Fault Tolerant Clock Synchronization

1
Fault Tolerant Clock Synchronization

• Three Algorithms
• by Lamport et. al.
• presented by
• Charles Ward and Nathan Wiegand

2
The Problem

• Synchronize clocks despite clock drift,
  arbitrary processor behaviour.

3
Two Faced Clocks
4
Mission Impossible

• Cannot achieve synchronization with 1/3 or more
  processors faulty without digital signatures.

Alice
Bob
1005
5
Naïve Approach

• The Interactive Convergence Algorithm (CNV)
• Each process reads the value of every process
  clock and sets its own clock to the average of
  these values except that if it reads a clock
  value differing from its own by more than d, then
  it replaces that value by its own clocks value
  when forming the average.

6
d 10, n 4, f 1
7
d 10, n 4, f 1
1013.75
1006.25
8
d 10, n 3, f 1
9
d 10, n 3, f 1
10
Byzantium and Her Generals

• n armies are camped outside the gates of an enemy
  city.
• Each army is commanded by a general.
• Some generals are traitors.
• Conditions
• All loyal generals will agree to retreat or
  attack.
• A small number of traitors cannot cause the loyal
  generals to adopt a bad plan.

11
Byzantium Redux

• Reformulate the problem as a single general and
  lieutenants.
• New conditions
• All loyal lieutenants decide upon the same course
  of action.
• If the commanding general is loyal then every
  loyal lieutenant obeys the order he sends.

12
Oral Messages Model

• Every sent message is correctly delivered.
• The receiver of a message knows who sent it.
• The absence of a message can be detected.

13
A Solution Using Oral Messages

• The OM(m) algorithm solves the Byzantine General
  problems for 3m1 loyal generals in the presence
  of m traitors.
• OM(0)
• General sends his value to every lieutenant.
• Each lieutenant uses the value from the general
  or retreat if he received no value.

14
Continued

• OM(m) (mgt0)
• General sends his value to every lieutenant.
• For each lieutenant i, Let vi be the value
  lieutenant i received from his general.
• Lieutenant i executes OM(m-1) with itself as the
  general using the value vi
• In executing OM(m-1) Lieutenant i receives some
  number of values (v1,vn-1) and chooses the
  majority to use.

15
Example (OM(1))
Lt. Zubmach
Lt. Wladyslaw Anders
Zdrajca
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
16
Example (OM(1))
Lt. Zubmach
Lt. Wladyslaw Anders
Zdrajca
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
17
Example (OM(1))
Lt. Zubmach
Lt. Wladyslaw Anders
Zdrajca
R,A,A
Attack! ?
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
A,R,A
18
Example 2 (OM(1))
Lt. Zubmach
Lt. Wladyslaw Anders
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
Zdrajca
19
Example 2 (OM(1))
Lt. Zubmach
Lt. Wladyslaw Anders
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
Zdrajca
20
Example 2 (OM(1))
Lt. Zubmach
Lt. Wladyslaw Anders
R,R,A
R,R,A
Retreat. ?
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
Zdrajca
R,R,A
21
Signed Message Model

• A loyal generals signature cannot be forged, and
  any alteration of the contents of his signed
  messages can be detected.
• Anyone can verify the authenticity of a generals
  signature.

22
Signed Message Algorithm SM(m)

• The SM(m) algorithm solves the Byzantine General
  problems in the presence of m traitors.
• SM(m)
• The general signs and sends his value to all
  lieutenants.
• Upon receipt of a message with value v, a
  lieutenant i
• Adds the value v to a list Vi
• If the message has fewer than m1 signatures
  (including that of the general) sign and send to
  all lieutenants who have not signed.
• After no more messages will be received, take the
  majority of values in Vi as the decision.

