论文标题
Yang-Baxter方程和密码学
Yang-Baxter equation and cryptography
论文作者
论文摘要
我们找到了一种方法，可以从Yang-Baxter方程的非分类参与式理论解中迭代构建一种无限非分类涉及的设定理论解决方案的无限家族。如果最初的溶液是不可逆转的，则所有诱导的溶液也是不可验证的。如果初始溶液是不可分解的，我们给出一个标准来决定所有诱导的溶液是否也是不可分解的。除了对杨 - 巴克斯特方程的大型（不可分解的）解决方案的构建兴趣外，该结构可能在密码学中有一些应用。确实，我们建议一种基于我们的构造的公共密钥加密方法和一种签名方法，并检查其优势和劣势。
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.
