Robust Publicly Verifiable Covert Security: Limited Information Leakage and Guaranteed Correctness with Low Overhead

Abstract

Protocols with \emph{publicly verifiable covert (PVC) security} offer high efficiency and an appealing feature: a covert party may deviate from the protocol, but with a probability (\eg $90\%$, referred to as the \emph{deterrence factor}), the honest party can identify this deviation and expose it using a publicly verifiable certificate. These protocols are particularly suitable for practical applications involving reputation-conscious parties. However, in the cases where misbehavior goes undetected (\eg with a probability of $10\%$), \emph{no security guarantee is provided for the honest party}, potentially resulting in a complete loss of input privacy and output correctness. In this paper, we tackle this critical problem by presenting a highly effective solution. We introduce and formally define an enhanced notion called \emph{robust PVC security}, such that even if the misbehavior remains undetected, the malicious party can only gain an additional $1$-bit of information about the honest party\u27s input while maintaining the correctness of the output. We propose a novel approach leveraging \emph{dual execution} and \emph{time-lock puzzles} to design a robust PVC-secure two-party protocol with \emph{low overhead} (depending on the deterrence factor). For instance, with a deterrence factor of $90\%$, our robust PVC-secure protocol incurs \emph{only additional ${\sim}10\%$ overhead} compared to the state-of-the-art PVC-secure protocol. Given the stronger security guarantees with low overhead, our protocol is highly suitable for practical applications of secure two-party computation