Quorum Systems in Permissionless Networks

Fail-prone systems, and their quorum systems, are useful tools for the design of distributed algorithms. However, fail-prone systems as studied so far require every process to know the full system membership in order to guarantee safety through globally intersecting quorums. Thus, they are of little help in an open, permissionless setting, where such knowledge may not be available. We propose to generalize the theory of fail-prone systems to make it applicable to permissionless systems. We do so by enabling processes not only to make assumptions about failures, but also to make assumptions about the assumptions of other processes. Thus, by transitivity, processes that do not even know of any common process may nevertheless have intersecting quorums and solve, for example, reliable broadcast. Our model generalizes existing models such as the classic fail-prone system model [Malkhi and Reiter, 1998] and the asymmetric fail-prone system model [Cachin and Tackmann, OPODIS 2019]. Moreover, it gives a characterization with standard formalism of the model used by the Stellar blockchain

An Algebraic Model For Quorum Systems

Quorum systems are a key mathematical abstraction in distributed fault-tolerant computing for capturing trust assumptions. A quorum system is a collection of subsets of all processes, called quorums, with the property that each pair of quorums have a non-empty intersection. They can be found at the core of many reliable distributed systems, such as cloud computing platforms, distributed storage systems and blockchains. In this paper we give a new interpretation of quorum systems, starting with classical majority-based quorum systems and extending this to Byzantine quorum systems. We propose an algebraic representation of the theory underlying quorum systems making use of multivariate polynomial ideals, incorporating properties of these systems, and studying their algebraic varieties. To achieve this goal we will exploit properties of Boolean Groebner bases. The nice nature of Boolean Groebner bases allows us to avoid part of the combinatorial computations required to check consistency and availability of quorum systems. Our results provide a novel approach to test quorum systems properties from both algebraic and algorithmic perspectives.Comment: 15 pages, 3 algorithm

A Survey on Consortium Blockchain Consensus Mechanisms

Blockchain is a distributed ledger that is decentralized, immutable, and transparent, which maintains a continuously growing list of transaction records ordered into blocks. As the core of blockchain, the consensus algorithm is an agreement to validate the correctness of blockchain transactions. For example, Bitcoin is a public blockchain where each node in Bitcoin uses the Proof of Work (PoW) algorithm to reach a consensus by competing to solve a puzzle. Unlike a public blockchain, a consortium blockchain is an enterprise-level blockchain that does not contend with the issues of creating a resource-saving global consensus protocol. This paper highilights several state-of-the art solutions in consensus algorithms for enterprise blockchain. For example, the HyperLedger by Linux Foundation includes implementing Practical Byzantine Fault Tolerance (PBFT) as the consensus algorithm. PBFT can tolerate a range of malicious nodes and reach consensus with quadratic complexity. Another consensus algorithm, HotStuff, implemented by Facebook Libra project, has achieved linear complexity of the authenticator. This paper presents the operational mechanisms of these and other consensus protocols, and analyzes and compares their advantages and drawbacks.Comment: under submissio