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arXiv · 2212.13807

Yang-Baxter equation and cryptography

Fabienne Chouraqui
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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.

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Fabienne Chouraqui. 2022-12-28. Yang-Baxter equation and cryptography. https://arxiv.org/abs/2212.13807

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