[Resource Topic] 2024/1571: Basefold in the List Decoding Regime

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Title:
Basefold in the List Decoding Regime

Authors: Ulrich Haböck

Abstract:

In this writeup we discuss the soundness of the Basefold multilinear polynomial commitment scheme [Zeilberger, Chen, Fisch 23] applied to Reed-Solomon codes, and run with proximity parameters up to the Johnson list decoding bound.
Our security analysis relies on a generalization of the celebrated correlated agreement theorem from [Ben-Sasson, et al., 20] to linear subcodes of Reed-Solomon codes, which turns out a by-product of the Guruswami-Sudan list decoder analysis.
We further highlight a non-linear variant of the subcode correlated
agreement theorem, which is flexible enough to apply to Basefold-like protocols such as recent optimizations of FRI-Binius [Diamond, Posen 24], and which we believe sufficient for proving the security of a recent multilinear version of STIR [Arnon, Chiesa, Fenzi, Yogev 24] in the list-decoding regime

ePrint: https://eprint.iacr.org/2024/1571

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