23
Example (SM(1))
Lt. Wladyslaw Anders
Zdrajca
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
A
24
Example (SM(1))
Lt. Wladyslaw Anders
Zdrajca
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
A
25
Example (SM(1))
Lt. Wladyslaw Anders
Zdrajca
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
A
26
Example (SM(1))
Lt. Wladyslaw Anders
Zdrajca
Attack! ?
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
A
27
Example (SM(1))
Lt. Wladyslaw Anders
R
Gen. Edward Smigly-rydz
Zdrajca
Lt. Bohdan Wronsky
A
28
Example (SM(1))
Lt. Wladyslaw Anders
R,A
R
Gen. Edward Smigly-rydz
Zdrajca
Lt. Bohdan Wronsky
A
29
Example (SM(1))
Lt. Wladyslaw Anders
R,A
Gen. Edward Smigly-rydz
Zdrajca
Lt. Bohdan Wronsky
A,R
A
30
Example (SM(1))
Lt. Wladyslaw Anders
R,A
Gen. Edward Smigly-rydz
Zdrajca
Lt. Bohdan Wronsky
A,R
31
Example (SM(1))
Lt. Wladyslaw Anders
R,A
Gen. Edward Smigly-rydz
Zdrajca
Lt. Bohdan Wronsky
A,R
32
OM and SM gt COM and CSM

• Both Byzantine Generals solutions can be modified
  for clock synchronization.
• Roughly speaking, COM(m) and CSM(m) are
  accomplished by applying, respectively, OM(m) and
  SM(m) n times.

33
COM(m)

• Each processor performs OM(m) acting as the
  general, passing clocks as messages.
• Each time a processor receives a clock
  corresponding to the execution of processor is
  algorithm it saves the clock in a list Vi.
• After all message passing is complete, processor
  j takes the median value of the list Vi as the
  clock value of processor i.
• It then sets it clock to the median of all these
  clock values.

34
Example (COM(1))
Lt. Zubmach
Lt. Wladyslaw Anders
wadliwy
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
35
Example (COM(1))
Lt. Zubmach
Lt. Wladyslaw Anders
wadliwy
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
36
Example (COM(1))
Lt. Zubmach
Lt. Wladyslaw Anders
wadliwy
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
37
CSM(m)

• Each processor performs SM(m) acting as the
  general, passing signed clocks as messages.
• Signed clocks cannot be forged or molested except
  that they can be prevented from ticking (set back
  in time).
• Each time a processor receives a clock
  corresponding to the execution of processor is
  algorithm it saves the clock in a list Vi.
• After all message passing is complete, processor
  j takes the maximum value of the list Vi as the
  clock value of processor i.
• It then sets it clock to the median of all these
  clock values.

38
Example (CSM(1))
Lt. Wladyslaw Anders
wadliwy
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
39
Example (CSM(1))
Lt. Wladyslaw Anders
wadliwy
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
40
Example (CSM(1))
Lt. Wladyslaw Anders
wadliwy
Gen. Edward Smigly-rydz
Lt. Bohdan Wronsky
41
The Simulator

• Supports fully connected network topology.
• Allows arbitrary number of processors.
• All messages and computation events (including
  clock ticks) for all processors are atomic and
  must be scheduled through the simulation event
  queue.
• No order guarantee over links.
• Messages carry arbitrary payloads.

42
Processor Class

• All processors, faulty and correct, inherit from
  a processor class.
• All processors have a clock time and a drift
  rate.
• All processors must implement processEvent()
• This limited subset of common behavior allows for
  flexibility in implementation.

43
Faulty Processors

• Four types
• Omission Fault never sends any messages.
• Bad Clock Fault performs normally but that its
  clock exceeds the admissible bounded rate of
  drift.
• Random Deviation Fault provides a value which
  deviates from its true clock value by a bounded
  random amount.
• Random Value Fault provides a random value

44
CNV 7 Procs, No Faults
45
CNV 1 Omission Fault
46
CNV 2 Omission Faults
47
CNV 3 Omission Faults
48
CNV 1 Bad Clock Fault
49
CNV 2 Bad Clock Faults
50
CNV 3 Bad Clock Faults
51
CNV 1 Random Dev. Fault
52
CNV 2 Random Dev. Faults
53
CNV 3 Random Dev. Faults
54
CNV 1 Random Faults
55
CNV 2 Random Faults
56
CNV 3 Random Faults
57
COM 7 Procs, No Faults
58
COM 1 Omission Fault
59
COM 2 Omission Faults
60
COM 3 Omission Faults
61
COM 1 Bad Clock Fault
62
COM 2 Bad Clock Faults
63
COM 3 Bad Clock Faults
64
COM 1 Random Dev. Fault
65
CSM 7 Procs, No Faults
66
CSM 1 Omission Fault
67
CSM 2 Omission Faults
68
CSM 3 Omission Faults
69
CSM 1 Bad Clock Fault
70
CSM 2 Bad Clock Faults
71
CSM 3 Bad Clock Faults
72
CSM 1 Random Dev. Fault