The Byzantine Generals Problem Leslie Lamport Robert Shostak

The Byzantine Generals Problem Leslie Lamport, Robert Shostak and Marshall Pease Presenter: Phyo Thiha Date: 4/1/2008

Introduction • Why this problem? § Computer Systems üReliability üSecurity

Initial Conditions 1. ALL loyal lieutenants obey the same order. 2. IF commanding general is loyal EVERY loyal lieutenant obeys the order he sends.

Impossibility Results • Valid for oral messages • NO solution for generals < 3 m+1 Commander attack C L 2: retreat Lieutenant 1 Lieutenant 2 Fig. 1. Lieutenant as traitor

Commander attack retreat C L 2: retreat Lieutenant 1 Lieutenant 2 Fig. 2. Commander as traitor

Assumptions A 1. Every message is delivered correctly A 2. Receiver knows the sender A 3. Failure can be detected

Majority Rule 1. Choose the majority value, if exists Else Retreat 2. IF from an ordered set, choose the Median

Algorithm • OM(0) 1) C : sends value to all Li 2) Li : IF receives, use value received ELSE Retreat • OM(m), m > 0 1) C : sends value to all Li 2) Li : IF receives, use vi ELSE Retreat Enter OM(m - 1) as commander for (n - 2) L’s 3) FOR each i, and each j i Lj : IF receives, use vj ELSE Retreat Li : use majority (v 1, …. , vn-1)

Demo: OM(1), L 3 as traitor C a L 1 a L 2 L 2 a L 3 a L 1 OM(1) a a L 3 L 1 said C said ‘a’ L 3 said C said ‘? ’ Result : Majority (a, a, ? ) = a OM(0) ? ? L 1 L 2

Demo: OM(1), ‘C’ as traitor C a L 1 a L 2 a L 3 L 2 r L 1 said C said ‘a’ C said ‘r’ L 3 said C said ‘a’ L 2 Result : Majority OM(1) a r L 3 L 1 OM(0) a a L 1 L 2 C said ‘a’ L 2 said C said ‘r’ L 3 said C said ‘a’ (a, r, a) = a; L 1 : Majority (a, r, a) = a

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