## Cryptology ePrint Archive: Report 2021/075

A Generalization of the Subfield Construction

Kamil Otal

Abstract: The subfield construction is one of the most promising methods to construct maximum distance separable (MDS) diffusion layers for block ciphers and cryptographic hash functions. In this paper, we give a generalization of this method and investigate the efficiency of our generalization. As a result, we provide several best MDS diffusions with respect to the number of XORs that the diffusion needs. For instance, we give (i) an involutory MDS diffusion $\mathbb{F}_{2^8}^{3} \rightarrow \mathbb{F}_{2^8}^{3}$ by 85 XORs and (ii) an involutory MDS diffusion $\mathbb{F}_{2^8}^{4} \rightarrow \mathbb{F}_{2^8}^{4}$ by 122 XORs, and hence present new records to the literature. Furthermore, we interpret the coding theoretical background of our generalization.

Category / Keywords: foundations / Maximum distance separable (MDS) matrices, subfield construction

Date: received 21 Jan 2021, last revised 21 Jan 2021

Contact author: kamil otal at gmail com

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2021/075

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