Logical clocks are a fundamental tool to establish causal ordering of events in a distributed system. They have been used as the building block in weakly consistent storage systems, causally ordered broadcast, distributed snapshots, deadlock detection, and distributed system debugging. However, prior logical clock constructs fail to work in a permissionless setting with Byzantine participants. In this work, we introduce Chrono, a novel logical clock system that targets an open and decentralized network. Chrono introduces a new logical clock construct, the Decaying Onion Bloom Clock (DOBC), that scales independently to the size of the network. To tolerate Byzantine behaviors, Chrono leverages non-uniform incrementally verifiable computation (IVC) to efficiently prove and verify the construction of DOBC clocks. We have applied Chrono to build two decentralized applications, a weakly consistent key-value store and an anti-censorship social network, demonstrating the power of scalable, verifiable causality in a decentralized network.

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