The noninteractive zero-knowledge proof (NIZKP) is underlying a broad spectrum of applications. The major categories of NIZKP are instantiated with deterministic hash functions in the real world. However, the outputs of deterministic hash ...Zero-knowledge proof (ZKP) is a fundamental cryptographic primitive that allows a prover to convince a verifier of the validity of a statement without leaking any further information. As an efficient variant of ZKP, noninteractive zero-knowledge proof (...