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Ideal Key Derivation and Encryption in Simulation-Based Security

Ralf Küsters and Max Tuengerthal

Many real-world protocols, such as SSL/TLS, SSH, IPsec, DNSSEC, IEEE~802.11i, and Kerberos, derive new keys from other keys. To be able to analyze such protocols in a composable way, in this paper we extend an ideal functionality for symmetric and public-key encryption proposed in previous work by a mechanism for key derivation. We also equip this functionality with message authentication codes (MACs), digital signatures, and ideal nonce generation. We show that the resulting ideal functionality can be realized based on standard cryptographic assumptions and constructions, hence, providing a solid foundation for faithful, composable cryptographic analysis of real-world security protocols. Based on this new functionality, we identify sufficient criteria for protocols to provide universally composable key exchange and secure channels. Since these criteria are based on the new ideal functionality, checking the criteria requires merely information-theoretic or even only syntactical arguments, rather than involved reduction arguments. As a case study, we use our method to analyze two central protocols of the IEEE~802.11i standard, namely the 4-Way Handshake Protocol and the CCM Protocol, proving composable security properties. As to the best of our knowledge, this constitutes the first rigorous cryptographic analysis of these protocols.