Batch Groth-Sahai

Abstract. In 2008, Groth and Sahai proposed a general methodology for constructing non-interactive zeroknowledge (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). Keywords. Pairing-based cryptography, Batch verification, Groth-Sahai proof system.

• Type: Conference
• Year: 2010
• Where: ACNS
• Authors: Olivier Blazy, Georg Fuchsbauer, Malika Izabachène, Amandine Jambert, Hervé Sibert, Damien Vergnaud
• Keywords: ACNS 2010, Batch Verification, Cryptology, Groth-sahai Proof System, Proof System