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

2. Introduction • Why this problem? • Computer Systems • Reliability • Security

3. Initial Conditions • ALL loyal lieutenants obey the same order. • IF commanding general is loyal EVERY loyal lieutenant obeys the order he sends.

4. Impossibility Results • Valid for oral messages • NO solution for generals < 3m+1 Commander attack attack CL2: retreat Lieutenant 1 Lieutenant 2 Fig. 1. Lieutenant as traitor

5. Commander attack retreat CL2: retreat Lieutenant 2 Lieutenant 1 Fig. 2. Commander as traitor

6. Assumptions A1. Every message is delivered correctly A2. Receiver knows the sender A3. Failure can be detected

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

8. Algorithm • OM(0) • C : sends value to allLi • Li: IF receives, use value received ELSE Retreat • OM(m), m > 0 • C : sends value to allLi • Li: IF receives, use vi ELSE Retreat Enter OM(m - 1)as commander for (n - 2) L’s • FOR each i, and each j i Lj: IF receives, use vj ELSE Retreat Li: use majority (v1, …., vn-1)

9. Demo: OM(1), L3 as traitor C OM(1) a a a L1 L2 L3 OM(0) a ? a a a ? L2 L3 L1 L3 L1 L2 L2 L1 said C said ‘a’ C said ‘a’ L3 said C said ‘?’ Result : Majority (a, a, ?) = a

10. Demo: OM(1), ‘C’as traitor C OM(1) a a r L1 L2 L3 OM(0) r a a a r a L2 L3 L1 L3 L1 L2 L2 L1 L1 said C said ‘a’ C said ‘a’ C said ‘r’ L2 said C said ‘r’ L3 said C said ‘a’ L3 said C said ‘a’ L2 Result : Majority (a, r, a) = a; L1: Majority (a, r, a) = a

11. THANK YOU! ??Questions?? Image Credit: http://zoom13.club.fr/ukindex.htm