Fine-Tuning Groth-Sahai Proofs

Abstract

Abstract. Groth-Sahai proofs are efficient non-interactive zero-knowledge proofs that have found widespread use in pairingbased 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.