Bounds and Combinatorial Structure of (k; N) Multi-receiver A-codes
نویسندگان
چکیده
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, we 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.
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