Block, A. R., Garreta, A., Katz, J., Thaler, J., Tiwari, P. R., & Zajac, M. (2023). Fiat-shamir security of fri and related snarks. Cryptology ePrint Archive,
Added by: Jack (2023-07-29 03:04) Last edited by: Jack (2023-07-29 03:05)
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Abstract
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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 𝛿-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 𝛿-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.
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