Byzantine Faults definition and problem statement impossibility 1/3/2019 Byzantine Faults definition and problem statement impossibility solution

Notation and Problem Statement 1/3/2019 Notation and Problem Statement from “The Byzantine Generals Problem” Lamport, Shostak and Pease, ACM transactions on Programming Languages and Systems 4(3), 1982 each general (process) may be either loyal (correct) or traitorous (faulty) one process is a leader (commanding general) who sends two types of orders: attack and retreat message communication, completely connected network, synchronous - absence of message can be detected oral record – no cryptography, each process knows which process the message came from, faulty process cannot interfere with communication of correct processes problem – a commanding general must send an order to n-1 generals such that all lieutenants decide on the order to obey all loyal lieutenants decide on the same order if the commanding general is loyal, then every loyal lieutenant obeys the order he sends

1/3/2019 Impossibility no solution for three generals can handle a single traitor generalization: no solution with fewer than 3m+1 generals can cope with m traitors

Solution number of faults m, total number of generals is at least 3m+1 1/3/2019 Solution number of faults m, total number of generals is at least 3m+1 default value is RETREAT commanding general executes OM(0), after that, each commander i sequentially executes OM(i)

Illustration for Four Generals 1/3/2019 Illustration for Four Generals blah