byzantine fault tolerance in stateful web service yilei zhang 30/10/2009
TRANSCRIPT
Byzantine Fault Tolerance in Stateful Web Service
Yilei ZHANG
30/10/2009
Outline
Byzantine generals problem BFT in Stateful Web service
Once upon a time...
The pictures are taken from: R. Goscinny and A. Uderzo, Asterix and Latraviata.
Communicating only by messenger
Generals must agree upon a common battle plan
Some of them may be traitors who will try to confuse the others
several divisions of the Byzantine army each commanded by its own general
Byzantine generals problem
Find an algorithm to ensure that: A. All loyal generals decide upon the same plan of
action. (consistent agreement) B. A small number of traitors cannot cause the
loyal generals to adopt a bad plan. (reasonable plan)
Notation vi: message sent by general i. n: number of generals. f: number of traitors.
Byzantine generals problem
Condition A: All loyal generals decide upon the same plan of action. (consistent agreement)
For condition A to be satisfied, the following must be true: 1. Every loyal general must obtain the same information v1 .
. . . , vn. 2. If the ith general is loyal, then the value that he sends m
ust be used by every loyal general as the value of vi.
Byzantine generals problem
To hold condition 1 & 2, how does a single general send his value to the others?
Remodeled as a commanding general sending an order to his lieutenants: IC1. All loyal lieutenants obey the same order. IC2. If the commanding general is loyal, then every loyal lie
utenant obeys the order he sends.
If n<3f+1, then there is no solution
Example: Poor Lieutenant 1’s Dilemma
Lieutenant 1
Attack
Attack
He said retreatLieutenant 2 (Traitor)
Commander
Lieutenant 1
Attack
Retreat
He said retreatLieutenant 2
Commander (Traitor)
The two situations are identical to me!
IC1 violated !
Attack Retreat
BFT
Solution for more than 3f+1 generals with f traitors Assumptions
A1. Every message that is sent is delivered correctly. A2. The receiver of a message knows who sent it. A3. The absence of a message can be detected.
Function 'majority': With the property that if a majority of the values vi equals v, then
majority(v1,...,vn-1) equals v. Order set Vi
Each lieutenant uses it to store orders from others Algorithm OM(m) can deal with m traitors
Defined recursively
Base case: OM(0)
Lieutenant i
atta
ckattack
Lieutenant k
Commander 0
Lieutenant j
attack
Commander sends messages to LieutenantsEach Lieutenant receives and records it.
Vi ={v0:attack} Vi ={v0:attack} Vi ={v0:attack}
OM(m)
Lieutenant i
attac
kattack
Lieutenant k
Commander
Lieutenant j
attack
……
attack
Each Lieutenant act as the commander in OM(m-1)Send messages to ‘his’ LieutenantsDo this recursively
attack
attack
Step 3: Majority Vote
Lieutenant 1 Lieutenant n-1
Commander
Lieutenant 2
My decision is: majority(v1,v2,…,v_n-1)
……
Me tooMe too
For any m, Algorithm OM(m) satisfies conditions IC1 and IC2 if there are more than 3m generals and at most m traitors
OM(1): Lieutenant 3 is a traitor
Lieutenant 1
Attack
Attack
Lieutenant 3 (Traitor)
Commander
Lieutenant 2
Attack
Attack
Attack
Retreat
Attack
Attack
Attack
Majority(attack,attack,attack)=attack Majority(attack,attack,retreat)
=attack
IC1 achievedIC2 achieved
OM(1): Commander is a traitor
Lieutenant 1
Attack
Retreat
IC1 achievedIC2 need not be satisfied
Lieutenant 3
Commander (Traitor)
Lieutenant 2
Attack
Retreat
Attack Retreat
Retreat Retreat
Retreat
Majority(attack,retreat,retreat)=retreat Majority(attack,retreat,retreat)
=retreat
Majority(attack,retreat,retreat)=retreat
BFT in stateful Web service
Voting center (a, b, a, c)->a
Majority voting 1: (a, a, a, b)->a 3: (a, b, a, b)->a/b 4: (a, b, a, b)->a/b
BFT 1: (a, x, a, b)->a 3: (a, x, a, b)->a 4: (a, x, a, b)->a