Chosen-ciphertext security is by now a standard security property for asymmetric encryption. Many generic constructions for building secure cryptosystems from primitives with lower level of security have been proposed. Providing security proofs has also become standard practice. There is, however, a lack of automated verification procedures that analyze such cryptosystems and provide security proofs. This paper presents an automated procedure for analyzing generic asymmetric encryption schemes in the random oracle model. It has been applied to several examples of encryption schemes among which the construction of Bellare-Rogaway 1993, of Pointcheval at PKC'2000 and REACT.

Abstract Several proof-assistants rely on the very formal basis of Pure Type Systems (PTS) as their foundations. We are concerned with the issues involved in the development of large proofs in these provers such as namespace management, development of reusable proof libraries and separate verification. Although implementations offer many features to address them, few theoretical foundations have been laid for them up to now. This is a problem as features dealing with modularity may have harmful, unsuspected effects on the reliability or usability of an implementation. In this paper, we propose an extension of Pure Type Systems with a module system, $\mathcal{MC}_2$ , adapted from SML-like module systems for programming languages. This system gives a theoretical framework addressing the issues mentioned above in a quite uniform way. It is intended to be a theoretical foundation for the module systems of proof-assistants such as Coq or Agda. We show how reliability and usability can be formalized as metatheoretical properties and prove they hold for $\mathcal{MC}_2$ .