Can we design a block cipher based on SP-network without loss of E/D similarity theoretically? I understand what SP-network (Substitution-Permutation Network) and Feistel Network look like. And those ciphers based on Feistel (e.g. DES) often achieve so called E/D similarity, which indicates that the cipher itself follows the same pattern during either encryption or decryption.
SPN, comparing with Feistel Network, can bring more &quot;confusion&quot; into the cipher indeed. But the ciphers deriving from SPN (e.g. AES) may not be able to realize this E/D similarity. For instance, we have to put the inverse SBOX into the AES decryption process.
Thus, can we design a block cipher based on SP-network without loss of E/D similarity theoretically? Thanks!
Actually, to deal with the conflict between the inverse SBOX and E/D similarity, we can just expand the original SP network into something like &quot;$S$-&gt;$P$-&gt;(entangled with key)-&gt;$P^{-1}$-&gt;$S^{-1}$&quot;. Then we can have a E/D similar block cipher. Some standard ciphers like PRINCE were designed this way.
However, it seems that we still can not make SPN itself to be of E/D similarity so we have to place extra components in it.