We introduce a novel concept of dual-system simulation-sound non-interactive zero-knowledge (NIZK) proofs. Dual-system NIZK proof system can be seen as a two-tier proof system. As opposed to the usual notion of zero-knowledge proofs, dual-system defines an intermediate partialsimulation world, where the proof simulator may have access to additional auxiliary information about the potential language member, for example a membership bit, and simulation of proofs is only guaranteed if the membership bit is correct. Further, dual-system NIZK proofs allow a quasi-adaptive setting where the CRS can be generated based on language parameters. This allows for the further possibility that the partial-world CRS simulator may have access to additional trapdoors related to the language parameters. We show that for important hard languages like the Diffie-Hellman language, such dual-system proof systems can be given which allow unbounded partial simulation soundness, and which further allow transi...
Charanjit S. Jutla, Arnab Roy 0003