Paper 2025/932 Original: eprint.iacr.org/2025/932 ↗
Integral cryptanalysis in characteristic $p$
Abstract
Integral and ultrametric integral cryptanalysis are generalized to finite rings of prime characteristic $p$ that are isomorphic to a product of fields. This extends, for instance, the complete state of the art in integral cryptanalysis from $\mathbf{F}_2^n$ to $\mathbf{F}_q^n$, for all prime powers $q$. A compact representation of transition matrices, based on convex polyhedra, is introduced to ensure that the proposed methods are computationally efficient even for large $p$. Automated tools are developed and applied to a few generic and several concrete primitives. The analysis shows that previous degree estimates for Feistel-GMiMC, HadesMiMC, AES-Prime, small-pSquare and mid-pSquare are overly optimistic. Furthermore, except for AES-Prime, these primitives do not meet their design criteria unless their number of rounds is substantially increased.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2025-08-26: last updated
- 2025-05-22: published
- Short URL
- https://ia.cr/2025/932
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2025/932,
author = {Tim Beyne and Michiel Verbauwhede},
title = {Integral cryptanalysis in characteristic $p$},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/932},
year = {2025},
url = {https://eprint.iacr.org/2025/932}
}