We consider the problem of private multiple linear computation (PMLC) over a replicated storage system with colluding and unresponsive constraints. In this scenario, the user wishes to privately compute $P$ linear combinations of $M$ files from a set of $N$ replicated servers without revealing any information about the coefficients of these linear combinations to any $T$ colluding servers, in the presence of $S$ unresponsive servers that do not provide any information in response to user queries. Our focus is on more general performance metrics where the communication and computational overheads incurred by the user are not neglected. Additionally, the communication and computational overheads for servers are also taken into consideration. Unlike most previous literature that primarily focused on download cost from servers as a performance metric, we propose a novel PMLC scheme to establish a flexible tradeoff between communication costs and computational complexities.

翻译：我们研究存在共谋与无响应约束的复制存储系统中的私有多重线性计算（PMLC）问题。在该场景下，用户希望从$N$个复制服务器组成的集合中私有地计算$M$个文件的$P$个线性组合，且不向任意$T$个共谋服务器泄露这些线性组合系数的任何信息，同时需考虑$S$个无响应服务器（这些服务器不会对用户查询提供任何信息）。我们的关注点在于更通用的性能指标，其中用户产生的通信与计算开销均不被忽略。此外，服务器端的通信与计算开销也被纳入考量。与以往大多数主要将服务器下载代价作为性能指标的文献不同，我们提出了一种新型PMLC方案，用以构建通信成本与计算复杂度之间的灵活权衡。