Abstract

For any authentication code for k source states and v messages having minimum possible deception probabilities (namely, P d 0 = k=v and P d 1 = (k \Gamma 1)=(v \Gamma 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. 1 Introduction Authentication codes were invented in 1974 by Gilbert, MacWilliams and Sloane [4]. The theory of authentication codes was developed throughout the 1980's by Simmons and others. Numerous papers have given constructions and bounds for authentication codes; see the list of references for a representative sample. For a survey of authentication code...

Citations