The Byzantine Generals Problem Leslie Lamport, Robert Shostak and Marshall Pease

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.

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Impossibility Results

• Valid for oral messages
• NO solution for generals lt 3m1

Commander
attack
attack
C?L2 retreat
Lieutenant 1
Lieutenant 2
Fig. 1. Lieutenant as traitor
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Commander
attack
retreat
Lieutenant 2
C?L2 retreat
Lieutenant 1
Fig. 2. Commander as traitor
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Assumptions

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

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Majority Rule

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

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Algorithm

• OM(0)
• C sends value to all Li
• Li IF receives, use value received
• ELSE Retreat
• OM(m), m gt 0
• C sends value to all Li
• Li IF receives, use vi
• ELSE Retreat
• Enter OM(m - 1) as commander for (n - 2) Ls
• FOR each i, and each j ? i
• Lj IF receives, use vj
• ELSE Retreat
• Li use majority (v1, ., vn-1)

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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
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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
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THANK YOU! ??Questions??

• Image Credit http//zoom13.club.fr/ukindex.htm