Paper 2025/1839 Original: eprint.iacr.org/2025/1839 ↗

Lattice-Based zk-SNARKs with Hybrid Verification Technique

Abstract

Zero-knowledge succinct arguments of knowledge (zkSNARK) provide short privacy-preserving proofs for general NP problems. Public verifiability of zkSNARK protocols is a desirable property, where the proof can be verified by anyone once generated. Designated-verifier zero-knowledge is useful when it is necessary that only one or a few individuals should have access to the verification result. All zkSNARK schemes are either fully publicly verifiable or can be verified by a designated verifier with a secret verification key. In this work, we propose a new notion of a hybrid verification mechanism. Here, the prover generates a proof that can be verified by a designated verifier. For this proof, the designated verifier can generate auxiliary information with its secret key. The combination of this proof and the auxiliary information allows any public verifier to verify the proof without any other information. We also introduce necessary security notions and mechanisms to identify a cheating designated verifier or the prover. Our hybrid verification zkSNARK construction is based on module lattices and adapts the zkSNARK construction by Ishai et al. (CCS 2021). In this construction, the designated verifier is required only once after proof generation to create the publicly verifiable proof. Our construction achieves a small constant-size proof and fast verification time, which is linear in the statement size.