Combinatorial Characterizations of Authentication Codes II

Authors:
Rolf S. Rees;Douglas R. Stinson
Affiliations:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland A1C 557, Canada;Computer Science and Engineering Department and Center for Communication and Information Science, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0115, USA
Venue:
Designs, Codes and Cryptography
Year:
1996

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Abstract

For any authentication code for k source states and v messages having minimum possible deception probabilities (namely, Pd0 = k/v and Pd1 = (k - 1)/(v - 1)), we show that there must be at least v encoding rules. (This can be thought of as an authentication-code analogue of Fisher's Inequality.) We derive several properties that an extremal code must satisfy, and we characterize the extremal codes for equiprobable source states as arising from symmetric balanced incomplete block designs. We also present an infinite class of extremal codes, in which the source states are not equiprobable, derived from affine planes.