Abstract. In this paper, we extend previous results relating the DolevYao model and the computational model. We add the possibility to exchange keys and consider cryptographic primitives such as signature. This work can be applied to check protocols in the computational model by using automatic verification tools in the formal model.To obtain this result, we introduce a precise definition for security criteria which leads to a nice reduction theorem. The reduction theorem is of interest on its own as it seems to be a powerful tool for proving equivalences between security criteria. Also, the proof of this theorem uses original ideas that seem to be applicable in other situations.

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Abstract. The composition of security definitions is a subtle issue. As most security protocols use a combination of security primitives, it is important to have general results that allow to combine such definitions. We present here a general result of composition for security criteria (i.e. security requirements). This result can be applied to deduce security of a criterion from security of one of its sub-criterion and an indistinguishability criterion. To illustrate our result, we introduce joint security for asymmetric and symmetric cryptography and prove that it is equivalent to classical security assumptions for both the asymmetric and symmetric encryption schemes. Using this, we give a modular proof of computational soundness of symbolic encryption. This result holds in the case of an adaptive adversary which can use both asymmetric and symmetric encryption.

In this paper, we report on our effort in enhancing our model-checker for cryptographic protocols with the ability to automatically generate a deductive proof that the protocol meets its specification. More specifically, we discuss a technique that allows to transform an abstract proof extracted from the model-checker to a proof that can be checked independently of the abstracting and model-checking process.

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