Combinatorial Classiication of Optimal Authentication Codes with Arbitration Satoshi Obana and Kaoru Kurosawa

Unconditionally secure authentication codes with arbitration (A 2-codes) protect against deceptions from the transmitter and the receiver as well as that from the opponent. We rst show that an optimal A 2-code implies an orthogonal array and an aane-resolvable design. Next we deene a new design, an aane-resolvable + BIBD, and prove that optimal A 2-codes are equivalent to this new design. From this equivalence, we derive a condition on the parameters for the existence of optimal A 2-codes. Further, we show tighter lower bounds on the size of keys than before for large sizes of source states which can be considered as an extension of the bounds on the related designs.