Reaching Agreement in the Presence of Faults

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Reaching Agreement in the Presence of Faults

• M. Pease, R. Shotak and L. Lamport

Sanjana Patel Dec 3, 2003
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Introduction

• The algorithm proposed by this paper offers the
  means by which independent processes can arrive
  at an exact mutual agreement.
• The algorithm works for greater than or equal to
  3m1 total processes (where m processes are
  faulty)

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Assumptions

• There are n isolated processes and no more than m
  are faulty
• Faulty processes need not be identified
• Processors communicate by means of two-party
  message
• The communication channel is fail-safe and has
  negligible delay
• Sender of a message is identifiable

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Goal

• Devise an algorithm based on an exchange of
  messages that allows each non-faulty process to
  compute an interactive consistency vector (of n
  values) such that
• The non-faulty processes compute the exact same
  vector
• The elements of the vector corresponding to a
  given non-faulty process is the private value of
  that process
• The above goal helps achieve interactive
  consistency
• The vector corresponding to the faulty process
  may be arbitrary as long as all non-faulty
  processes compute the exact same value for any
  faulty process

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No-Fault Case

• If there are no faults, each process will have
  the same interactive consistency vector (i.e.,
  Each process has an identical vector containing
  the private values of each process)

P1
P2
1,2,3,4
1,2,3,4
1
2
3
4
P3
P4
1,2,3,4
1,2,3,4
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Single-Fault Case

• Consider obtaining interactive consistency for
  m1 and n4
• Two rounds of information exchange are required
• Exchange private values in the first round
• Exchange results of the first round in the second
  round
• All non-faulty processes can record NIL for the
  faulty process ICV value or the majority value
  for the faulty process is used

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Single-Fault Case
P21,2,Z,4 P31,B,3,4 P41,2,Y,4
P11,2,3,4 P3A,2,Z,4 P41,2,Y,4
1
2
P1
P2
3
Z
P11,2,3,4 P31,2,Y,4 P21,2,Z,4
Y
P3
P4
1,2,3,4
4
Based on Majority, ICV used will be 1,2,NIL,4
as there is no majority value for P3 (all
processes have a different value for P3)
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M-fault Case

• m1 rounds of information exchange are required
  to obtain interactive consistency in a system of
  m faulty processes
• Either the majority or NIL is used for vector
  values
• If broadcast is used for communication from round
  2 onwards, a maximum of n(m1) messages are
  exchanged before an agreement is reached.

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Impossibility for n lt 3m1
1
P21,2,Z P31,B,3
P1
P11,2,3 P3A,2,Z
3
2
Z
P2
P3
1,2,3
There is no majority value for any of the ICV
values so no agreement can be reached.
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Algorithm using Authenticators

• The problem of reaching an agreement with n lt
  3m1 is based on the assumption that a faulty
  process may refuse to pass-on or fabricate the
  values it received from other processes
• Authentication can be used to guard against the
  above so that a faulty process may lie about its
  own value or refuse to send its own value but
  cannot relay altered values without other
  processes being able to identify it as faulty.

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Algorithm using Authenticators

• An authenticator is an argument appended to the
  data, that can be created by the sender only
• The receiver should be able to use the
  authenticator to verify the sender and that the
  value was not altered.
• Public Key/Private Key infrastructure can be used
  to achieve the above in combination with Message
  Hashing

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Example
1
P21,2,Z P31,2,3
P1
P11,2,3 P31,2,Z
3
2
Z
P2
P3
1,2,3
Since P3 cannot lie about P1 or P2s values
without reveling itself as faulty, an agreement.
ICV value of 1,2,NIL is used.
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Conclusion

• The problem of obtaining interactive consistency
  is fundamental to the design of distributed
  fault-tolerant systems
• The algorithm is needed for at least three
  aspects of design
• Synchronization of clocks
• Stabilization of input from sensors
• Agreement of results of diagnostic tests
• Preliminary research assumed that a simple
  majority was sufficient. Realization that simple
  majorities were insufficient led to the results
  reported in this paper

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QA?