Paper 2024/1835

Hybrid Zero-Knowledge from Garbled Circuits

Abstract

We present techniques for constructing zero-knowledge argument systems from garbled circuits, extending the GC-to-ZK compiler by Jawurek, Kerschbaum, and Orlandi (ACM CCS 2023) and the GC-to-Σ compiler by Hazay and Venkitasubramaniam (J. Crypto, 2020) to the following directions: - Our schemes are hybrid, commit-and-prove zero-knowledge argument systems that establish a connection between secrets embedded in algebraic commitments and a relation represented by a Boolean circuit. - Our schemes incorporate diverse cross-domain secrets embedded within distinct algebraic commitments, simultaneously supporting Pedersen-like commitments and lattice-based commitments. As an application, we develop circuit-represented compositions of Σ-protocols that support attractive access structures, such as weighted thresholds, that can be easily represented by a small circuit. For predicates P1, . . . , Pn individually associated with a Σ-protocol, and a predicate C represented by a Boolean circuit, we construct a Σ-protocol for proving C(P1, . . . , Pn) = 1. This result answers positively an open question posed by Abe, et. al., at TCC 2021.