Can we design a block cipher based on SP-network without loss of E/D similarity theoretically?
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.