Hybrid Zero-Knowledge from Garbled Circuits and Circuit-Based Composition of  \(\Sigma \) -Protocols

We present techniques for constructing zero-knowledge argument systems from garbled circuits, extending a theoretical framework by Hazay and Venkitasubramaniam (J. Crypto, 2020) to the following directions: The above result is then applied to develop circuit-represented compositions of \(\Sigma \) -protocols. For predicates \(P_1,\dots ,P_n\) individually associated with a \(\Sigma \) -protocol, and a predicate C represented by a Boolean circuit, we construct a \(\Sigma \) -protocol for proving \(C(P_1,\dots ,P_n)\) = 1. This result answers positively an open question posed by Abe, et al., at TCC 2021.