Özet:

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.

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