Hybrid zero-knowledge from garbled circuits

We present techniques for constructing zero-knowledge argument systems from garbled circuits, extending the GC-to-ZK compiler by Jawurek Et al. (2013) and the GC-to- $$\varSigma $$ compiler by Hazay and Venkitasubramaniam (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 $$\varSigma $$ -protocols that support attractive access structures, such as weighted thresholds, that can be easily represented by a small circuit. For predicates $$P_1,\dots ,P_n$$ individually associated with a $$\varSigma $$ -protocol, and a predicate C represented by a Boolean circuit, we construct a $$\varSigma $$ -protocol for proving $$C(P_1,\dots ,P_n)$$ = 1. This result answers positively an open question posed by Abe, et. al. (2021).