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1 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

1 Kurkowski M.

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The Completeness Theorem for a Logic of Authentication

Kurkowski M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2000/2001

Vol. 8

37--44

In a distributed computational system, security depends heavily on the use of secure protocols such as authentication protocols. In the past few years, a lot of attention has been paid to the use of special logics to analyze cryptographic authentication protocols. Burrows, Abadi, Needham and others have proposed a few logics for the analysis of these protocols (called BAN-Iogics). These are specialized versions of modal logics of belief, with special constructs for expressing some of the central concepts used in authentication processes. These logics have revealed many subtleties and serious flaws in published and widely applied protocols. Unfortunately, they have also created some confusions, for example they are not complete. In the present paper we introduce a new logic of authentication, which is a modification of the BAN logic. It provides a convenient formal language for specifying and reasoning about cryptographic protocols requirements. We also provide an axiomatic inference system, a model of computation and semantics. We present some important properties of our logic, first of all the Completeness Theorem.