Vitalik says making ZK proofs ‘understandable’ is necessary for Ethereum

Making zero-knowledge proofs (ZKPs) “understandable and accessible” to people is necessary to keep the Ethereum ecosystem “open and welcoming” to people without a mathematics degree, Ethereum co-founder Vitalik Buterin tweeted Oct 26.

ZKPs are often referred to as “moon math” because of their complexity.

I’m so happy that Ethereum has such a strong culture of trying hard to make all our moon math as understandable and accessible to people as possible. https://t.co/o9n2Xms4Zw

— vitalik.eth (@VitalikButerin) October 26, 2022

Buterin added that “Decentralization requires NOT giving up and waving a PhD around saying “it’s a black box, we’re smart, trust us”.”

Scroll, a zero-knowledge layer 2 Ethereum scaling solution, explained in a blog how polynomial commitment schemes, a critical part of several ZKPs, work and how they can help scale Ethereum.

Polynomials are mathematical expressions that represent more than two algebraic terms. According to the Scroll blog, polynomials can help represent large data efficiently.

A commitment scheme is a cryptographic protocol in which one commits to a message and keeps it hidden but can reveal the message later. However, the committer cannot change the message once he has committed to it, which makes commitment schemes binding.

In a polynomial commitment scheme, one commits to a polynomial instead of a message. The polynomial commitment scheme meets all the properties of normal commitment schemes. But it has an additional feature that enables the committer to prove that he committed to a certain polynomial that satisfies the required properties without revealing the polynomial itself.

KZG in Scaling Ethereum

While there are different polynomial commitment schemes, Kate-Zaverucha-Goldberg (KZG) is popular in the blockchain space and is used by Scroll’s proof systems. KZG is also due to be integrated into Ethereum with Proto-Danksharding, to be implemented through EIP-4844, which was proposed in February…