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.
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.
Key exchange protocols allow two parties to agree on a shared secret over an untrusted channel. A huge number of scientific works on key exchange have been published since the discovery of the first key exchange protocol, designed in 1976 by Diffie and Hellman [DH76]. The most prominent of these works is the game-based security model by Bellare and Rogaway [BR93], published in 1993 and, today, known as the "golden standard" for the security of key exchange protocols. The main purpose of key exchange protocols is to establish keys for a symmetric-key protocol such as a secure channel. Ideally, if both, the key exchange protocol and the channel protocol, are secure, then we would hope that they can be securely composed. While this is true for simulation-based security models [Can01, KT11, BPW03], game-based models usually lack composition theorems altogether. That is unfortunate, as they are often more suitable for real-life protocols such as TLS. Our first two composition theorems address the composition of BR-secure key exchange protocols with arbitrary symmetric-key protocols. We formally establish that an additional condition is necessary, namely, the key exchange requires a public session matching algorithm. Maybe surprisingly, many important key agreement protocols are not BR-secure due to the popular technique of explicit key confirmation. We devise a more flexible yet sufficiently strong model for this class of protocols and prove that it is closed under reductions. Overall, we devellop a tool for the modular analysis of real-life protocols and exemplify the use of our framwork on a profile of the TLS protocol. As in the case of most practical cryptography, information-theoretic security for key exchange protocols is out of reach, i.e., impossible in a formal sense. Therefore, protocols such as TLS rely on computational assumptions, e.g., the Diffie-Hellmann assumption or the hardness of factoring numbers. As the security of protocols is tightly related to the underlying complexity assumptions, researchers have been striving for simpler and weaker assumptions. The holy grail in this area is to base key agreement, one-way functions or simply any type of cryptography on the mere assumptions that NP does not equal P [FF93, BT03, AGGM06]. While positive results in this area remain elusive, there has been some recent progress on negative results [HMX10, PTV11], showing that cryptographic primitives such as hash functions cannot be based on NP-hardness unless coAM is contained in NP. In this thesis, we provide two oracle results that show that, via relativizing techniques, these negative results do not carry over to key agreement and regular one-way functions. In particular, we give an oracle relative to which the intersection of NP and coNP is easy while infinitely many often secure key agreement exists; and we give an oracle relative to which languages in the intersection of AM and coAM is easy while regular function families exists that are infinitely many often one-way.
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.
Secure communication has become an essential ingredient of our daily life. Mostly unnoticed, cryptography is protecting our interactions today when we read emails or do banking over the Internet, withdraw cash at an ATM, or chat with friends on our smartphone. Security in such communication is enabled through two components. First, two parties that wish to communicate securely engage in a key exchange protocol in order to establish a shared secret key known only to them. The established key is then used in a follow-up secure channel protocol in order to protect the actual data communicated against eavesdropping or malicious modification on the way. In modern cryptography, security is formalized through abstract mathematical security models which describe the considered class of attacks a cryptographic system is supposed to withstand. Such models enable formal reasoning that no attacker can, in reasonable time, break the security of a system assuming the security of its underlying building blocks or that certain mathematical problems are hard to solve. Given that the assumptions made are valid, security proofs in that sense hence rule out a certain class of attackers with well-defined capabilities. In order for such results to be meaningful for the actually deployed cryptographic systems, it is of utmost importance that security models capture the system's behavior and threats faced in that 'real world' as accurately as possible, yet not be overly demanding in order to still allow for efficient constructions. If a security model fails to capture a realistic attack in practice, such an attack remains viable on a cryptographic system despite a proof of security in that model, at worst voiding the system's overall practical security. In this thesis, we reconsider the established security models for key exchange and secure channel protocols. To this end, we study novel and advanced security aspects that have been introduced in recent designs of some of the most important security protocols deployed, or that escaped a formal treatment so far. We introduce enhanced security models in order to capture these advanced aspects and apply them to analyze the security of major practical key exchange and secure channel protocols, either directly or through comparatively close generic protocol designs. Key exchange