We present a systematic approach to define and study authentication notions in authenticated key-exchange protocols. We propose and use a flexible and expressive predicate-based definitional framework. Our definitions capture key and entity authentication, in both implicit and explicit variants, as well as key and entity confirmation, for authenticated key-exchange protocols. In particular, we capture critical notions in the authentication space such as key-compromise impersonation resistance and security against unknown key-share attacks. We first discuss these definitions within the Bellare-Rogaway model and then extend them to Canetti-Krawczyk-style models. We then show two useful applications of our framework. First, we look at the authentication guarantees of three representative protocols to draw several useful lessons for protocol design. The core technical contribution of this paper is then to formally establish that composition of secure implicitly authenticated key-exchange with subsequent confirmation protocols yields explicit authentication guarantees. Without a formal separation of implicit and explicit authentication from secrecy, a proof of this folklore result could not have been established.
We present a systematic approach to define and study authentication notions in authenticated key-exchange protocols. We propose and use a flexible and expressive predicate-based definitional framework. Our definitions capture key and entity authentication, in both implicit and explicit variants, as well as key and entity confirmation, for authenticated key-exchange protocols. In particular, we capture critical notions in the authentication space such as key-compromise impersonation resistance and security against unknown key-share attacks. We first discuss these definitions within the Bellare-Rogaway model and then extend them to Canetti-Krawczyk-style models. We then show two useful applications of our framework. First, we look at the authentication guarantees of three representative protocols to draw several useful lessons for protocol design. The core technical contribution of this paper is then to formally establish that composition of secure implicitly authenticated key-exchange with subsequent confirmation protocols yields explicit authentication guarantees. Without a formal separation of implicit and explicit authentication from secrecy, a proof of this folklore result could not have been established.
Assessing the security of key exchange protocols is a crucial task and turned out to be highly non-trivial.Many protocols proposed in the past have subsequently been broken.In order to provide a formal framework for security proofs, various security models have been defined.In this thesis, we analyse several such security models for key exchange protocols using the paradigm of constructive cryptography.We examine the exact constructive security guarantees and semantics that these notions provide.In particular, we compare constructive security definitions with a model proposed by Bellare and Rogaway, SK-security by Canetti and Krawczyk and a formal model for secure key exchange proposed by Shoup.i
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.
Authenticated Key Exchange (AKE) protocols are a core building block of all modern communications, connecting the distribution benefits of public-key cryptography to the performance benefits of symmetric-key cryptography. Modern AKE protocols are proven secure in game-based security models that offer considerably more security guarantees than the seminal Bellare-Rogaway model from 1993, in order to capture real-world security properties such as various notions of forward secrecy and resistance against predictable or bad pseudorandom number generators. For most of these security models, it is claimed that they offer “the best possible security”, based on informal arguments that at best hold under unstated assumptions. This has led to a fragmented landscape of AKE security models with seemingly contradictory results.We provide the first systematization of the limits of game-based security models for two-party AKE protocols. Our treatment covers classical stateless protocols as well as a restricted class of modern stateful protocols. Our analysis uncovers how the details of the considered protocol class have crucial implications for (im)possibility results, and reveals how different security goals can be achieved in different relevant classes of AKE protocols. From our formal impossibility results, we derive strong security models for these classes and give protocols that satisfy them.
Abstract. In 2001, Canetti and Krawczyk proposed a security model (CKmodel) for authentication protocols. They also gave an indistinguishabilitybased definition for key exchange protocols. Since then the model has almost exclusively been used for analyzing key exchange protocols, although it can be applied to authentication protocols in general. The model not only captures a large class of attacks but also provides a modular approach to the design of authentication protocols. However, the model does not capture the property of Key Compromise Impersonation (KCI) Resilience. Until now, analysis concerning this property has mostly been done heuristically and restricted to key exchange protocols only. Previous attempts on formalizing KCI have mostly been done in some ad hoc manner and additional proofs have to be given specifically for the security of KCI resilience. In this paper, we propose an extension to the CK-model, which allows, for the first time, the KCI attacks to be considered in authentication protocols in general, rather than restricted to key exchange protocols, and no more additional proofs are required specifically for KCI security. With the revival of interest in identity-based (ID-based) cryptography, there have been many new ID-based key exchange protocols proposed. Despite the fact that some of them have been proven in some restricted versions of a model proposed by Bellare and Rogaway in 1993 and some others have been proven in the original CK-model, there is no rigorous model specifically for ID-based key exchange security. In particular, forward secrecy against compromised Key Generation Server (KGS-FS) has never been captured even though this notion is more important and stronger than the perfect forward secrecy in ID-based key exchange. For this, we further extend our model to ID-based setting and capture the property of KGS-FS for ID-based key exchange security. 1
Authenticated key exchange protocols are ubiquitous in modern-day life. They are used to secure numerous types of data exchange, ranging from online banking to instant messaging conversations. In this thesis, we extend the state of the art for authenticated key exchange security, following the three themes of realistic, strong and provable. First, we tackle the theme of provable security. We develop generic techniques, applicable to a wide range of security models, to assist in proofs of security of cryptographic schemes. Specifically, a "game hopping" proof is a powerful technique to prove strong statements about the security of a protocol. However, the proof technique often involves esoteric and repetitive steps. We demystify the methodology and prove generic theorems to reduce the length and complexity of a wide class of game hopping proofs. Next, we use this new framework to analyse strong and previously unstudied formal security guarantees of authenticated key exchange protocols. These protocols are able to achieve strong security guarantees because they share and update state across sessions. Using our framework, we are able to push the state of the art by defying the folklore of what was previously thought provable of authenticated key exchange protocols. Specifically, it was previously thought that no protocol can achieve a security guarantee about communication with a peer if the peer was already fully compromised. We show that this is not true by formally defining a new concept, which we name post-compromise security. We capture an intuitive "self-healing" property of protocols. We then construct and formally prove protocols can achieve this strong security notion. Finally, we leverage all of this work to analyse realistic protocols. Signal, which is used to encrypt messages in WhatsApp, Facebook Messenger and Google Allo amongst others, is one such protocol we consider. Despite being used by billions of people, Signal was completely unstudied in the academic literature prior to this work. Two reasons for this were that Signal had no documentation at the time and it did not fit into existing models: it shares state across sessions and has over ten different types of key, most of which continually update. Despite its complexity, we are able to use the other work in this thesis to give the first ever analysis and proof of security of Signal. Overall, this thesis aims to bridge the gap between theory and practice in the current state of the art of authenticated key exchange protocols.