Low cost constant round MPC combining BMR and oblivious transfer

Abstract

In this work, we present two new actively secure, constant round multi-party computation (MPC)protocols with security against all-but-one corruptions. Our protocols both start with an actively secure MPC protocol, which may have linear round complexity in the depth of the circuit, and compile it into a constant round protocol based on garbled circuits, with very low overhead.

1. Our first protocol takes a generic approach using any secret-sharing-based MPC protocol for binary circuits, and a correlated oblivious transfer functionality.
2. Our second protocol builds on secret-sharing-based MPC with information-theoretic MACs. This approach is less flexible, being based on a specific form of MPC, but requires no additional oblivious transfers to compute the garbled circuit.

In both approaches, the underlying secret-sharing-based protocol is only used for one actively secure $F_2$ multiplication per AND gate. An interesting consequence of this is that, with current techniques,constant round MPC for binary circuits is not much more expensive than practical, non-constant round protocols.

We demonstrate the practicality of our second protocol with an implementation, and perform ex-periments with up to 9 parties securely computing the AES and SHA-256 circuits. Our running times improve upon the best possible performance with previous protocols in this setting by 60 times.

This paper was accepted to the Journal of Cryptology.