  In this paper, we analyze the problem of optimally allocating resources in a
distributed and privacy-preserving manner. We propose a novel distributed
optimal resource allocation algorithm with privacy-preserving guarantees, which
operates over a directed communication network. Our algorithm converges in
finite time and allows each node to process and transmit quantized messages.
Our algorithm utilizes a distributed quantized average consensus strategy
combined with a privacy-preserving mechanism. We show that the algorithm
converges in finite-time, and we prove that, under specific conditions on the
network topology, nodes are able to preserve the privacy of their initial
state. Finally, to illustrate the results, we consider an example where test
kits need to be optimally allocated proportionally to the number of infections
in a region. It is shown that the proposed privacy-preserving resource
allocation algorithm performs well with an appropriate convergence rate under
privacy guarantees.
