Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out

The Byzantine Generals Problem Leslie Lamport_ Robert Shostak

VIEWS: 6 PAGES: 11

									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


                        CL2: retreat
   Lieutenant 1                                   Lieutenant 2

                  Fig. 1. Lieutenant as traitor
                    Commander


      attack                             retreat




                    CL2: 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

								
To top