International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Batch Groth-Sahai

Olivier Blazy
Georg Fuchsbauer
Malika Izabachène
Amandine Jambert
Hervé Sibert
Damien Vergnaud
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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).
  title={Batch Groth-Sahai},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols / Pairing-based cryptography, Batch verification, Groth-Sahai proof system},
  note={ 14643 received 26 Jan 2010, last revised 3 Feb 2010},
  author={Olivier Blazy and Georg Fuchsbauer and Malika Izabachène and Amandine Jambert and Hervé Sibert and Damien Vergnaud},