Low Cost Constant Round MPC Combining BMR and Oblivious Transfer

In this work, we present two new universally composable, actively secure, constant round multi-party protocols for generating BMR garbled circuits with free-XOR and reduced costs.

(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 specialized protocol uses secret-sharing based MPC with information-theoretic MACs. This approach is less general, but requires no additional correlated OTs to compute the garbled circuit.

In both approaches, the underlying secret-sharing based protocol is only used for one secure F2F2 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 experiments with up to 99 parties securely computing the AES and SHA-256 circuits. Our running times improve upon the best possible performance with previous BMR-based protocols by 60 times.