Download presentation

Presentation is loading. Please wait.

Published byKenyon Halliwill Modified over 2 years ago

1
Byzantine Generals

2
Outline r Byzantine generals problem

3
Introduction r Coping with failures in computer systems r Failed component sends conflicting information to different parts of system. r Agreement in the presence of faults. r P2P Networks? Good nodes have to “ agree to do the same thing ”. m Faulty nodes generate corrupted and misleading messages. m Non-malicious: Software bugs, hardware failures, power failures m Malicious reasons: Machine compromised.

4
Problem Definition

5
r Generals = Computer Components r The abstract problem… m Each division of Byzantine army is directed by its own general. m There are n Generals, some of which are traitors. m All armies are camped outside enemy castle, observing enemy. m Communicate with each other by messengers. m Requirements: G1: All loyal generals decide upon the same plan of action G2: A small number of traitors cannot cause the loyal generals to adopt a bad plan m Note: We do not have to identify the traitors.

6
Reduction of General Problem Byzantine Generals Problem (BGP): m A commanding general (commander) must send an order to his n-1 lieutenants. r Interactive Consistency Conditions: m IC1: All loyal lieutenants obey the same order. m IC2: If the commanding general is loyal, then every loyal lieutenant obeys the order he sends. r Note: If General is loyal, IC2 => IC1.

7
3-General Impossibly Example r 3 generals, 1 traitor among them. r Two messages: Attack (A) or Retreat (R) r Shaded – Traitor r L1 sees (A,R). Who is the traitor? C or L2? r Fig 1: L1 has to attack to satisfy IC2. r Fig 2: L1 attacks, L2 retreats. IC1 violated.

8
General Impossibility r In general, no solutions with fewer than 3m+1 generals can cope with m traitors. r Proof by contradiction. m Assume there is a solution for 3m Generals with m traitors. m Reduce to 3-General problem.

9
Solution I – Oral Messages r If there are 3m+1 generals, solution allows up to m traitors. r Oral messages – the sending of content is entirely under the control of sender. r Assumptions on oral messages: m A1 – Each message that is sent is delivered correctly. m A2 – The receiver of a message knows who sent it. m A3 – The absence of a message can be detected. r Assumes: m Traitors cannot interfere with communication as third party. m Traitors cannot send fake messages m Traitors cannot interfere by being silent. Default order to “ retreat ” for silent traitor.

10
Oral Messages (Cont) r Algorithm OM(0) m Commander send his value to every lieutenant. m Each lieutenant (L) use the value received from commander, or RETREAT if no value is received. r Algorithm OM(m), m>0 1. Commander sends his value to every Lieutenant (v i ) 2. Each Lieutenant acts as commander for OM(m-1) and sends v i to the other n-2 lieutenants (or RETREAT) 3. For each i, and each j<>i, let v j be the value lieutenant i receives from lieutenant j in step (2) using OM(m-1). Lieutenant i uses the majority of (v 1, …, v n-1 ). 4. Why j<>i? “ Trust myself more than what others said I said. ”

11
Restate Algorithm r OM(M): m Commander sends out command. m Each lieutenant acts as commander in OM(m-1). Sends out command to other lieutenants. m Use majority to compute value based on commands received by other lieutenants in OM(m- 1) r Revisit Interactive Consistency goals: m IC1: All loyal lieutenants obey the same command. m IC2: If the commanding general is loyal, then every loyal lieutenant obeys the command he sends.

12
Example (n=4, m=1, L3 is traitor) C L1L2L3 v v v r In OM(1) Commander (C) sends command to L1, L2,L3

13
Example (n=4, m=1, L3 is traitor) C L1L2L3 v v r In OM(0) L1 sends command to L2,L3

14
Example (n=4, m=1, L3 is traitor) C L1L2L3 v v r In OM(0) L2 sends command to L1,L3

15
Example (n=4, m=1, L3 is traitor) C L1L2L3 x v r In OM(0) L3 sends command to L1,L2

16
Example (n=4, m=1, L3 is faulty) r L1 m L1 receives “v” from commander “v” from L2 “v” from L3 m Majority(v,v,x) is v r L2 m L2 receives “v” from commander “v” from L1 “x” from L3 m Majority(v,v,x) is v

17
Example (n=4, m=1, C is traitor) C L1L2L3 x y z r In OM(1) Commander (C) sends command to L1, L2,L3

18
Example (n=4, m=1, C is traitor) C L1L2L3 x x r In OM(0) L1 sends command to L2,L3

19
Example (n=4, m=1, C is traitor) C L1L2L3 y y r In OM(0) L2 sends command to L1,L3

20
Example (n=4, m=1, C is traitor) C L1L2L3 z z r In OM(0) L3 sends command to L1,L2

21
Example (n=4, m=1, C is faulty) r L1 m L1 receives “x” from commander “y” from L2 “z” from L3 m Majority(x,y,z) is default value r L2 m L2 receives “y” from commander “x” from L1 “z” from L3 m Majority(x,y,z) is default value

22
Example (n=4, m=1, L3 is faulty) r L1, L2,L3 satisfy IC1 r IC2 is irrelevant since commander is traitor

23
Expensive Communication r OM(m) invokes n-1 OM(m-1) r OM(m-1) invokes n-2 OM(m-2) r OM(m-2) invokes n-3 OM(m-3) r … r OM(m-k) will be called (n-1)…(n-k) times r O(n m ) – Expensive!

24
Problem r Lots of messages required to handle even 1 faulty process r Need minimum 4 processes to handle 1 fault, 7 to handle 2 faults, etc. m But as system gets larger, probability of a fault also increases r If we use signed messages, instead of oral messages, can handle f faults with 2f+1 processes m Simple majority requirement m Still lots of messages sent though, plus cost of signing

25
Summary r BGP solutions are expensive (communication overheads and signatures) r Use of redundancy and voting to achieve reliability. What if >1/3 nodes (processors) are faulty? r 3m+1 replicas for m failures. Is that expensive? Tradeoffs between reliability and performance (E.g. Oceanstore ’ s primary and secondary replicas) r How would you determine m in a practical system?

Similar presentations

OK

The Byzantine Generals Problem L. Lamport R. Shostak M. Pease Presented by: Emmanuel Grumbach Raphael Unglik January 2004.

The Byzantine Generals Problem L. Lamport R. Shostak M. Pease Presented by: Emmanuel Grumbach Raphael Unglik January 2004.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on symbols of french revolution Ppt on microcontroller based digital thermometer Ppt on track feed battery charger Ppt on healthy food and healthy living Ppt on line drawing algorithms Ppt on new technology free download Ppt on federalism in india Ppt on folk dances of india Download ppt on historical monuments in india Ppt on acute coronary syndrome ppt