Private Computation of Polynomials over Networks

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.