KZG_polynomial_commitment_scheme

Zero knowledge proofs have garnered an air of mystery around them, due to their mathematical complexity. They are affectionately referred to as “moon math,” as they are seen by most as otherworldly magic.

最近在看SNARK的一些内容，KZG作为一种十分经典的polynomial commitment scheme当然避免不了要仔细研读一下，这篇博客就先记录一下他的组成（12.18），后面抽时间仔细研读一下论文再完善一下。

Introduction

A polynomial commitment scheme is a commitment scheme with some nice additional properties. In a general commitment scheme, the committer commits to a message \(m\) by outputting some commitment \(c\). The committer can then later reveal the message \(m\), and a verifier can validate that indeed the commitment \(c\) corresponds to \(m\).

A commitment scheme should be "binding" (once publishing \(c\), the committer should not be able to find some other message \(m\) ' \(\neq m\) which also corresponds to \(c\) ) and "hiding" (publishing \(c\) should not reveal any information about the underlying message \(m\) ).