A Subversion-Resistant SNARK

摘要

While zk-SNARKs are widely studied, the question of what happens when the CRS has been subverted has received little attention. In ASIACRYPT 2016, Bellare, Fuchsbauer and Scafuro showed the first negative and positive results in this direction, proving also that it is impossible to achieve subversion soundness and (even non-subversion) zero knowledge at the same time. On the positive side, they constructed an involved sound and Sub-ZK argument system for NP. We make Groth's zk-SNARK for CIRCUIT-SAT from EUROCRYPT 2016 computationally knowledge-sound and perfectly composable Sub-ZK with minimal changes. We just require the CRS trapdoor to be extractable and the CRS to be publicly verifiable. To achieve the latter, we add some new elements to the CRS and construct an efficient CRS verification algorithm. We also provide a definitional framework for sound and Sub-ZK SNARKs and describe implementation results of the new Sub-ZK SNARK.