One of the most successful applications of peer-to-peer communication networks is in the context of blockchain protocols, which-in Satoshi Nakamoto's own words-rely on the "nature of information being easy to spread and hard to stifle." Significant efforts were invested in the last decade into analyzing the security of these protocols, and invariably the security arguments known for longest-chain Nakamoto-style consensus use an idealization of this tenet. Unfortunately, the real-world implementations of peer-topeer gossip-style networks used by blockchain protocols rely on a number of ad-hoc attack mitigation strategies that leave a glaring gap between the idealized communication layer assumed in formal security arguments for blockchains and the real world, where a wide array of attacks have been showcased.

The Messaging Layer Security (MLS) project is an IETF effort aiming to establish an industry-wide standard for secure group messaging (SGM). Its development is supported by several major secure-messaging providers (with a combined user base in the billions) and a growing body of academic research. MLS has evolved over many iterations to become a complex, non-trivial, yet relatively ad-hoc cryptographic protocol. In an effort to tame its complexity and build confidence in its security, past analyses of MLS have restricted themselves to sub-protocols of MLS---most prominently a type of sub-protocol embodying so-called continuous group key agreement (CGKA). However, to date the task of proving or even defining the security of the full MLS protocol has been left open. In this work, we fill in this missing piece. First, we formally capture the security of SGM protocols by defining a corresponding security game, which is parametrized by a safety predicate that characterizes the exact level of security achieved by a construction. Then, we cast MLS as an SGM protocol, showing how to modularly build it from the following three main components (and some additional standard cryptographic primitives) in a black-box fashion: (a) CGKA, (b) forward-secure group AEAD (FS-GAEAD), which is a new primitive and roughly corresponds to an "epoch'' of group messaging, and (c) a so-called PRF-PRNG, which is a two-input hash function that is a pseudorandom function (resp.\ generator with input) in its first (resp.\ second) input. Crucially, the security predicate for the SGM security of MLS can be expressed purely as a function of the security predicates of the underlying primitives, which allows to swap out any of the components and immediately obtain a security statement for the resulting SGM construction. Furthermore, we provide instantiations of all component primitives, in particular of CGKA with MLS's TreeKEM sub-protocol (which we prove adaptively secure) and of FS-GAEAD with a novel construction (which has already been adopted by MLS). Along the way we introduce a collection of new techniques, primitives, and results with applications to other SGM protocols and beyond. For example, we extend the Generalized Selective Decryption proof technique (which is central in CGKA literature) and prove adaptive security for another (practical) more secure CGKA protocol called RTreeKEM (Alwen et al.,\ CRYPTO '20). The modularity of our approach immediately yields a corollary characterizing the security of an SGM construction using RTreeKEM.

One approach toward basing public-key encryption (PKE) schemes on weak and credible assumptions is to build “stronger” or more general schemes generically from “weaker” or more restricted ones. One particular line of work in this context was initiated by Myers and Shelat (FOCS ’09) and continued by Hohenberger, Lewko, and Waters (Eurocrypt ’12), who provide constructions of multi-bit CCA-secure PKE from single-bit CCA-secure PKE. It is well known that encrypting each bit of a plaintext string independently is not CCA-secure—the resulting scheme is malleable. We therefore investigate whether this malleability can be dealt with using the conceptually simple approach of applying a suitable non-malleable code (Dziembowski et al., ICS ’10) to the plaintext and subsequently encrypting the resulting codeword bit by bit. We find that an attacker’s ability to ask multiple decryption queries requires that the underlying code be continuously non-malleable (Faust et al., TCC ’14). Since, as we show, this flavor of non-malleability can only be achieved if the code is allowed to “self-destruct,” the resulting scheme inherits this property and therefore only achieves a weaker variant of CCA security. We formalize this new notion of so-called indistinguishability under self-destruct attacks (IND-SDA) as CCA security with the restriction that the decryption oracle stops working once the attacker submits an invalid ciphertext. We first show that the above approach based on non-malleable codes yields a solution to the problem of domain extension for IND-SDA-secure PKE, provided that the underlying code is continuously non-malleable against (a reduced form of) bit-wise tampering. Then, we prove that the code of Dziembowski et al. is actually already continuously non-malleable against bit-wise tampering. We further investigate the notion of security under self-destruct attacks and combine IND-SDA security with non-malleability under chosen-ciphertext attacks (NM-CPA) to obtain the strictly stronger notion of non-malleability under self-destruct attacks (NM-SDA). We show that NM-SDA security can be obtained from basic IND-CPA security by means of a black-box construction based on the seminal work by Choi et al. (TCC ’08). Finally, we provide a domain extension technique for building a multi-bit NM-SDA scheme from a single-bit NM-SDA scheme. To achieve this goal, we define and construct a novel type of continuous non-malleable code, called secret-state NMC, since, as we show, standard continuous NMCs are insufficient for the natural “encode-then-encrypt-bit-by-bit” approach to work.

An important benchmark for multi-party computation protocols (MPC) is their round complexity. For several important MPC tasks, (tight) lower bounds on the round complexity are known. However, for some of these tasks, such as broadcast, the lower bounds can be circumvented when the termination round of every party is not a priori known, and simultaneous termination is not guaranteed. Protocols with this property are called probabilistic-termination (PT) protocols. Running PT protocols in parallel affects the round complexity of the resulting protocol in somewhat unexpected ways. For instance, an execution of m protocols with constant expected round complexity might take O(log m) rounds to complete. In a seminal work, Ben-Or and El-Yaniv (Distributed Computing '03) developed a technique for parallel execution of arbitrarily many broadcast protocols, while preserving expected round complexity. More recently, Cohen et al. (CRYPTO '16) devised a framework for universal composition of PT protocols, and provided the first composable parallel-broadcast protocol with a simulation-based proof. These constructions crucially rely on the fact that broadcast is ``privacy free,'' and do not generalize to arbitrary protocols in a straightforward way. This raises the question of whether it is possible to execute arbitrary PT protocols in parallel, without increasing the round complexity. In this paper we tackle this question and provide both feasibility and infeasibility results. We construct a round-preserving protocol compiler, secure against a dishonest minority of actively corrupted parties, that compiles arbitrary protocols into a protocol realizing their parallel composition, while having a black-box access to the underlying protocols. Furthermore, we prove that the same cannot be achieved, using known techniques, given only black-box access to the functionalities realized by the protocols, unless merely security against semi-honest corruptions is required, for which case we provide a protocol.

Commitment schemes that admit zero-knowledge proofs for relations among committed values are known as commit-and-prove functionalities or notarized envelopes. An important role in this context play equality proofs among commitments. They appear in various contexts of multi-party computation, circuit satisfiability or inclusion proofs. Using commit- and-prove functionalities admitting equality, we investigate blackbox constructions of commit-and-prove functionalities admitting more complex relations. Typically, these constructions have to create commitments to additional values to achieve a certain level of soundness. An important efficiency measure is the number of such additional commitments. We prove that, for the natural and quite general class of 3-round public-coin zero-knowledge protocols, implementing the inequality relation, or any of the relations NAND, NOR, or XOR, essentially requires at least 2n additional commitments in order to achieve a soundness of 2-n. A folklore protocol shows that this bound is tight for inequality.