International Association for Cryptologic Research (IACR)
Abstract
While NIZK arguments in the CRS model are widely studied, the question of what happens when the CRS was subverted has received little attention. In ASIACRYPT 2016, Bellare, Fuchsbauer, and Scafuro showed the first negative and positive results in the case of NIZK, 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 subversion-zero-knowledge (Sub-ZK) non-succinct NIZK argument for NP. We consider the practically very relevant case of zk-SNARKs. We make Groth\u27s zk-SNARK for \textsc{Circuit-SAT} from EUROCRYPT 2016 computationally knowledge-sound and perfectly composable Sub-ZK with minimal changes. We only 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 knowledge-sound and Sub-ZK SNARKs
