  In recent years, edge computing (EC) has attracted great attention for its
high-speed computing and low-latency characteristics. However, there are many
challenges in the implementation of EC. Firstly, user's privacy has been raised
as a major concern because the edge devices may be untrustworthy. In the case
of Private Edge Computing (PEC), a user wants to compute a matrix
multiplication between its local matrix and one of the matrices in a library,
which has been redundantly stored in edge devices. When utilizing resources of
edge devices, the privacy requires that each edge device cannot know which
matrix stored on it is desired by the user for the multiplication. Secondly,
edge devices usually have limited communication and storage resources, which
makes it impossible for them to store all matrices in the library. In this
paper, we consider the limited resources of edge devices and propose an unified
framework for PEC. Within the framework, we study two highly-coupled problems,
(1) storage allocation, that determines which matrices are stored on each edge
device, and (2) computation design, that determines which matrices (or linear
combinations of them) in each edge device are selected to participate in the
computing process with the privacy consideration. Specifically, we give a
general storage allocation scheme and then design two feasible private
computation schemes, i.e., General Private Computation (GPC) scheme and Private
Coded Computation (PCC) scheme. In particular, GPC can be applied in general
case and PCC can only be applied in special cases, while PCC achieves less
communication load. We theoretically analyze the proposed computing schemes and
compare them with other schemes. Finally, we conduct extensive simulations to
show the effectiveness of the proposed schemes.
