I would like to insert a key deriving function into EAX mode, in order to hamper brute-force attacks for a key-size restricted cipher (56 bits). The modification inserts an identical multi-block pattern $S$ behind the corresponing tweaks:
Original: $OMAC(T||...)$ where 128-bit tweak $T$ is either
The state of the MAC behind $S$ is different for disjunct tweaks, because the MAC's state behind $S$ can be decrypted back to the original tweak, and identical states would yield identical tweaks.
Is this EAX extension weakening the (provable) security of EAX?