Topology-Hiding Computation for Networks with Unknown Delays 📺
Topology-Hiding Computation (THC) allows a set of parties to securely compute a function over an incomplete network without revealing information on the network topology. Since its introduction in TCC’15 by Moran et al., the research on THC has focused on reducing the communication complexity, allowing larger graph classes, and tolerating stronger corruption types. All of these results consider a fully synchronous model with a known upper bound on the maximal delay of all communication channels. Unfortunately, in any realistic setting this bound has to be extremely large, which makes all fully synchronous protocols inefficient. In the literature on multi-party computation, this is solved by considering the fully asynchronous model. However, THC is unachievable in this model (and even hard to define), leaving even the definition of a meaningful model as an open problem. The contributions of this paper are threefold. First, we introduce a meaningful model of unknown and random communication delays for which THC is both definable and achievable. The probability distributions of the delays can be arbitrary for each channel, but one needs to make the (necessary) assumption that the delays are independent. The existing fully-synchronous THC protocols do not work in this setting and would, in particular, leak information about the topology. Second, in the model with trusted stateless hardware boxes introduced at Eurocrypt’18 by Ball et al., we present a THC protocol that works for any graph class. Third, we explore what is achievable in the standard model without trusted hardware and present a THC protocol for specific graph types (cycles and trees) secure under the DDH assumption. The speed of all protocols scales with the actual (unknown) delay times, in contrast to all previously known THC protocols whose speed is determined by the assumed upper bound on the network delay.
Continuous Group Key Agreement with Active Security
A continuous group key agreement (CGKA) protocol allows a long-lived group of parties to agree on a continuous stream of fresh secret key material. CGKA protocols allow parties to join and leave mid-session but may neither rely on special group managers, trusted third parties, nor on any assumptions about if, when, or for how long members are online. CGKA captures the core of an emerging generation of highly practical end-to-end secure group messaging (SGM) protocols. In light of their practical origins, past work on CGKA protocols have been subject to stringent engineering and efficiency constraints at the cost of diminished security properties. In this work, we somewhat relax those constraints, instead considering progressively more powerful adversaries. To that end, we present 3 new security notions of increasing strength. Already the weakest of the 3 (passive security) captures attacks to which all prior CGKA constructions are vulnerable. Moreover, the 2 stronger (active security) notions even allow the adversary to use parties' exposed states combined with full network control to mount attacks. In particular, this is closely related to so-called insider attacks which involve malicious group members actively deviating from the protocol. Although insiders are of explicit interest to practical CGKA/SGM designers, our understanding of this class of attackers is still quite nascent. Indeed, we believe ours to be the first security notions in the literature to precisely formulate meaningful guarantees against (a broad class of) insiders. For each of the 3 new security notions we give a new CGKA scheme enjoying sub-linear (potentially even logarithmic) communication complexity in the number of group members (on par with the asymptotics of state-of-the-art practical constructions). We prove each scheme optimally secure, in the sense that the only security violations possible are those necessarily implied by correctness.
Efficient Ratcheting: Almost-Optimal Guarantees for Secure Messaging
In the era of mass surveillance and information breaches, privacy of Internet communication, and messaging in particular, is a growing concern. As secure messaging protocols are executed on the not-so-secure end-user devices, and because their sessions are long-lived, they aim to guarantee strong security even if secret states and local randomness can be exposed.The most basic security properties, including forward secrecy, can be achieved using standard techniques such as authenticated encryption. Modern protocols, such as Signal, go one step further and additionally provide the so-called backward secrecy, or healing from state exposures. These additional guarantees come at the price of a moderate efficiency loss (they require public-key primitives).On the opposite side of the security spectrum are the works by Jaeger and Stepanovs and by Poettering and Rösler, which characterize the optimal security a secure-messaging scheme can achieve. However, their proof-of-concept constructions suffer from an extreme efficiency loss compared to Signal. Moreover, this caveat seems inherent.This paper explores the area in between: our starting point are the basic, efficient constructions, and then we ask how far we can go towards the optimal security without losing too much efficiency. We present a construction with guarantees much stronger than those achieved by Signal, and slightly weaker than optimal, yet its efficiency is closer to that of Signal (only standard public-key cryptography is used).On a technical level, achieving optimal guarantees inherently requires key-updating public-key primitives, where the update information is allowed to be public. We consider secret update information instead. Since a state exposure temporally breaks confidentiality, we carefully design such secretly-updatable primitives whose security degrades gracefully if the supposedly secret update information leaks.
