Unconditionally Secure Asynchronous Multiparty Computation with Linear Communication Complexity

We present two unconditionally secure asynchronous multiparty computation (AMPC) protocols among nparties with an amortized communication complexity of O(n) field elements per multiplication gate and whichcan tolerate a computationally unbounded active adversary corrupting t < n/4 parties. These are the first AMPCprotocols with linear communication complexity per multiplication gate. Our first protocol is statistically securein a completely asynchronous setting and improves on the previous best AMPC protocol in the same setting by afactor of Θ(n). Our second protocol is perfectly secure in a hybrid setting, where one round of communicationis assumed to be synchronous and improves on the previous best AMPC protocol in the hybrid setting by afactor of Θ(n).The central contribution common to both the protocols is a new, simple and communication efficient, albeitnatural framework for the preprocessing (offline) phase that is used to generate sharings of random multiplica-tion triples, to be used later for the circuit evaluation. The framework is built on two new components, both ofwhich are instantiated robustly: the first component allows the parties to verifiably share random multiplicationtriples. The second component allows the parties to securely extract sharings of random multiplication triplesfrom a set of sharings of multiplication triples, verifiably shared by individual parties. Our framework is simpleand does not involve either of the existing somewhat complex, but popular techniques, namely player elimina-tion and dispute control, used in the preprocessing phase of most of the existing protocols. The framework is ofindependent interest and can be adapted to other MPC scenarios to improve the overall round complexity. ∗Department of Computer Science, University of Bristol, UK, Email: [email protected].†Department of Computer Science, ETH Zurich, Switzerland, Email: [email protected]‡Department of Computer Science, University of Bristol, UK, Email: [email protected].