An algebraic attack on the key exchange protocol based upon a modified tropical structure

Abstract

In this paper, we analyze the key exchange protocol based on an algebraic structure derived from a tropical semiring. The security of this key exchange scheme depends on an attacker's inability to solve a system of non-linear equations to obtain the private parameters. However, we propose an algebraic attack on this key exchange scheme using only the public parameters. We thoroughly evaluate the protocol's security against algebraic attacks through comprehensive cryptanalysis. We study the behavior of matrix sequences produced during key exchange, looking for any almost linear periodicity property that could affect the cryptanalysis. We provide the algorithm and an example to illustrate our attack, demonstrating that this key exchange protocol is not secure. Additionally, we examine how different parameter selections and matrix sizes impact the protocol's security. Ultimately, this cryptanalysis enhances tropical cryptography by expanding our understanding of the security implications of modified tropical semiring-based key exchange protocols.