Optimal Authentication Systems

In this paper we define an optimal authentication systems as a system whose minimum probability of deception is k/M, k and M being the number of source states and cryptograms respectively, and satisfies information theoretic bounds on the value of impersonation and substitution games. We will characterize order-1 perfect systems and δ-perfect systems and prove their optimality when E, the number of encoding rules, satisfies certain bounds. We will show that both types of systems, in this case, also have best game theoretic performance. This will be used to prove that optimal systems exist only if E ≥ M2/k2 and for less value of E probability of deception is always greater than k/M. We will prove that doubly perfect codes are optimal systems with minimum value of E and perfect systems are not optimal. Characterization of doubly perfect systems follows from characterization theorems mentioned earlier. We give constructions for each class.