Yang-Baxter equation and cryptography

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.