Escala, A; Groth, J; (2014) Fine-Tuning Groth-Sahai Proofs. In: Krawczyk, H, (ed.) Public-Key Cryptography – PKC 2014. 17th International Conference on Practice and Theory in Public-Key Cryptography, Buenos Aires, Argentina, March 26-28, 2014. Proceedings. (pp. pp. 630-649). Springer Berlin Heidelberg

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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. --- 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. --- 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. --- 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. --- We define a type-based commit-and-prove scheme, which allows commitments to be reused in many different proofs.

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