Linear Overhead Optimally-Resilient Robust MPC Using Preprocessing

We present a new technique for robust secret reconstruction with $$\mathcal {O}n$$ communication complexity. By applying this technique, we achieve $$\mathcal {O}n$$ communication complexity per multiplication for a wide class of robust practical Multi-Party Computation MPC protocols. In particular our technique applies to robust threshold computationally secure protocols in the case of $$t<n/2$$ in the pre-processing model. Previously in the pre-processing model, $$\mathcal {O}n$$ communication complexity per multiplication was only known in the case of computationally secure non-robust protocols in the dishonest majority setting i.e. with $$t<n$$ and in the case of perfectly-secure robust protocols with $$t<n/3$$. A similar protocol was sketched by Damgard and Nielsen, but no details were given to enable an estimate of the communication complexity. Surprisingly our robust reconstruction protocol applies for both the synchronous and asynchronous settings.