  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.
