Paper 2010/040

Batch Groth-Sahai

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


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).

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Cryptographic protocols
Publication info
Published elsewhere. Unknown where it was published
Pairing-based cryptographyBatch verificationGroth-Sahai proof system
Contact author(s)
damien vergnaud @ ens fr
2010-02-03: last of 2 revisions
2010-01-29: received
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      author = {Olivier Blazy and Georg Fuchsbauer and Malika Izabachène and Amandine Jambert and Hervé Sibert and Damien Vergnaud},
      title = {Batch Groth-Sahai},
      howpublished = {Cryptology ePrint Archive, Paper 2010/040},
      year = {2010},
      note = {\url{}},
      url = {}
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