Shorter Quasi-Adaptive NIZK Proofs for Linear Subspaces
The authors define a novel notion of quasi-adaptive Non-Interactive Zero Knowledge (NIZK) proofs for probability distributions on parametrized languages. It is quasi-adaptive in the sense that the Common Reference String (CRS) generator can generate the CRS depending on the language parameters. However, the simulation is required to be uniform, i.e., a single efficient simulator should work for the whole class of parametrized languages. For distributions on languages that are linear subspaces of vector spaces over bilinear groups, they give quasi-adaptive computationally sound NIZKs that are shorter and more efficient than Groth-Sahai NIZKs.