隐私的代价：基于图的多秘密共享的随机性复杂度
The Price of Privacy: Randomness Complexity of Graph-Based Multi-Secret Sharing
- Institute of Science and Technology Austria（奥地利科学技术研究所）
- University of Warsaw（华沙大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究基于图的多秘密共享中最小随机性需求，将三秘密结果推广至四秘密及任意数量秘密，并完全刻画了完全图上四参与者的最小随机状态数及任意图中单随机比特的充分条件。
AI中文摘要：
我们研究了在由一张图连接的各方之间共享可能相关的秘密比特所需的随机性。一个经销商将份额放置在边上，使得每个参与者可以从其关联的份额中恢复自己的秘密，并且除了自身秘密所揭示的信息外，无法得知其他参与者的任何信息。Anilkumar等人完全确定了三个二进制秘密所需的最小随机性。我们将这项研究扩展到四个秘密，并针对一般图上的任意数量秘密获得了结果。对于完全图上的四个参与者，我们确定了每种允许的秘密组合所需的最小随机状态数：可能的值为一、二、三和四。我们还刻画了在任意图上仅需一个随机比特即可满足的条件。
英文摘要：
We study the randomness required to share possibly correlated secret bits among parties connected by a graph. A dealer places shares on the edges so that each party can recover its own secret from its incident shares and learn nothing about the others beyond what its own secret reveals. Anilkumar et al. completely determined the minimum randomness required for three binary secrets. We extend this study to four secrets and obtain results for arbitrary numbers of secrets on general graphs. For four parties on a complete graph, we determine the minimum number of random states for every set of permitted secret combinations: the possible values are one, two, three and four. We also characterize when one random bit suffices on an arbitrary graph.