A Unified and Composable Take on Ratcheting
Ratcheting, an umbrella term for certain techniques for achieving secure messaging with strong guarantees, has spurred much interest in the cryptographic community, with several novel protocols proposed as of lately. Most of them are composed from several sub-protocols, often sharing similar ideas across different protocols. Thus, one could hope to reuse the sub-protocols to build new protocols achieving different security, efficiency, and usability trade-offs. This is especially desirable in view of the community’s current aim for group messaging, which has a significantly larger design space. However, the underlying ideas are usually not made explicit, but rather implicitly encoded in a (fairly complex) security game, primarily targeted at the overall security proof. This not only hinders modular protocol design, but also makes the suitability of a protocol for a particular application difficult to assess.In this work we demonstrate that ratcheting components can be modeled in a composable framework, allowing for their reuse in a modular fashion. To this end, we first propose an extension of the Constructive Cryptography framework by so-called global event histories, to allow for a clean modularization even if the component modules are not fully independent but actually subtly intertwined, as in most ratcheting protocols. Second, we model a unified, flexibly instantiable type of strong security statement for secure messaging within that framework. Third, we show that one can phrase strong guarantees for a number of sub-protocols from the existing literature in this model with only minor modifications, slightly stronger assumptions, and reasonably intuitive formalizations.When expressing existing protocols’ guarantees in a simulation-based framework, one has to address the so-called commitment problem. We do so by reflecting the removal of access to certain oracles under specific conditions, appearing in game-based security definitions, in the real world of our composable statements. We also propose a novel non-committing protocol for settings where the number of messages a party can send before receiving a reply is bounded.
Topology-Hiding Computation Beyond Semi-Honest Adversaries
Topology-hiding communication protocols allow a set of parties, connected by an incomplete network with unknown communication graph, where each party only knows its neighbors, to construct a complete communication network such that the network topology remains hidden even from a powerful adversary who can corrupt parties. This communication network can then be used to perform arbitrary tasks, for example secure multi-party computation, in a topology-hiding manner. Previously proposed protocols could only tolerate passive corruption. This paper proposes protocols that can also tolerate fail-corruption (i.e., the adversary can crash any party at any point in time) and so-called semi-malicious corruption (i.e., the adversary can control a corrupted party’s randomness), without leaking more than an arbitrarily small fraction of a bit of information about the topology. A small-leakage protocol was recently proposed by Ball et al. [Eurocrypt’18], but only under the unrealistic set-up assumption that each party has a trusted hardware module containing secret correlated pre-set keys, and with the further two restrictions that only passively corrupted parties can be crashed by the adversary, and semi-malicious corruption is not tolerated. Since leaking a small amount of information is unavoidable, as is the need to abort the protocol in case of failures, our protocols seem to achieve the best possible goal in a model with fail-corruption.Further contributions of the paper are applications of the protocol to obtain secure MPC protocols, which requires a way to bound the aggregated leakage when multiple small-leakage protocols are executed in parallel or sequentially. Moreover, while previous protocols are based on the DDH assumption, a new so-called PKCR public-key encryption scheme based on the LWE assumption is proposed, allowing to base topology-hiding computation on LWE. Furthermore, a protocol using fully-homomorphic encryption achieving very low round complexity is proposed.