Yang-Baxter equation and cryptography

TL;DR

This paper introduces a method to generate large solutions to the Yang-Baxter equation and explores their potential applications in cryptography, including public key encryption and signature schemes.

Contribution

It provides a novel iterative construction of large involutive solutions and proposes cryptographic protocols based on these mathematical structures.

Findings

Constructed an infinite family of large involutive solutions

Provided criteria for irretractability and indecomposability preservation

Suggested cryptographic schemes with analyzed strengths and weaknesses

Abstract

We find a method to construct iteratively from a non-degenerate involutive set-theoretic solution of the Yang-Baxter equation an infinite family of very large non-degenerate involutive set-theoretic solutions. In case the initial solution is irretractable, all the induced solutions are also irretractable. In case the initial solution is indecomposable, we give a criterion to decide whether all the induced solutions are also indecomposable. Besides the interest in the construction of large (indecomposable) solutions of the Yang-Baxter equation, this construction may have some applications in cryptography. Indeed, we suggest a public key encryption method and a signature method based on our construction, and examine their strengths and weaknesses.