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 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).
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Blazy, O., Fuchsbauer, G., Izabachène, M., Jambert, A., Sibert, H., Vergnaud, D. (2010). Batch Groth–Sahai. In: Zhou, J., Yung, M. (eds) Applied Cryptography and Network Security. ACNS 2010. Lecture Notes in Computer Science, vol 6123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13708-2_14
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