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The Byzantine Generals Problem Leslie Lamport, Robert Shostak and Marshall Pease Presenter: Phyo Thiha Date: 4/1/2008 Introduction • Why this problem? Computer Systems Reliability Security 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 < 3m+1 Commander attack attack CL2: retreat Lieutenant 1 Lieutenant 2 Fig. 1. Lieutenant as traitor Commander attack retreat CL2: retreat Lieutenant 1 Lieutenant 2 Fig. 2. Commander as traitor Assumptions A1. Every message is delivered correctly A2. Receiver knows the sender A3. 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 (v1, …., vn-1) Demo: OM(1), L3 as traitor C a a OM(1) a L1 L2 L3 a ? OM(0) 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 Demo: OM(1), ‘C’ as traitor C a a OM(1) r L1 L2 L3 r a OM(0) a a r a L2 L3 L1 L3 L1 L2 L2 L1 said C said ‘a’ L1 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 THANK YOU! ??Questions?? Image Credit: http://zoom13.club.fr/ukindex.htm
"The Byzantine Generals Problem Leslie Lamport_ Robert Shostak "