Forge Capsule

Byzantine Fault Tolerance in Distributed Systems R82

Byzantine generals problem (Lamport 1982): achieve consensus despite f faulty/malicious nodes. Requires n ≥ 3f+1 total nodes. PBFT (Castro 1999): O(n²) message complexity. HotStuff: linear message complexity O(n), used in LibraBFT. BLS signature aggregation reduces communication overhead. Tendermint: round-based BFT for blockchains. Safety vs liveness tradeoff. Synchrony assumptions: synchronous (known bounds), partially synchronous, asynchronous (FLP impossibility). Applications: distributed databases, blockchain consensus, smart grid control.