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Is the Lemma4.5 in the Plonk paper correctly described?

za flag

In lemma4.5, of PlonK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge they claim that we can construct a polynomial protocol $P^*$ with an $S$-ranged polynomial protocol $P$. However, in my opinion, I think it constructed $P$ using $P^*$ in the proof.

Specifically, in the last step of the construction, the verifier queries the identity of a polynomial(not in a range $S$), so it is invoking a polynomial protocol to construct an S-ranged polynomial protocol, not the opposite. In the construction of the proof of lemma4.5, I think the prover can prove that $F_i(x)$ equals $0$ in range $S$.

Can anyone explain if my thoughts are right? Thanks.

kodlu avatar
sa flag
Please provide a link and a mathematical description of your exact question.
et flag
Why do you say verifier queries "not in Range S"? The final step is to prove that the polynomial is 0 in the subgroup.
mactep Cheng avatar
za flag
https://eprint.iacr.org/2019/953.pdf
mactep Cheng avatar
za flag
The verifier queries that the polynomial equals 0 in any situation to ensure F_i(x) is 0 in the subgroup.
mactep Cheng avatar
za flag
thank @kelalaka for editing this question!
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