A Generalization of the Subfield Construction

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 \begin{itemize} \item an involutory MDS diffusion $\mathbb{F}_{2^8}^{3} \rightarrow \mathbb{F}_{2^8}^{3}$ by 85 d-XORs and \item an involutory MDS diffusion $\mathbb{F}_{2^8}^{4} \rightarrow \mathbb{F}_{2^8}^{4}$ by 122 d-XORs \end{itemize} and hence present new records to the literature. Furthermore, we interpret the coding theoretical background of our generalization.