Paper 2020/1337

Multiplicative Depth Independent & Efficient MPC in the Presence of Mixed Adversary

Achintya Desai, Shubham Raj, and Kannan Srinathan

Abstract

An extensive research of MPC protocols in different adversarial settings over the past few years has led to various improvements. Goyal et al.\cite{goyal2019communication} in their paper addressed the issue of an efficient MPC protocol in active adversarial setting by removing the dependency on multiplication depth $D_m$ in the arithmetic circuit. This development was followed by Hirt et al. in ITC 2020, which proposed an efficient MPC protocol tolerating mixed adversary with communication complexity of $O((c_i+c_m+c_o)n\kappa +c_{i}BA(\kappa )+D_m(n^3\kappa +nBA(\kappa )))$ bits, where $D_m$ is the multiplicative depth of the circuit and $\kappa$ is the size of an element in the field. Additionally, Hirt et al.\cite{hirt2020efficient}, proposed an open problem to construct a protocol for the mixed adversarial setting, independent of the multiplicative depth $$, with linear communication complexity. In this paper, we resolve this problem in the affirmative by providing an efficient MPC protocol in the mixed adversarial setting independent of the multiplicative depth of the circuit.

Note: Revised with proof