Abstract: The present disclosure provides a method for generating and verifying a non-interactive zero-knowledge proof with subversion zero-knowledge security against malicious common reference strings. The method includes providing a non-interactive zero-knowledge proof system with subversion zero-knowledge security, generating and verifying the proof using a combination of a provided non-interactive zero-knowledge proof system, a delayed-input two-message publicly-verifiable S-notion zero-knowledge argument system, and a non-interactive perfectly binding and T-extractable commitment scheme. The method further includes generating a common reference string, generating a proof, and verifying the proof for an outer NIZK system. The system comprises generating an inner common reference string, computing a first message, computing a second message, committing to the second message, computing an inner proof, and verifying the inner proof using an inner NIZK system.