Composition with Knowledge Assumptions

Zero-knowledge succinct non-interactive arguments (zk-SNARKs) rely on knowledge assumptions for their security. Meanwhile, as the complexity and scale of cryptographic systems continues to grow, composition secure protocols is vital importance. The current gold standards composable security, Universal Composability Constructive Cryptography frameworks cannot capture assumptions, core proofs prohibit white-box extraction. In this paper, we present a formal model allowing assumptions. Despite showing impossibility general case, demonstrate model’s usefulness when limiting few instances at time. We finish by providing first instance simultaneously zk-SNARK, using existing results within our framework.