protocols have so far always been understood as establishing a single secret key, and then terminating their operation. This changed in recent practical designs, specifically of Google's QUIC ("Quick UDP Internet Connections") protocol and the upcoming version 1.3 of the Transport Layer Security (TLS) protocol, the latter being the de-facto standard for security protocols. Both protocols derive multiple keys in what we formalize in this thesis as a multi-stage key exchange (MSKE) protocol, with the derived keys potentially depending on each other and differing in cryptographic strength. Our MSKE security model allows us to capture such dependencies and differences between all keys established in a single framework. In this thesis, we apply our model to assess the security of both the QUIC and the TLS 1.3 key exchange design. For QUIC, we are able to confirm the intended overall security but at the same time highlight an undesirable dependency between the two keys QUIC derives. For TLS 1.3, we begin by analyzing the main key exchange mode as well as a reduced resumption mode. Our analysis attests that TLS 1.3 achieves strong security for all keys derived without undesired dependencies, in particular confirming several of this new TLS version's design goals. We then also compare the QUIC and TLS 1.3 designs with respect to a novel 'zero round-trip time' key exchange mode establishing an initial key with minimal latency, studying how differences in these designs affect the achievable key exchange security. As this thesis' last contribution in the realm of key exchange, we formalize the notion of key confirmation which ensures one party in a key exchange execution that the other party indeed holds the same key. Despite being frequently mentioned in practical protocol specifications, key confirmation was never comprehensively treated so far. In particular, our formalization exposes an inherent, slight difference in the confirmation guarantees both communication partners can obtain and enables us to analyze the key confirmation properties of TLS 1.3. Secure channels have so far been modeled as protecting a sequence of distinct messages using a single secret key. Our first contribution in the realm of channels originates from the observation that, in practice, secure channel protocols like TLS actually do not allow an application to transmit distinct, or atomic, messages. Instead, they provide applications with a streaming interface to transmit a stream of bits without any inherent demarcation of individual messages. Necessarily, the security guarantees of such an interface differ significantly from those considered in cryptographic models so far. In particular, messages may be fragmented in transport, and the recipient may obtain the sent stream in a different fragmentation, which has in the past led to confusion and practical attacks on major application protocol implementations. In this thesis, we formalize such stream-based channels and introduce corresponding security notions of confidentiality and integrity capturing the inherently increased complexity. We then present a generic construction of a stream-based channel based on authenticated encryption with associated data (AEAD) that achieves the strongest security notions in our model and serves as validation of the similar TLS channel design. We also study the security of such applications whose messages are inherently atomic and which need to safely transport these messages over a streaming, i.e., possibly fragmenting, channel. Formalizing the desired security properties in terms of confidentiality and integrity in such a setting, we investigate and confirm the security of the widely adopted approach to encode the application's messages into the continuous data stream. Finally, we study a novel paradigm employed in the TLS 1.3 channel design, namely to update the keys used to secure a channel during that channel's lifetime in order to strengthen its security. We propose and formalize the notion of multi-key channels deploying such sequences of keys and capture their advanced security properties in a hierarchical framework of confidentiality and integrity notions. We show that our hierarchy of notions naturally connects to the established notions for single-key channels and instantiate its strongest security notions with a generic AEAD-based construction. Being comparatively close to the TLS 1.3 channel protocol, our construction furthermore enables a comparative design discussion.
Authenticated key-exchange protocols allow two participants A and B , communicating over a public network and each holding an authentication means to exchange a shared secret value. Methods designed to deal with this cryptographic problem ensure A (resp. B ) that no other participants aside from B (resp. A ) can learn any information about the agreed value and often also ensure A and B that their respective partner has actually computed this value. A natural extension to this cryptographic method is to consider a pool of participants exchanging a shared secret value and to provide a formal treatment for it. Starting from the famous two-party Diffie--Hellman (DH) key-exchange protocol and from its authenticated variants, security experts have extended it to the multiparty setting for over a decade and, in the past few years, completed a formal analysis in the framework of modern cryptography. The present paper synthesizes this body of work on the provably-secure authenticated group DH key exchange.
