Multi-party protocol for agreement of shared secret permutations-keys of significant dimension with their isomorphic representations

Abstract

The processes of generating large-dimension permutation matrices and their matrix powers, including in their new isomorphic spaces, are examined, along with their features and advantages for modeling a protocol for the agreement of a main cooperative secret key-permutation by a group of participants. Operations of multiple permutations are proposed instead of raising the corresponding permutation matrices to powers, which are the basic procedures of the proposed cooperative protocol for agreeing on a common secret key-permutation, formed and transmitted in its isomorphic representation. The proposed accelerated methods of raising permutations to significant powers have been verified. The results of modeling the cooperative protocol for the agreement of the secret key-permutation, its algorithmic steps, and operations have demonstrated the adequacy and advantages of isomorphic representations for describing and functioning processes of matrix models and the proposed protocol. Additionally, the results show that the proposed protocol significantly enhances computational efficiency and security, effectively preventing brute-force attacks even with highdimensional keys. The practical implications of this work include improved secure communications in distributed systems and potential applications in fields requiring robust cryptographic methods, such as cybersecurity, data protection, and secure communications in IoT networks. The study demonstrated that isomorphic representations of permutation matrices not only provide high cryptographic strength but also significantly accelerate computational processes, which is critical for applications requiring realtime processing of large data volumes. The verification of the proposed methods confirms their effectiveness and reliability in various usage scenarios.