptography more efficient. The proposed cryptography comes with a large key space and its security relies on the Discrete Logarithm Problem (DLP).

Keywords

• Fibonacci matrix
• Block Matrix
• Cryptography
• Keyspace