In this work, a distributed server system composed of multiple servers that holds some coded files and multiple users that are interested in retrieving the linear functions of the files is investigated, where the servers are robust, blind and adversarial in the sense that any $J$ servers can together recover all files, while any $I$ colluding servers cannot obtain any information about the files, and at most $A$ servers maliciously provides erroneous information. In addition, the file library must be secure from a wiretapper who obtains all the signals, and the demands of any subset of users must kept private from the other users and servers, even if they collude. A coding scheme is proposed by incorporating the ideas of Shamir's secret sharing and key superposition into the framework of Placement Delivery Array (PDA), originally proposed to characterize the single-server coded caching system without any security or privacy constraints. It is shown that PDAs associated to Maddah-Ali and Niesen's coded caching scheme results in an achievable memory-storage-communication region, such that the storage size and communication load were optimal to within a multiplicative gap, except for the small memory regime when the number of files was smaller than the number of users.

翻译：本文研究了一个分布式服务器系统，该系统由多个存储编码文件的服务器以及多个希望检索文件线性函数的用户组成。服务器具有鲁棒性、盲性和对抗性：任意$J$个服务器可共同恢复所有文件，而任意$I$个合谋服务器无法获取文件的任何信息，且至多$A$个服务器会恶意提供错误信息。此外，文件库必须对窃听者（其可获取所有传输信号）保持安全，且任意用户子集的需求必须对其他用户及服务器（即使它们合谋）保持隐私。通过将Shamir秘密共享和密钥叠加的思想融入最初为无安全隐私约束的单服务器缓存系统设计的放置传递阵列框架，本文提出了一种编码方案。研究表明，与Maddah-Ali和Niesen编码缓存方案相关的PDA可实现一个存储-通信可行区域，使得存储开销与通信负载在乘法差距意义下达到最优（仅当文件数量少于用户数量的小存储容量区间除外）。