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I'm writing my thesis about Zero-Knowledge Proofs and I'm trying to write a short and instructive introduction to zk-SNARKs at the moment (I have to stay within a certain limit of pages).

I introduced the general paradigm that SNARKs are often constructed as the combination of polynomial commitments and polynomial interactive oracle proofs (IOP's) and then rendered non-interactive using Fiat-Shamir.

I want to give a simple example for both polynomial IOP's and commitment schemes. Ideally they should be somewhat compatible to make it obvious to the reader how the combination of these techniques satisfies all the properties a ZK-SNARK must have.

So far I introduced Pedersen commitments and I'm considering which polynomial IOP I should use. In my opinion the most instructive and short protocol to use would be the simple equality test of two committed polynomials using the Schwartz-Zippel Lemma, because it shows why polynomials are so useful for SNARKs.

Can this be considered as an IOP? If not are there any protocols you would recommend?

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  • $\begingroup$ To make your questions more readable I would suggest using two line-endings and split the text in paragraphs, separating the question at the very least. Just adding a single line ending will result in the same MarkDown rendering, i.e. it is only useful to people looking at the source. Please use caps for names and a spell checker. $\endgroup$
    – Maarten Bodewes ♦
    Commented Aug 29 at 12:39

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