International Association
for Cryptologic Research

In May 2020, Zoom Video Communications, Inc. (Zoom) announced a multi-step plan to comprehensively support end-to-end encrypted (E2EE) group video calls and subsequently rolled out basic E2EE support to customers in October 2020. In this work we provide the first formal security analysis of Zoom's E2EE protocol, and also lay foundation to the general problem of E2EE group video communication. We observe that the vast security literature analyzing asynchronous messaging does not translate well to synchronous video calls. Namely, while strong forms of forward secrecy and post compromise security are less important for (typically short-lived) video calls, various liveness properties become crucial. For example, mandating that participants quickly learn of updates to the meeting roster and key, media streams being displayed are recent, and banned participants promptly lose any access to the meeting. Our main results are as follows: 1. Propose a new notion of leader-based continuous group key agreement with liveness, which accurately captures the E2EE properties specific to the synchronous communication scenario. 2. Prove security of the core of Zoom's E2EE meetings protocol in the above well-defined model. 3. Propose ways to strengthen Zoom's liveness properties by simple modifications to the original protocol, which have since been deployed in production.

The Messaging Layer Security (MLS) protocol is an open standard for end-to-end (E2E) secure group messaging being developed by the IETF, poised for deployment to consumers, industry, and government. It is designed to provide E2E privacy and authenticity for messages in long-lived sessions whenever possible, despite the participation (at times) of malicious insiders that can adaptively interact with the PKI at will, actively deviate from the protocol, leak honest parties' states, and fully control the network. The core of the MLS protocol (from which it inherits essentially all of its efficiency and security properties) is a Continuous Group Key Agreement (CGKA) protocol. It provides asynchronous E2E group management by allowing group members to agree on a fresh independent symmetric key after every change to the group's state (e.g. when someone joins/leaves the group). In this work, we make progress towards a precise understanding of the insider security of MLS (Draft 12). On the theory side, we overcome several subtleties to formulate the first notion of insider security for CGKA (or group messaging). Next, we isolate the core components of MLS to obtain a CGKA protocol we dub Insider Secure TreeKEM (ITK). Finally, we give a rigorous security proof for ITK. In particular, this work also initiates the study of insider secure CGKA and group messaging protocols. Along the way we give three new (very practical) attacks on MLS and corresponding fixes. (Those fixes have now been included into the standard.) We also describe a second attack against MLS-like CGKA protocols proven secure under all previously considered security notions (including those designed specifically to analyze MLS). These attacks highlight the pitfalls in simplifying security notions even in the name of tractability.

Forward-secure encryption (FSE) allows communicating parties to refresh their keys across epochs, in a way that compromising the current secret key leaves all prior encrypted communication secure. We investigate a novel dimension in the design of FSE schemes: fast-forwarding (FF). This refers to the ability of a stale communication party, that is "stuck" in an old epoch, to efficiently "catch up" to the newest state, and frequently arises in practice. While this dimension was not explicitly considered in prior work, we observe that one can augment prior FSEs -- both in symmetric- and public-key settings -- to support fast-forwarding which is sublinear in the number of epochs. However, the resulting schemes have disadvantages: the symmetric-key scheme is a security parameter slower than any conventional stream cipher, while the public-key scheme inherits the inefficiencies of the HIBE-based forward-secure PKE. To address these inefficiencies, we look at the common real-life situation which we call the bulletin board model, where communicating parties rely on some infrastructure -- such as an application provider -- to help them store and deliver ciphertexts to each other. We then define and construct FF-FSE in the bulletin board model, which addresses the above-mentioned disadvantages. In particular, * Our FF-stream-cipher in the bulletin-board model has: (a) constant state size; (b) constant normal (no fast-forward) operation; and (c) logarithmic fast-forward property. This essentially matches the efficiency of non-fast-forwardable stream ciphers, at the cost of constant communication complexity with the bulletin board per update. * Our public-key FF-FSE avoids HIBE-based techniques by instead using so-called updatable public-key encryption (UPKE), introduced in several recent works (and more efficient than public-key FSEs). Our UPKE-based scheme uses a novel type of "update graph" that we construct in this work. Our graph has constant in-degree, logarithmic diameter, and logarithmic "cut property" which is essential for the efficiency of our schemes. Combined with recent UPKE schemes, we get two FF-FSEs in the bulletin board model, under DDH and LWE.

