Paper 2026/1787 Original: eprint.iacr.org/2026/1787 ↗
A Practical Optimization for Wiedemann XL
Abstract
Wiedemann XL is a variant of the XL algorithm that has been widely used in algebraic attacks. Usually, the cost of applying Widemann XL is estimated as 3N^2 ω, where N is the width of the Macaulay matrix, and ω is the average row weight of the Macaulay matrix. Among 3N^2 ω, 2N^2 ω is from the 1st phase of the algorithm, while N^2 ω is from the 3rd phase of the algorithm. This paper shows a practical optimization that reduces the cost of the 3rd phase by a huge factor so that its cost becomes essentially negligible compared to that of the 1st phase. Our optimization makes use of the fact that, to obtain a solution of the multivariate system, only a few coordinates of the kernel vectors are needed.
Metadata
- Available format(s)
PDF- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- History
- 2026-09-01: last updated
- 2026-08-24: published
- Short URL
- https://ia.cr/2026/1787
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2026/1787,
author = {Tung Chou and Ruben Niederhagen},
title = {A Practical Optimization for Wiedemann XL},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1787},
year = {2026},
url = {https://eprint.iacr.org/2026/1787}
}