Combinatorial classification of optimal authentication codes with arbitration

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 first show that an optimal A(2)-code implies an orthogonal array and an affine alpha-resolvable design. Next we define a n ew design, an affine alpha-resolvable + BIBD, and prove that optimal A(2)-c odes are equivalent to this new design. From this equivalence, we derive a condition on the parameters for the existence of optimal A(2)-codes. Furthe r, we show tighter lower bounds on the size of keys than before for large s izes of source states which can be considered as an extension of the bounds on the related designs.