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

2. Notation and Problem Statement
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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

3. 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

4. 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)

5. Illustration for Four Generals
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Illustration for Four Generals
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