Paper 2021/1689
Proof of a conjecture on a special class of matrices over commutative rings of characteristic 2
Baofeng Wu
Abstract
In this note, we prove the conjecture posed by Keller and Rosemarin at Eurocrypt 2021 on the nullity of a matrix polynomial of a block matrix with Hadamard type blocks over commutative rings of characteristic 2. Therefore, it confirms the conjectural optimal bound on the dimension of invariant subspace of the Starkad cipher using the HADES design strategy. We also give characterizations of the algebraic structure formed by Hadamard matrices over commutative rings.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Hadamard matrixblock matrixCharacteristic polynomialCayley–Hamilton theorem
- Contact author(s)
- wubaofeng @ iie ac cn
- History
- 2021-12-30: received
- Short URL
- https://ia.cr/2021/1689
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/1689,
author = {Baofeng Wu},
title = {Proof of a conjecture on a special class of matrices over commutative rings of characteristic 2},
howpublished = {Cryptology ePrint Archive, Paper 2021/1689},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/1689}},
url = {https://eprint.iacr.org/2021/1689}
}
