Less is more: relaxed yet composable security notions for key exchange

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Although they do not suffer from clear attacks, various key agreement protocols (for example that used within the TLS protocol) are deemed as insecure by existing security models for key exchange. The reason is that the derived keys are used within the key exchange step, violating the usual key-indistinguishability requirement. In this paper, we propose a new security definition for key exchange protocols that offers two important benefits. Our notion is weaker than the more established ones and thus allows the analysis of a larger class of protocols. Furthermore, security in the sense that we define enjoys rather general composability properties. In addition, our composability properties are derived within game-based formalisms and do not appeal to any simulation-based paradigm. Specifically, we show that for protocols, whose security relies exclusively on some underlying symmetric primitive, can be securely composed with key exchange protocols provided that two main requirements hold: (1) No adversary can break the underlying primitive, even when the primitive uses keys obtained from executions of the key exchange protocol in the presence of the adversary (this is essentially the security requirement that we introduce and formalize in this paper), and (2) the security of the protocol can be reduced to that of the primitive, no matter how the keys for the primitive are distributed. Proving that the two conditions are satisfied, and then applying our generic theorem should be simpler than performing a monolithic analysis of the composed protocol. We exemplify our results in the case of a profile of the TLS protocol.