Paper 2026/1393
On the Differential Uniformity of Polynomials over Galois Rings
, University of Bergen, Nasjonal sikkerhetsmyndighetAbstract
Design of hash functions and pseudo-random permutations over Galois extensions of $\mathbb Z_q$ for prime powers $q$ has recently gained some interest in relation to recent directions in advanced cryptography, such as multiparty computation and zero-knowledge protocol design. Thus investigating optimality of cryptographic properties of S-boxes defined by polynomials over Galois rings is of interest. Of particular interest is the differential uniformity of such functions. To our knowledge, there are very few results on the differential uniformity for polynomials over Galois rings $\mathrm{GR}(p^k,m)$ when $k,m\geq 2$. Motivated by designing secure hash functions and block ciphers over Galois rings, a main contribution of this paper is an investigation into the differential properties of polynomials over Galois rings. Finally, we provide a classification of APN permutations in $\mathrm{GR}(4,2)$ up to affine and CCZ-equivalence.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Published elsewhere. Minor revision. https://link.springer.com/article/10.1007/s12095-026-00895-x
- DOI
- 10.1007/s12095-026-00895-x
- Keywords
- differential uniformityGalois ringsdifferential cryptanalysisAPN permutations
- Contact author(s)
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sondre ronjom @ uib no
arne sandrib @ student uib no - History
- 2026-07-12: approved
- 2026-07-08: received
- See all versions
- Short URL
- https://ia.cr/2026/1393
- License
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CC BY
BibTeX
@misc{cryptoeprint:2026/1393,
author = {Sondre Rønjom and Arne Sandrib},
title = {On the Differential Uniformity of Polynomials over Galois Rings},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1393},
year = {2026},
doi = {10.1007/s12095-026-00895-x},
url = {https://eprint.iacr.org/2026/1393}
}
