Bounds and Combinatorial Structure of (k,n)Multi-Receiver A-Codes

Authors:
Satoshi Obana;Kaoru Kurosawa
Affiliations:
Computer and Communication Media Research, NEC Corporation, 4-1-1 Miyazaki, Miyamae-ku, Kawasaki, Kanagawa 216-8555, Japan;Department of Communication and Integrated Systems, O-okayama, Meguro-ku, Tokyo 152-8552, Japan
Venue:
Designs, Codes and Cryptography
Year:
2001

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Abstract

In the model of(k,n) multi-receiver authentication codes ( A-codes),a transmitter broadcasts a message m to nreceivers in such a way that not only an outside opponent butalso any k-1 receivers cannot cheat any other receiver.In this paper, we derive lower bounds on the cheating probabilitiesand the sizes of keys of (k,n) multi-receiver A-codes.The scheme proposed by Desmedt, Frankel and Yung meets all ourbounds with equalities. This means that our bounds are tightand their scheme is optimum. We further show a combinatorialstructure of optimum (k,n) multi-receiver A-codes.A notion of TWOOAs is introduced. A TWOOA is a pair of orthogonalarrays which satisfy a certain condition. We then prove thatan optimum (k,n) multi-receiver A-codeis equivalent to a TWOOA.