论文标题
图形和超图及其应用的自动形态随机造成
Automorphism Shuffles for Graphs and Hypergraphs and Its Applications
论文作者
论文摘要
在基于卡的密码学中，使用了一块物理卡来实现安全计算。随机将卡序列置入式卡以及一些概率分布的混音，可确保基于卡的协议的安全性。作者提出了一种称为Graph Shuffles的新型散装类，该杂种通过有向图（新一代计算2022）随机列入卡序列。对于带有$ n $顶点和$ m $边缘的定向图$ g $，可以用$ 2（n+m）$卡的堆碎散装来实现此类洗牌。在本文中，我们研究了图形进行，并提供了实施，应用程序以及对其进行略微概括。首先，我们为$ 2N+M $卡的图形散装提出了新的协议。其次，作为图形散装的新应用，我们表明，任何循环组的循环组混合机（在循环基团上都有一个随机群）都是与某些图相关联的图形散装。第三，我们定义了超图式的散装，这是通过超图的自动形态的散装，并表明任何超钻shuffle也可以用桩杂造的散装实现。
In card-based cryptography, a deck of physical cards is used to achieve secure computation. A shuffle, which randomly permutes a card-sequence along with some probability distribution, ensures the security of a card-based protocol. The authors proposed a new class of shuffles called graph shuffles, which randomly permutes a card-sequence by an automorphism of a directed graph (New Generation Computing 2022). For a directed graph $G$ with $n$ vertices and $m$ edges, such a shuffle could be implemented with pile-scramble shuffles with $2(n+m)$ cards. In this paper, we study graph shuffles and give an implementation, an application, and a slight generalization of them. First, we propose a new protocol for graph shuffles with $2n+m$ cards. Second, as a new application of graph shuffles, we show that any cyclic group shuffle, which is a shuffle over a cyclic group, is a graph shuffle associated with some graph. Third, we define a hypergraph shuffle, which is a shuffle by an automorphism of a hypergraph, and show that any hypergraph shuffle can also be implemented with pile-scramble shuffles.
