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A New Bound for Substitution Attack

We define two classes of strategies for substitution attack and derive lower bounds on the probability of deception for each class for codes with perfect protection for impersonation. We show that the equality of the two bounds uniquely determines the number of encoding rules and forces the incidence matrix of the code to be that of a BIBD. It also implies that random selection from the remaining cryptograms gives the same probability of deception to the enemy as random selection from the set of keys that am incident with the intercepted codeword.