Efficient Short Adaptive NIZK for NP

In Eurocrypt 2013, Gennaro et al. proposed an efficient non-adaptive short QAP-based NIZK argument for Circuit-SAT, where non-adaptivity means that the CRS depends on the statement to be proven. While their argument can be made adaptive by using universal circuits, this increases the prover computation by a logarithmic multiplicative factor. By following the QAP-based approach, we propose an efficient product argument, and then use it together with a modified shift argument of Fauzi et al. in the modular framework of Groth to design an adaptive short NIZK argument for Subset-Sum and several other NP-complete languages that has the same complexity parameters as the QAP-based non-adaptive argument, resulting in the first adaptive short NIZK arguments for NP where the prover computation is dominated by a linear number of cryptographic operations. We also construct the most efficient known range argument.