English

Yang-Baxter equation and cryptography

Group Theory 2022-12-29 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2212.13807,
  title  = {Yang-Baxter equation and cryptography},
  author = {Fabienne Chouraqui},
  journal= {arXiv preprint arXiv:2212.13807},
  year   = {2022}
}
R2 v1 2026-06-28T07:54:46.955Z