Non-Interactive Zero-Knowledge Functional Proofs

Gongxian Zeng, Junzuo Lai, Zhengan Huang, Linru Zhang, Xiangning Wang, Kwok-Yan Lam, Huaxiong Wang, Jian Weng

Abstract: In this paper, we consider to generalize NIZK by empowering a prover to share a witness in a fine-grained manner with verifiers. Roughly, the prover is able to authorize a verifier to obtain extra information of witness, i.e., besides verifying the truth of the statement, the verifier can additionally obtain certain function of the witness from the accepting proof using a secret functional key provided by the prover. To fulfill these requirements, we introduce a new primitive called \emph{non-interactive zero-knowledge functional proofs (fNIZKs)}, and formalize its security notions. We provide a generic construction of fNIZK for any $\textsf{NP}$ relation $\mathcal{R}$, which enables the prover to share any function of the witness with a verifier. For a widely-used relation about set membership proof (implying range proof), we construct a concrete and efficient fNIZK, through new building blocks (set membership encryption and dual inner-product encryption), which might be of independent interest.