  This study concentrates on preserving privacy in a network of agents where
each agent seeks to evaluate a general polynomial function over the private
values of her immediate neighbors. We provide an algorithm for the exact
evaluation of such functions while preserving privacy of the involved agents.
The solution is based on a reformulation of polynomials and adoption of two
cryptographic primitives: Paillier as a Partially Homomorphic Encryption scheme
and multiplicative-additive secret sharing. The provided algorithm is fully
distributed, lightweight in communication, robust to dropout of agents, and can
accommodate a wide class of functions. Moreover, system theoretic and secure
multi-party conditions guaranteeing the privacy preservation of an agent's
private values against a set of colluding agents are established. The
theoretical developments are complemented by numerical investigations
illustrating the accuracy of the algorithm and the resulting computational
cost.
