The simultaneous secret exchange protocol is the key tool for contract signing protocols and certified mail protocols. This paper proposes efficient simultaneous secret exchange protocols (or gradual secret releasing protocols) that are based on general assumptions such as the existence of one-way permutations and one-way functions, while the existing efficient simultaneous secret exchange protocols are based on more constrained assumptions such as specific number theoretic problems and the existence of oblivious transfer primitives (or trap-door one-way permutations). Moreover, while the existing simultaneous secret exchange protocols have an additional requirement that the underlying commit (encryption) function is “ideal”, the above-mentioned “general assumptions” are provably sufficient for our schemes. Therefore, our protocols are provably secure under the general assumptions. In addition, our protocols are at least as efficient as the existing practical protocols, when efficient one-way permutations and one-way functions are used.
The simultaneous secret exchange protocol is the key tool for contract signing protocols and certified mail protocols. This paper proposes efficient simultaneous secret exchange protocols (or gradual secret releasing protocols) that are based on general assumptions such as the existence of one-way permutations and one-way functions, while the existing efficient simultaneous secret exchange protocols are based on more constrained assumptions such as specific number theoretic problems and the existence of oblivious transfer primitives (or trap-door one-way permutations). Moreover, while the existing simultaneous secret exchange protocols have an additional requirement that the underlying commit (encryption) function is “ideal”, the above-mentioned “general assumptions” are provably sufficient for our schemes. Therefore, our protocols are provably secure under the general assumptions. In addition, our protocols are at least as efficient as the existing practical protocols, when efficient one-way permutations and one-way functions are used.
Over the past four decades, computational power and algorithmic strategies have advanced tremendously resulting in an enormous increase in the key sizes required for secure cryptosystems such as RSA. At the same time, the electronic devices have grown smaller and portable requiring algorithms running on them to be optimized in size and efficiency while providing security, at least, equivalent to that provided on a typical desktop computer. As a result, the industry is moving towards newer cryptosystems such as ECC and NTRU that are well suited for resource constrained environments. While, ECC claims to provide security equivalent to that of RSA for a fraction of key size, NTRU is inherently suited for embedded systems technology. However, implementation of new cryptosystems requires the development of protocols analogous to those developed using older cryptosystems. In this thesis, we fulfill a part of this requirement by providing protocols for Oblivious Transfer using ECC and NTRU. Oblivious Transfer, in turn, has applications in simultaneous contract signing, digital certified mail, simultaneous exchange of secrets, secure multiparty computations, private information retrieval, etc. Furthermore, we introduce the idea of basing Oblivious Transfer on public-key exchange protocols. The presentation in the thesis uses Diffie-Hellman Key Exchange, but the scheme is generalizable to any cryptosystem that has a public-key exchange strategy. In fact, our proposal may especially be suited for Quantum Cryptography where the security of key exchange protocols has been proven.
Randomized protocols for signing contracts, certified mail, and flipping a coin are presented. The protocols use a 1-out-of-2 oblivious transfer subprotocol which is axiomatically defined. The 1-out-of-2 oblivious transfer allows one party to transfer exactly one secret, out of two recognizable secrets, to his counterpart. The first (second) secret is received with probability one half, while the sender is ignorant of which secret has been received. An implementation of the 1-out-of-2 oblivious transfer, using any public key cryptosystem, is presented.
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.
With a certified-mail protocol, one fairly exchanges a message for a receipt. No satisfactory protocols without any third party are possible, hence optimistic protocols are the best one can hope for. Here a third party is only involved if one party tries to cheat. Certified-mail protocols are known in the literature, but there was no rigorous definition yet, in particular for the optimistic case and for many interleaved executions. We provide two such definitions. One defines individual integrity and secrecy requirements. The other defines an ideal system and uses a general simulatability definition. We show the relation between the definitions, present an efficient protocol, and prove its security in detail. Apart from the intrinsic benefits of provably secure certified mail, this paper serves as an example that a serious-sized practical protocol can be rigorously proven with respect to a general simulatability definition and an abstract specification accessible to formal me...
We show that some problems in information security can be solved without using one-way functions. The latter are usually regarded as a central concept of cryptography, but the very existence of one-way functions depends on difficult conjectures in complexity theory, most notably on the notorious “” conjecture. This is why cryptographic primitives that do not employ one-way functions are often called “unconditionally secure”. In this paper, we suggest protocols for secure computation of the sum, product, and some other functions of two or more elements of an arbitrary constructible ring, without using any one-way functions. A new input that we offer here is that, in contrast with other proposals, we conceal “intermediate results” of a computation. For example, when we compute the sum of k numbers, only the final result is known to the parties; partial sums are not known to anybody. Other applications of our method include voting/rating over insecure channels and a rather elegant and efficient solution of the “two millionaires problem”. Then, while it is fairly obvious that a secure (bit) commitment between two parties is impossible without a one-way function, we show that it is possible if the number of parties is at least 3. We also show how our unconditionally secure (bit) commitment scheme for three parties can be used to arrange an unconditionally secure (bit) commitment between just two parties if they use a “dummy” (e.g., a computer) as the third party. We explain how our concept of a “dummy” is different from the well-known concept of a “trusted third party”. Based on a similar idea, we also offer an unconditionally secure k - n oblivious transfer protocol between two parties who use a “dummy”. We also suggest a protocol, without using a one-way function, for the so-called “mental poker”, i.e., a fair card dealing (and playing) over distance. Finally, we propose a secret sharing scheme where an advantage over Shamir's and other known secret sharing schemes is that nobody, including the dealer, ends up knowing the shares (of the secret) owned by any particular player. It should be mentioned that computational cost of our protocols is negligible to the point that all of them can be executed without a computer.
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.