A construction for authentication/secrecy codes from certain combinatorial designs (Q1112007)

If we agree to use one of v possible messages to communicate one of k possible source states, then an opponent can successfully impersonate a transmitter with probability at least k/v, and can successfully substitute a message with a fraudulent one with probability at last (k- 1)/(v-1). We wish to limit an opponent to these bounds. In addition, we desire that the observation of any two messages in the communication channel will give an opponent no clue as to the two source states. We describe a construction for a code which achieves these goals, and which does so with the minimum possible number of encoding rules (namely, \(v\cdot (v-1)/2)\). The construction uses a structure from combinatorial design theory known as a perpendicular array.