International Association
for Cryptologic Research

We establish new results on the Fiat-Shamir (FS) security of several protocols that are widely used in practice, and we provide general tools for establishing similar results for others. More precisely, we: (1) prove the FS security of the FRI and batched FRI protocols; (2) analyze a general class of protocols, which we call \emph{$\delta$-correlated}, that use low-degree proximity testing as a subroutine (this includes many ``Plonk-like'' protocols (e.g., Plonky2 and Redshift), ethSTARK, RISC Zero, etc.); and (3) prove FS security of the aforementioned ``Plonk-like'' protocols, and sketch how to prove the same for the others. We obtain our first result by analyzing the round-by-round (RBR) soundness and RBR knowledge soundness of FRI. For the second result, we prove that if a $\delta$-correlated protocol is RBR (knowledge) sound under the assumption that adversaries always send low-degree polynomials, then it is RBR (knowledge) sound in general. Equipped with this tool, we prove our third result by formally showing that ``Plonk-like'' protocols are RBR (knowledge) sound under the assumption that adversaries always send low-degree polynomials. We then outline analogous arguments for the remainder of the aforementioned protocols. To the best of our knowledge, ours is the first formal analysis of the Fiat-Shamir security of FRI and widely deployed protocols that invoke it.