Better Preprocessing for Secure Multiparty Computation

Abstract

We present techniques and protocols for the preprocessing of secure multiparty computation (MPC), focusing on the so-called SPDZ MPC scheme [19] and its derivatives [16,18,1]. These MPC schemes consist of a so-called preprocessing or offline phase where correlated randomness is generated that is independent of the inputs and the evaluated function, and an online phase where such correlated randomness is consumed to securely and efficiently evaluate circuits. In the recent years, it has been shown that such protocols (such as [4,31,27] ) turn out to be very efficient in practice. While much research has been conducted towards optimizing the online phase of the MPC protocols, there seems to have been less focus on the offline phase of such protocols (except for [16]). With this work, we want to close this gap and give a toolbox of techniques that aim at optimizing the preprocessing. We support both instantiations over small fields and large rings using somewhat homomorphic encryption and the Paillier cryptosystem [34], respectively. In the case of small fields, we show how the preprocessing overhead can basically be made independent of the field characteristic and present a more efficient (amortized) zero-knowledge proof of plaintext knowledge. In the case of large rings, we present a protocol based on the Paillier cryptosystem which has a lower message complexity than previous protocols and employs more efficient zero-knowledge proofs that, to the best of our knowledge, were not presented in previous work.