Shorter Non-Interactive Zero-Knowledge Arguments and ZAPs for Algebraic Languages.

We put forth a new framework for building pairing-based non-interactive zero-knowledge (\\(\\mathsf {NIZK}\\)) arguments for a wide class of algebraic languages, which are an extension of linear languages, containing disjunctions of linear languages and more. Our approach differs from the Groth-Sahai methodology, in that we rely on pairings to compile a \\(\\varSigma \\)-protocol into a \\(\\mathsf {NIZK}\\). Our framework enjoys a number of interesting features:\r\n\r\n\r\nconceptual simplicity, parameters derive from the \\(\\varSigma \\)-protocol;\r\n\r\n\r\nproofs as short as resulting from the Fiat-Shamir heuristic applied to the underlying \\(\\varSigma \\)-protocol;\r\n\r\n\r\nfully adaptive soundness and perfect zero-knowledge in the common random string model with a single random group element as CRS;\r\n\r\n\r\nyields simple and efficient two-round, public coin, publicly-verifiable perfect witness-indistinguishable (WI) arguments(ZAPs) in the plain model. To our knowledge, this is the first construction of two-rounds statistical witness-indistinguishable arguments from pairing assumptions.