论文标题
分区晶格和身份验证的四生直接功能
Four-generated direct powers of partition lattices and authentication
论文作者
论文摘要
对于整数$ n \ geq 5 $，H。Strietz（1975）和L.Zádori（1986）证明，所有分区的晶格部分$（n）$的$ \ {1,2，\ dots，n \} $是四分机的。开发L.Zádori特别优雅的结构，我们证明，即使是$ k $ thind Direct Power Parter Part $（n）^k $ part $（n）$也是许多生成的，但对于许多代表$ k $，也只有有限的许多指数。例如，对于每$ k \ leq 3 \ cdot 10^{89} $，part $（n）^k $都是四生成的，并且它具有一个四元素生成集，对于每$ k \ leq 1.4 \ cdot 10^{34} $而言，它并不是抗抗逆金。与这些结果有关，我们概述了如何在身份验证和秘密密钥加密中使用这些晶格的协议。
For an integer $n\geq 5$, H. Strietz (1975) and L. Zádori (1986) proved that the lattice Part$(n)$ of all partitions of $\{1,2,\dots,n\}$ is four-generated. Developing L. Zádori's particularly elegant construction further, we prove that even the $k$-th direct power Part$(n)^k$ of Part$(n)$ is four-generated for many but only finitely many exponents $k$. E.g., Part$(n)^k$ is four-generated for every $k\leq 3\cdot 10^{89}$, and it has a four element generating set that is not an antichain for every $k\leq 1.4\cdot 10^{34}$. In connection with these results, we outline a protocol how to use these lattices in authentication and secret key cryptography.
