Full-State Keyed Sponge (aka Donkey Sponge) appears to cross over into block cipher mode territory such as Full Block Cipher Feedback Mode:
Full State Keyed Sponge (FKS) construction:
FKS has been shown to be a secure way to obtain a MAC.1
FKS and Full-Block CFB are the same constructs, there apparently even exists a CFB-MAC as per: Where is CFB-MAC defined?
There also exists something similar: CBC-MAC
We can transform the unkeyed permutation at the core of a sponge into a fully keyed permutation (with round keys or Even-Mansour). It would become a large state block cipher.
Could we not use the resulting construct to perform efficient AEAD with a completely free MAC at the end?
Sponge Duplex constructions pay for the MAC with additional compute operations on the hidden state. And given the need for multiple rounds of diffusion and confusion in the permutation, the additional operations can never compete directly on performance with one-time polynomial MACs.
