Abstract
In this paper we introduce the notion of essentially s-fold secure authentication systems of level l (2 ≤ l ≤ s). These are authentication systems in which the Bad Guy’s chances to cheat after observing l messages are only where K is the number of keys, and after s messages are only for a suitable constant c. We construct a suitable class of essentially s-fold secure authentication systems of level l; these systems are defined by using algebraic varieties in finite projective spaces.
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