Batch Groth-Sahai

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 NPreductions, these proof systems are still inefficient due to the number of pairing computations required for verification. We apply recent techniques of batch verification to the Groth-Sahai proof systems and succeed 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) as well as for specific popular protocols relying on their methodology (namely Groth’s group signatures and the P-signatures by Belenkiy, Chase, Kohlweiss and Lysyanskaya).