Bounds and combinatorial structure of (k,n) multi-receiver A-codes
In the model of (k. n) multi-receiver authentication codes(A-codes:). a transmitter broadcasts a message m to n receivers in such a way that not only an outside opponent but also any k - 1 receivers cannot cheat any other receiver. In this paper, wt: derive lower bounds on the cheating probabilities and the sizes of keys of (k. n) multi-receiver A-codes. The scheme proposed by Desmedt, Frankel and Yung meets all our bounds with equalities. This means that our bounds are tight and their scheme is optimum. We further show a combinatorial structure of optimum (k, n) multi-receiver A-codes. A notion of TWOOAs is introduced. A TWOOA is a pair of orthogonal arrays which satisfy a certain condition. We then prove that an optimum (k, n) multi-receiver A-code is equivalent to a TWOOA.
bound multi-receiver orthogonal array cryptography authentication code