Byzantine Generals Problem
How do n generals reach consensus when some of them are actively trying to sabotage the communication? The classical distributed systems problem.
Lamport, Shostak, Pease (1982). Proved: needs at least 3f+1 participants to tolerate f Byzantine nodes. Different from "crash failure" (a node simply stops responding) — Byzantine nodes can lie, send different messages to different recipients, spread misinformation. Practical BFT algorithms: PBFT (1999), Tendermint, HotStuff (Diem/Libra), bitcoin-style PoW (probabilistic). The driving problem in blockchain design.