Cryptology ePrint Archive: Report 2010/040

Batch Groth-Sahai

Olivier Blazy and Georg Fuchsbauer and Malika Izabachène and Amandine Jambert and Hervé Sibert and Damien Vergnaud

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).

Category / Keywords: cryptographic protocols / Pairing-based cryptography, Batch verification, Groth-Sahai proof system

Date: received 26 Jan 2010, last revised 3 Feb 2010

Contact author: damien vergnaud at ens fr

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Version: 20100203:155316 (All versions of this report)

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