Future-Proofing Key Exchange Protocols

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Key exchange protocols, first introduced by Diffie and Hellman in 1976, are one of the most widely-deployed cryptographic protocols. They allow two parties, that have never interacted before, to establish shared secrets. These shared cryptographic keys may subsequently be used to establish a secure communication channel. Use cases include the classic client-server setting that is for example at play when browsing the internet, but also chats via end-to-end-encrypted instant messaging applications. Security-wise, we generally demand of key exchange protocols to achieve key secrecy and authentication. While, informally, authentication ensures that the communicating parties have confidence in the identity of their peers, key secrecy ensures that any shared cryptographic key that is established via the key exchange protocol is only known to the participants in the protocol and can be used securely in cryptographic protocols, i.e., is sufficiently random. In 1993, Bellare and Rogaway gave a first formalization of key exchange protocol security that captures these properties with respect to powerful adversaries with full control over the network. Their model constitutes the basis of the many subsequent treatments of authenticated key exchange security, including the models presented in this thesis. The common methodological approach underlying all of these formalizations is the provable security paradigm, which has become a standard tool in assessing the security of cryptographic protocols and primitives. So-called security models specify the expected security guarantees of the scheme in question with regards to a well-defined class of adversaries. Proofs that validate these security claims do so by reducing the security of the overall scheme to the security of the underlying cryptographic primitives and hardness assumptions. However, advances in computational power and more sophisticated cryptanalytic capabilities often render exactly these components insecure. Especially the advent of quantum computers will have a devastating effect on much of today's public key cryptography. This is especially true for key exchange protocols since they rely crucially on public-key algorithms. In this thesis, our focus in future-proofing key exchange protocols is two-fold. First, we focus on extending security models for key exchange protocols to capture the (un)expected break of cryptographic primitives and hardness assumptions. The aim is to gain assurances with respect to future adversaries and to investigate the effects of primitive failures on key exchange protocols. More specifically, we explore how key exchange protocols can be safely transitioned to new, post-quantum secure algorithms with hybrid techniques. Hybrids combine classical and post-quantum algorithms such that the overall key agreement scheme remains secure as long as one of the two base schemes remains secure. For this, we introduce security notions for key encapsulation mechanisms that account for adversaries with varying levels of quantum capabilities and present three new constructions for hybrid key encapsulation mechanisms. Our hybrid designs are practice-inspired and for example capture draft proposals for hybrid modes in the Transport Layer Security (TLS) protocol, which is one of the most widely-deployed cryptographic protocols that enables key agreement. Furthermore, our notion of breakdown resilience for key exchange protocols allows to gauge the security of past session keys in the event of a failure of a cryptographic component in the key exchange. We exercise our model on variants of the post-quantum secure key exchange protocol NewHope by Alkim et al. Thereby, we confirm the intuition that, in order to guard against adversaries that only have access to quantum computing power in the (more distant) future, it is sufficient to use classically-secure authentication mechanisms alongside post-quantum key agreement to achieve authenticated key exchange. As with any mathematical statement, theorems in the provable security paradigm are only as valid as the underlying assumptions. A careful consideration of any newly made assumption is thus essential to ensure the meaningfulness of the statement itself and make the assumption a viable tool for future analyses. Thus, secondly, we systematically classify the PRF-ODH assumption, a complexity-theoretic hardness assumption that has been used in key exchange security analyses of such prominent protocols as TLS, Signal, and Wireguard. In particular, we give a unified, parametrized definition of the assumption encompassing different variants that are present in the literature. We relate the resulting parametrized notions in terms of their strength and show where these assumptions fit in the collection of well-understood related hardness assumptions. We finally sketch our result on the impossibility of instantiating this assumption in the standard model, thereby disposing of the uncertainty in the community whether PRF-ODH is in fact a standard model assumption, i.e., removes the usage of some idealized assumptions in key exchange protocol proofs.