Abstract. The use of formal methods to verify security protocols with respect to secrecy and authentication has become standard practice. In contrast, the formalization of other security goals, such as privacy, has received less attention. Due to the increasing importance of privacy in the current society, formal methods will also become indispensable in this area. Therefore, we propose a formal definition of the notion of anonymity in presence of an observing intruder. We validate this definition by analyzing a well-known anonymity preserving protocol, viz. onion routing.

Probability, be it inherent or explicitly introduced, has become an important issue in the verification of programs. In this paper we study a formalism which allows reasoning about programs which can act probabilistically. To describe probabilistic programs, a basic programming language with an operator for probabilistic choice is introduced and a denotational semantics is given for this language. To specify properties of probabilistic programs, standard first order logic predicates are insufficient, so a notion of probabilistic predicates is introduced. A Hoare-style proof system to check properties of probabilistic programs is given. The proof system for a sublanguage is shown to be sound and complete; the properties that can be derived are exactly the valid properties. Finally some typical examples illustrate the use of the probabilistic predicates and the proof system.

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