### 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.

Available format(s)
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Contact author(s)
wubaofeng @ iie ac cn
History
Short URL
https://ia.cr/2021/1689

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}
}

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