Proofs of knowledge (PoK) are one of the most fundamental notions in cryptography. The appeal of this notion is that it provides a general template that an application can suitably instantiate by choosing a specific relation. Nonetheless, several important applications have been brought to light, including proofs-of-ownership of files or two-factor authentication, which do not fit the PoK template but naturally appear to be special cases of a more general notion of proofs of knowledge or possession. One would thus expect that their security properties, in particular privacy and soundness, are simply derived as concrete instantiation of a common generalized PoK concept with well understood security semantics. Unfortunately, such a notion does not exist, resulting in a variety of tailor-made security definitions whose plausibility must be checked on a case-by-case basis. In this work, we close this gap by providing the theoretical foundations of a generalized notion of PoK that encompasses dynamic and setup-dependent relations as well as interactive statement derivations. This novel combination enables an application to directly specify relations that depend on an assumed setup, such as a random oracle, a database or ledger, and to have statements be agreed upon interactively and dynamically between parties based on the state of the setup. Our new notion is called \emph{agree-and-prove} and provides clear semantics of correctness, soundness, and zero-knowledge in the above generalized scenario. As an application, we first consider proofs-of-ownership of files for client-side file deduplication. We cast the problem and some of its prominent schemes in our agree-and-prove framework and formally analyze their security. Leveraging our generic zero-knowledge formalization, we then devise a novel scheme that is provably the privacy-preserving analogue of the well-known Merkle-Tree based protocol. As a second application, we consider two-factor entity authentication to showcase how the agree-and-prove notion encompasses proofs of ability, such as proving the correct usage of an abstract hardware token.

Composable security definitions, at times called simulation-based definitions, provide strong security guarantees that hold in any context. However, they are also met with some skepticism due to many impossibility results; goals such as commitments and zero-knowledge that are achievable in a stand-alone sense were shown to be unachievable composably (without a setup) since provably no efficient simulator exists. In particular, in the context of adaptive security, the so-called "simulator commitment problem" arises: once a party gets corrupted, an efficient simulator is unable to be consistent with its pre-corruption outputs. A natural question is whether such impossibility results are unavoidable or only artifacts of frameworks being too restrictive. In this work, we propose a novel type of composable security statement that evades the commitment problem. Our new type is able to express the composable guarantees of schemes that previously did not have a clear composable understanding. To this end, we leverage the concept of system specifications in the Constructive Cryptography framework, capturing the conjunction of several interval-wise guarantees, each specifying the guarantees between two events. We develop the required theory and present the corresponding new composition theorem. We present three applications of our theory. First, we show in the context of symmetric encryption with adaptive corruption how our notion naturally captures the expected confidentiality guarantee---the messages remain confidential until either party gets corrupted---and that it can be achieved by any standard semantically secure scheme (negating the need for non-committing encryption). Second, we present a composable formalization of (so far only known to be standalone secure) commitment protocols, which is instantiable without a trusted setup like a CRS. We show it to be sufficient for being used in coin tossing over the telephone, one of the early intuitive applications of commitments. Third, we reexamine a result by Hofheinz, Matt, and Maurer [Asiacrypt'15] implying that IND-ID-CPA security is not the right notion for identity-based encryption, unmasking this claim as an unnecessary framework artifact.

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.

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.

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.

Information-theoretic secret-key agreement between two parties Alice and Bob is a well-studied problem that is provably impossible in a plain model with public (authenticated) communication, but is known to be possible in a model where the parties also have access to some correlated randomness. One particular type of such correlated randomness is the so-called satellite setting, where uniform random bits (e.g., sent by a satellite) are received by the parties and the adversary Eve over inherently noisy channels. The antenna size determines the error probability, and the antenna is the adversary’s limiting resource much as computing power is the limiting resource in traditional complexity-based security. The natural assumption about the adversary is that her antenna is at most Q times larger than both Alice’s and Bob’s antenna, where, to be realistic, Q can be very large.The goal of this paper is to characterize the secret-key rate per transmitted bit in terms of Q. Traditional results in this so-called satellite setting are phrased in terms of the error probabilities $$\epsilon _A$$ϵA, $$\epsilon _B$$ϵB, and $$\epsilon _E$$ϵE, of the binary symmetric channels through which the parties receive the bits and, quite surprisingly, the secret-key rate has been shown to be strictly positive unless Eve’s channel is perfect ($$\epsilon _E=0$$ϵE=0) or either Alice’s or Bob’s channel output is independent of the transmitted bit (i.e., $$\epsilon _A=0.5$$ϵA=0.5 or $$\epsilon _B=0.5$$ϵB=0.5). However, the best proven lower bound, if interpreted in terms of the channel quality ratio Q, is only exponentially small in Q. The main result of this paper is that the secret-key rate decreases asymptotically only like $$1/Q^2$$1/Q2 if the per-bit signal energy, affecting the quality of all channels, is treated as a system parameter that can be optimized. Moreover, this bound is tight if Alice and Bob have the same antenna sizes.Motivated by considering a fixed sending signal power, in which case the per-bit energy is inversely proportional to the bit-rate, we also propose a definition of the secret-key rate per second (rather than per transmitted bit) and prove that it decreases asymptotically only like 1/Q.