[Resource Topic] 2020/1337: Multiplicative Depth Independent & Efficient MPC in the Presence of Mixed Adversary

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

Authors: Achintya Desai, Shubham Raj, 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_iBA(\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 D_m, 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.

ePrint: https://eprint.iacr.org/2020/1337

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