Rafail Ostrovsky (UCLA)
In the setting of unconditionally-secure MPC, where (dishonest) players are unbounded and no cryptographic assumptions are used, it was known since the 1980's that an honest majority of players is both necessary and sufficient to achieve privacy and correctness, assuming secure point-to-point and broadcast channels. The main open question that was left is to establish the exact communication complexity. In all works, there was a large gap between the communication complexity of the best known protocols in the malicious setting and in the honest-but-curious setting, where players do not deviate from the protocol.
We settle the above question by showing an unconditionally-secure MPC protocol, secure against a dishonest minority of malicious players, that matches the communication complexity of the best known MPC protocol in the honest-but-curious setting. More specifically, we present a new n-player MPC protocol that is secure against a computationally-unbounded malicious adversary that can adaptively corrupt up to t<n/2 of the players. For polynomially-large binary circuits that are not too unshaped, our protocol has an amortized communication complexity of O(n*log(n) + k/n^c) bits per multiplication (i.e. AND) gate, where k denotes the security parameter and c is an arbitrary non-negative constant. This improves on the previously most efficient protocol with the same security guarantee, which offers an amortized communication complexity of O(n^2*k) bits per multiplication gate. For any k polynomial in n, the amortized communication complexity of our protocol matches the O(n*log(n)) bit communication complexity of the best known MPC protocol with passive security.
We introduce several novel techniques that are of independent interest and we believe will have wider applicability. One is a novel idea of computing authentication tags by means of a mini MPC, which allows us to avoid expensive double-sharings; the other is a batch-wise multiplication verification that allows us to speedup Beaver's multiplication triples. The techniques draw from the PCP world and this infusion of new techniques from other domains of computational complexity may find further uses in the context of MPC.