W e propose an extension of the B A N logic to reason about a secure protocol in a hostile and/or unknown environment. Probabilities, attached to the sentences and rules of the logic, allow us t o quantify the beliefs of principals and represent the insecurities and uncertainties of a real life situation. W e develop a probabilistic logic and obtain tight lower bounds on the probability of the conclusion which correspond to the minimum trust that can be put on the goal of the protocol. This gives us a powerful tool lo model and study the performance of secure protocols. W e discuss a probabilistic semantic f o r B A N logic and apply the results t o the Needham-Schroeder protocol. The paper concludes by discussing the merits of these results and mentioning some open problems.

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