Abstract
Groth-Sahai proofs are efficient non-interactive zero-knowledge proofs that have found widespread use in pairing-based cryptography. We propose efficiency improvements of Groth-Sahai proofs in the SXDH setting, which is the one that yields the most efficient non-interactive zero-knowledge proofs.
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We replace some of the commitments with ElGamal encryptions, which reduces the prover’s computation and for some types of equations reduces the proof size.
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Groth-Sahai proofs are zero-knowledge when no public elements are paired to each other. We observe that they are also zero-knowledge when base elements for the groups are paired to public constants.
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The prover’s computation can be reduced by letting her pick her own common reference string. By giving a proof she has picked a valid common reference string this does not compromise soundness.
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We define a type-based commit-and-prove scheme, which allows commitments to be reused in many different proofs.
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Escala, A., Groth, J. (2014). Fine-Tuning Groth-Sahai Proofs. In: Krawczyk, H. (eds) Public-Key Cryptography – PKC 2014. PKC 2014. Lecture Notes in Computer Science, vol 8383. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54631-0_36
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