Non Interactive Zero Knowledge Proof
The Non Interactive Zero Knowledge Proof referred as to NIZK prove the statement without revealing any information about the statement. There are some types of NIZK for example SNORKs, STARKs and so on. In this section, we describe the SNARKs and especially Pinocchio Protocol. It's a little bit complicated technology so I divide into three parts.
Abstract
The SNARKs converts the computation problems into the polynomial equations. We can not only hide the computation itself but also verify the computation faster than compute it again. That's why the SNARKs is also used for scaling solution for example zk rollup.
Detail
The SNARKs has three steps.
Converting computation which we want to prove without revealing additional information into polynomial equations. In Pinocchio Protocol, we need to generate polynonial equations for each computation. The polynomial equations are decided for corresponding computation.
Hiding the secret as polynomial coefficients, opening with evaluating that polynomials at point, and we can prove the computation was done correctly.
The polynomial coefficients are encrypted to keep the secret so we need perform evaluation with remaining encrypted. The Homomorphic Encryption can perform the multiple time addition and one time multiplication for encrypted number using elliptic curve and pairing.