Paper 2024/1571 Original: eprint.iacr.org/2024/1571 ↗
Basefold in the List Decoding Regime
Abstract
In this document 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 a row-batched version of FRI-Binius [Diamond, Posen 24] and WHIR [Arnon, Chiesa, Fenzi, Yogev 24] in the list-decoding regime.
Metadata
- Available format(s)
PDF- Category
- Cryptographic protocols
- Publication info
- Preprint.
- History
- 2025-09-04: last updated
- 2024-10-05: published
- Short URL
- https://ia.cr/2024/1571
- License
- https://creativecommons.org/licenses/by-sa/4.0/
BibTeX
@misc{cryptoeprint:2024/1571,
author = {Ulrich Haböck},
title = {Basefold in the List Decoding Regime},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/1571},
year = {2024},
url = {https://eprint.iacr.org/2024/1571}
}