Distributed Protocols with Threshold and General Trust Assumptions

Distributed systems today power almost all online applications. Consequently, a wide range of distributed protocols, such as consensus, and distributed cryptographic primitives are being researched and deployed in practice. This thesis addresses multiple aspects of distributed protocols and cryptographic schemes, enhancing their resilience, efficiency, and scalability. Fundamental to every secure distributed protocols are its trust assumptions. These assumptions not only measure a protocol's resilience but also determine its scope of application, as well as, in some sense, the expressiveness and freedom of the participating parties. Dominant in practice is so far the threshold setting, where at most some f out of the n parties may fail in any execution. However, in this setting, all parties are viewed as identical, making correlations indescribable. These constraints can be surpassed with general trust assumptions, which allow arbitrary sets of parties to fail in an execution. Despite significant theoretical efforts, relevant practical aspects of this setting are yet to be addressed. Our work fills this gap. We show how general trust assumptions can be efficiently specified, encoded, and used in distributed protocols and cryptographic schemes. Additionally, we investigate a consensus protocol and distributed cryptographic schemes with general trust assumptions. Moreover, we show how the general trust assumptions of different systems, with intersecting or disjoint sets of participants, can be composed into a unified system. When it comes to decentralized systems, such as blockchains, efficiency and scalability are often compromised due to the total ordering of all user transactions. Guerraoui (Distributed Computing, 2022) have contradicted the common design of major blockchains, proving that consensus is not required to prevent double-spending in a cryptocurrency. Modern blockchains support a variety of distributed applications beyond cryptocurrencies, which let users execute arbitrary code in a distributed and decentralized fashion. In this work we explore the synchronization requirements of a family of Ethereum smart contracts and formally establish the subsets of participants that need to synchronize their transactions. Moreover, a common requirement of all asynchronous consensus protocols is randomness. A simple and efficient approach is to employ threshold cryptography for this. However, this necessitates in practice a distributed setup protocol, often leading to performance bottlenecks. Blum (TCC 2020) propose a solution bypassing this requirement, which is, however, practically inefficient, due to the employment of fully homomorphic encryption. Recognizing that randomness for consensus does not need to be perfect (that is, always unpredictable and agreed-upon) we propose a practical and concretely-efficient protocol for randomness generation. Lastly, this thesis addresses the issue of deniability in distributed systems. The problem arises from the fact that a digital signature authenticates a message for an indefinite period. We introduce a scheme that allows the recipients to verify signatures, while allowing plausible deniability for signers. This scheme transforms a polynomial commitment scheme into a digital signature scheme