Paper 2026/2444
Extending the Schur--Macaulay Framework for UOV Attacks via Truncated Polynomial Algebras
Abstract
Building on the wedge-attack framework of Ding, Li, and Tao , we reformulate the Schur-Macaulay matrix approach of Merz and Ran in polynomial terms and develop a unified treatment using truncated polynomial algebras over fields of positive characteristic $p$. By working in $p$-truncated polynomial algebras, our formulation applies to the Unbalanced Oil and Vinegar (UOV) problem over arbitrary finite fields. Divided powers and transfer relations yield additional public relations within the ideal-inclusion framework, leading to quotient-dimension criteria for recovering graded components of the hidden oil-space ideal. As an application, we analyze the third-round QR-UOV parameter sets and obtain lower estimates of attack complexity for some of them.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- UOV problem; divided powers; derivation
- Contact author(s)
-
lpg22 @ bimsa cn
taosy22 @ mails tsinghua edu cn - History
- 2026-10-14: approved
- 2026-10-11: received
- See all versions
- Short URL
- https://ia.cr/2026/2444
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2026/2444,
author = {Peigen Li and Siyong Tao},
title = {Extending the Schur--Macaulay Framework for {UOV} Attacks via Truncated Polynomial Algebras},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2444},
year = {2026},
url = {https://eprint.iacr.org/2026/2444}
}
