Two party key exchange protocol based on duo circulant matrices for the IoT environment

This paper proposes a new two-party key exchange protocol based on the max-plus semiring, which is the set of matrices over the set of integers along with negative infinity. We introduce the set of \(\alpha\) $\alpha$ - \(v\) $v$ - \(w\) $w$ -duo circulant matrices, forming an abelian subset of the max-plus semiring. Additionally, we demonstrate that the collection of all \(\alpha\) $\alpha$ - \(v\) $v$ - \(w\) $w$ -duo circulant matrices is the commutative subset of the max-plus semiring. We introduce a key exchange protocol based on \(\alpha\) $\alpha$ - \(v\) $v$ - \(w\) $w$ -duo circulant matrices with detailed key generation schemes. We compare our proposed protocol, based on \(\alpha\) $\alpha$ - \(v\) $v$ - \(w\) $w$ -duo circulant matrices, with existing tropical protocols in terms of time complexity and memory usage. Furthermore, we examine the security and demonstrate that our proposed protocol is resistant to prevalent attacks on tropical two-party key exchange protocols. The NP-Hardness of solving tropical non-linear equations strengthens the reliability of our proposed protocol. In this paper, our objective is to propose the integration of our protocol into the Internet of Things (IoT) environment.