Nowadays many crucial network applications rely on the existence of a confidential channel established by authenticated key exchange (AKE) protocols over public networks.With the rapid development of cyber technology, novel attacks to cryptosystem emerge in an endless stream.This has also led to the development of AKE solutions to provide increasingly stronger security guarantees.In this thesis we focus on provision of practical constructions for AKE protocols which are provably secure in a strong sense without resorting to random oracles.We first we present three new efficient compilers to generically turn passively secure key exchange protocols (KE) into authenticated key exchange protocols (AKE) where security also holds in the presence of active adversaries.Our compilers are not only a useful tool for the design of new AKE systems with many additional security properties in a modular and less error-prone fashion, but they also help to relax the assumptions on existing, practical key exchange mechanisms which are not known to be provably secure AKE protocols.Security of our compilers is shown in a strong modified CK model where the adversary is allowed to reveal either long-term secret key or state information of the protocol participants.On the second, we study the open problem on constructing eCK secure two party AKE protocol without random oracles and NAXOS trick.A generic construction satisfying those requirements is given based on well-known cryptographic primitives following the guideline of efficiency.Then a concrete protocol is proposed which is the first eCK secure protocol in the standard model under both standard assumptions and post-specified peer setting (i.e.without knowing any cryptographic information about its communication peer).Both proposed schemes can be more efficiently implemented with secure device than previous works which are eCK secure in the standard model, where the secure device might be normally used to store the long-term private key and to implement codes of protocol which need to be resilience of state leakage.Finally, we generalize our one-round two party AKE construction to group case that yields an efficient tripartite AKE protocol based on bilinear maps and a candidate group AKE protocol (with more than three members) based on multilinear maps.Up to now they are the first solutions which can be proved secure in the g-eCK model without random oracles.Meanwhile we make first step to show how to simplify the security proof for one-round group AKE under g-eCK model.i
With the advancement in Internet-based technologies, network applications are no longer just limited to one-to-one communication; instead, it has become a publicly accessible resource. Regardless of this growth, such applications bring specific challenges concerning authentication, integrity, and privacy. Cryptography stands as an ideal solution to overcome these issues through an interactive method of secure communication called Key Exchange. Key exchange protocols allow two or more entities to agree upon a shared secret transmitted over a public channel without revealing any information to an eavesdropper.
This thesis contributes to the design and analysis of the variants of key exchange protocols along with their applications. As per the security requirements, the proposed schemes are either designed in an interactive model or a non-interactive model. Each scheme undergoes a series of formal and informal security analysis. The formal analysis provides simulation result using cryptographic models. Whereas, an informal analysis showcases the theoretical proves on known attacks where an adversary controls the network. The performance analysis maps the protocol’s efficiency based on the computation cost and communication size.
The first contribution introduces an interactive two-party authenticated key exchange protocol. We begin by investigating the security flaws in an existing system such as, lack of user anonymity, trace attack, clogging attack, and failure to resist replay attack. Then proposed an authenticated self-certified key exchange protocol that overcomes the addressed issues. Also, it eliminates the requirements of a trusted certificate authority to authorize the entities. The scheme achieves anonymity during session execution, mutual authentication and enables session key agreement.Based on the ideology, an application is designed, forsecure communication between ad-hoc nodes in a mobile ad-hoc network.
The second contribution contributes to the design of an Identity-based authenticated three-party key exchange protocol that overcomes the incapability of managing huge
peer-to-peer communication and high computation cost faced by two-party authenticated key exchange protocols. The proposed scheme preserves user privacy by enabling the property of anonymity and ensures non-repudiation. Based on the ideology, an application is designed to establish a secure session key between two users with the help of a trusted server for an electronic payment system.
The third contribution proposes an interactive pairing-free certificateless authenticated group key agreement scheme suitable for a resource constrained mobile network. The scheme allows any user to join or leave the group dynamically. The key agreement protocol devised in this scheme ensures un-deniability property by incorporating the signcryption, and unsigncryption algorithm.
The final contribution presents a non-interactive Identity-based deniable authentication protocol that allows an intended receiver to identify the origin of a given message without being able to prove sender’s identity to a third party.