Privacy, efficiency & fault tolerance in aggregate computations on massive star networks

We consider the challenge of performing efficient, fault-tolerant, privacy-preserving aggregate computations in a star topology, i.e., a massive number of participants connected to a single untrusted aggregator. The privacy constraints are that the participants do not discover each other´s data, and the aggregator obtains the final results while remaining oblivious to each participant´s individual contribution to the aggregate. In achieving these goals, previous approaches have either assumed a trusted dealer that distributes keys to the participants and the aggregator, or introduced additional parties that withhold the decryption key from the aggregator, or applied secret sharing with either pairwise communication amongst the participants or O(N2) ciphertext overhead at the aggregator. In contrast, we describe a protocol based on Shamir secret sharing and homomorphic encryption without assuming any additional parties. We also eliminate all pairwise communication amongst the participants and still require only O(N1+ε) overhead at the aggregator, where ε ≪ 1 can be achieved for massively multiparty computation. Our protocol arranges the star-connected participants into a logical hierarchy that facilitates parallelization, while allowing for user churn, i.e., a specified number of participants can go offline after providing their data, and new participants can join at a later stage of the computation.