  Distributed linearly separable computation, where a user asks some
distributed servers to compute a linearly separable function, was recently
formulated by the same authors and aims to alleviate the bottlenecks of
stragglers and communication cost in distributed computation. For this purpose,
the data center assigns a subset of input datasets to each server, and each
server computes some coded packets on the assigned datasets, which are then
sent to the user. The user should recover the task function from the answers of
a subset of servers, such the effect of stragglers could be tolerated. In this
paper, we formulate a novel secure framework for this distributed linearly
separable computation, where we aim to let the user only retrieve the desired
task function without obtaining any other information about the input datasets,
even if it receives the answers of all servers. In order to preserve the
security of the input datasets, some common randomness variable independent of
the datasets should be introduced into the transmission. We show that any
non-secure linear-coding based computing scheme for the original distributed
linearly separable computation problem, can be made secure without increasing
the communication cost. Then we focus on the case where the computation cost of
each server is minimum and aim to minimize the size of the randomness variable
introduced in the system while achieving the optimal communication cost. We
first propose an information theoretic converse bound on the randomness size.
We then propose secure computing schemes based on two well-known data
assignments, namely fractional repetition assignment and cyclic assignment. We
then propose a computing scheme with novel assignment, which strictly
outperforms the above two schemes. Some additional optimality results are also
obtained.
