| Summary: | In this paper, a new framework is developed for proving and adapting the recently proposed multiple-of-8 property and mixture-differential distinguishers. The above properties are formulated as immediate consequences of an equivalence relation on the input pairs, under which the difference at the output of the round function is invariant. This approach provides a further understanding of these newly developed distinguishers. For example, it clearly shows that the branch number of the linear layer does not influence the validity of the property, on the contrary of what was previously believed. We further provide an extension of the mixture-differential distinguishers and multiple-of-8 property to any SPN and to a larger class of subspaces. These adapted properties can then be exhibited in a systematic way for other ciphers than the AES. We illustrate this with the examples of Midori, Klein, LED and Skinny.
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