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I would like to insert a key deriving function into EAX mode, in order to hamper...

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 corresponding tweaks:

Original: OMAC(T||...) where the 128-bit tweak T is either 0, 1, 2.

Modification: OMAC(T||S||...)

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?

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