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Forgive me if this seems like a trivial question. I've read that AES is a SP network. However, when reading about P-boxes in SPNs they say that they simply shuffle bits around. In AES the ShiftRows step is definitely shuffling bits around, but MixColumns step is not a bit permutation. Does this make AES something more than a SP network, or can the definition of a P-box simply be stretched a bit?

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I think Substitution-Permutation Network is kept for historical reasons. Nowadays, we call SPNs even if Permutation is replaced by a general linear layer. Of course, the AES linear layer (concretely, MixColumns) is not a bit-permutation.

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