In order to ensure memory properties of an operating system, it is important to verify the implementation of its heap manager. In the case of an existing operating system, such a verification is a difficult task because the heap manager is usually written in a low-level language that makes use of pointers, and it is usually not written with verification in mind. Our main contribution in this paper is to verify the heap manager of an existing operating system, namely Topsy. For this purpose, we use separation logic, an extension of Hoare logic to deal with pointers. Thanks to our verification, we found several issues in the original source code. Another output of our verification is our Coq implementation of separation logic.

Abstract. Game-playing is an approach to write security proofs that are easy to verify. In this approach, security definitions and intractable problems are written as programs called games and reductionist security proofs are sequences of game transformations. This bias towards programming languages suggests the implementation of a tool based on compiler techniques (syntactic program transformations) to build security proofs, but it also raises the question of the soundness of such a tool. In this paper, we advocate the formalization of game-playing in a proof assistant as a tool to build security proofs. In a proof assistant, starting from just the formal definition of a probabilistic programming language, all the properties required in game-based security proofs can be proved internally as lemmas whose soundness is ensured by proof theory. Concretely, we show how to formalize the game-playing framework of Bellare and Rogaway in the Coq proof assistant, how to prove formally reusable lemmas such as the fundamental lemma of game-playing, and how to use them to formally prove the PRP/PRF Switching Lemma.

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