Quorum systems are a key abstraction in distributed fault-tolerant computing for capturing trust assumptions. They can be found at the core of many algorithms for implementing reliable broadcasts, shared memory, consensus and other problems. This paper introduces asymmetric Byzantine quorum systems that model subjective trust. Every process is free to choose which combinations of other processes it trusts and which ones it considers faulty. Asymmetric quorum systems strictly generalize standard Byzantine quorum systems, which have only one global trust assumption for all processes. This work also presents protocols that implement abstractions of shared memory and broadcast primitives with processes prone to Byzantine faults and asymmetric trust. The model and protocols pave the way for realizing more elaborate algorithms with asymmetric trust.
The also features open membership and lets every node express its own set of trusted nodes @cite_22 . Generalizing from Ripple's flat lists of unique nodes, every node declares a collection of trusted sets called , whereby a slice is the subset of a quorum convincing one particular node of agreement.'' A in Stellar is a set of nodes sufficient to reach agreement,'' defined as a set of nodes that contains one slice for each member node. The quorum choices of all nodes together yield a . The Stellar white paper states properties of FBQS and protocols that build on them. However, these protocols do not map to known protocol primitives in distributed computing.
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While several consensus algorithms exist for the Byzantine Generals Problem, specifically as it pertains to distributed payment systems, many suffer from high latency induced by the requirement that all nodes within the network communicate synchronously. In this work, we present a novel consensus algorithm that circumvents this requirement by utilizing collectively-trusted subnetworks within the larger network. We show that the “trust” required of these subnetworks is in fact minimal and can be further reduced with principled choice of the member nodes. In addition, we show that minimal connectivity is required to maintain agreement throughout the whole network. The result is a low-latency consensus algorithm which still maintains robustness in the face of Byzantine failures. We present this algorithm in its embodiment in the Ripple Protocol.