Batch Groth-Sahai

Abstract : In 2008, Groth and Sahai proposed a general methodology for constructing non-interactive zero-knowledge (and witness-indistinguishable) proofs in bilinear groups. While avoiding expensive NP-reductions, these proof systems are still inefficient due to a number of pairing computations required for verification. We apply recent techniques of batch verification to the Groth-Sahai proof systems and manage to improve significantly the complexity of proof verification. We give explicit batch verification formulas for generic Groth-Sahai equations (whose cost is less than a tenth of the original) and also for specific popular protocols relying on their methodology (namely Groth's group signatures and Belenkiy-Chase-Kohlweiss-Lysyanskaya's P-signatures).