An Efficient Transform from Sigma Protocols to NIZK with a CRS and Non-programmable Random Oracle

In this short paper, we present a Fiat-Shamir type transform that takes any Sigma protocol for a relation R and outputs a non-interactive zero-knowledge proof (not of knowledge) for the associated language LR, in the common reference string model. As in the Fiat-Shamir transform, we use a hash function H. However, zero-knowledge is achieved under standard assumptions in the common reference string model (without any random oracle), and soundness is achieved in the non-programmable random oracle model. The concrete computational complexity of the transform is only slightly higher than the original Fiat-Shamir transform.