This study concentrates on preserving privacy in a network of agents where
each agent desires to evaluate a polynomial function over the private values of
its immediate neighbors. We provide an algorithm for the exact evaluation of
this function while preserving privacy of the involved agents. The solution is
based on two cryptographic primitives: Paillier as a Partially Homomorphic
Encryption scheme and multiplicative-additive secret sharing. The provided
scheme covers a large class of polynomial functions in distributed systems.
Moreover, conditions guaranteeing the privacy preservation of the private value
of an agent against a set of colluding agents are derived. The simulation
results demonstrate that the proposed scheme can be employed in a network to
enhance privacy at the cost of extra communication and computation budgets.

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