Byzantine Generals Problem in the Light of P2P Computing

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Byzantine Generals Problem in the Light of P2P
Computing
University of Parma Department of Information
Engineering Parma, Italy

• Natalya Fedotova
• Luca Veltri
• International Workshop on Ubiquitous Access
  Control
• July 17, 2006 San Jose, California, USA

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DHT based P2P networks

• Efficient routing performance
• High scalability
• High exact-match accuracy of search
• Simple API

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DHT based P2P networks

• Main types of attacks
• Incorrect lookup routing
• Incorrect routing updates
• Partition
• Rapid joins and leaves
• Inconsistent behavior
• Storage and retrieval attack

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Byzantine Generals Problem

• Takes place in distributed computer systems in
  the presence of malfunctioning components that
  give conflicting information to other parts of
  the system
• Causes a Byzantine failure, an arbitrary fault
  that occurs during the execution of some
  algorithm by a distributed computer system, and
  as a result
• a failure to pass to the next step in the
  algorithm
• systems inability to correctly implement the
  actual algorithm
• arbitrary execution of a step different from one
  predicated by the algorithm (incorrect hops)
• Originally described by L.Lamport, R.Shostak and
  M.Pease in 1982, who were the first to apply the
  concept of BGP to distributed computer systems

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Byzantine Generals Problem the original concept

• There are n generals of Byzantine army with their
  divisions
• They have to reach an agreement on a common plan
  of action
• These generals are geographically separated and
  they have to communicate with each other through
  messengers
• Some of them are traitors

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Byzantine Generals Problem the original concept

• To cope with t traitors there must be at least
  3t 1 generals and, given the possibility for all
  generals to exchange the messages with each
  other, must exist some recursive algorithm of
  information exchange, equal for all generals, so,
  that
• all generals make the final decisions
• all loyal generals decide upon the same plan of
  action
• this final plan of loyal generals must coincide
  with final decision of one loyal general at least
  

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Byzantine Generals Problem in DHT based P2P
environment

• nodes
• misbehaving nodes
• incorrect routing information
• impossibility of efficient
• hash lookup

• generals
• traitors
• false information
• impossibility of agreement on
• a common decision

It is possible to apply some approaches used in
the case of Byzantine failure
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Byzantine Generals Problem in DHT based P2P
environment

• Problems of application
• great number of participants
• permanent joins and leaves
• one node cannot contact directly all others
• the number of messages circulating on the network
  during the process of traitor detection using the
  algorithm by Lamport, Shostak Pease is
• Nmsg (n - 1)(n 2) ... (n t 1) (n 1)!
  / t!
• increase of the traffic and the overload of the
  network

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Byzantine Generals Problem in DHT based P2P
environment

• Proposed approach
• lets consider P2P network as a number of peer
  groups individuated by some principle
• each node launches the algorithm only within its
  group, and then
• Nmsg ((ni - 1)(ni 2) ... (ni ti 1))k
• ni the average number of nodes in one group
  formed around one given node i
• ti the average number of traitors in one
  group
• k the number of groups on the network
• for small groups of peers the classical solution
  of BGP by Lamport and Shostak becomes efficient

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Possible criteria to individuate the groups

• the most frequent contacts among the nodes
• common interests
• closeness of identifiers according to
  XOR-metric

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Codat concept as one of possible mechanisms to
individuate the groups

• Codat Code Data
• originally described by JXTA platform developers
• is a unit of information shared and exchanged
  within a peer group
• means a content that could be either code or data
  and is used as a placeholder for any types of
  data
• is uniquely identified via a unique CodatID and
  can belong to only one peer group
• contains a document (a content advertisement)
  that represents the data it holds

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Diagrams of Nm change at k increased for t
1/5N (N the number of nodes in the network )
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Diagrams of Nm change at k increased for t
1/3N (N the number of nodes in the network )
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Conclusions

• it is possible to apply successfully the
  classical solutions for BGP by Lamport and
  Shostak in P2P environment
• application of these solutions helps to reduce
  the number of messages circulating on the network
• BUT
• here only completely separated groups are
  considered
• in this case we deal with the malicious node who
  demonstrates poor behavior regarding all the
  nodes

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Future work

• What other mechanisms can we use to individuate a
  group?
• How can we optimize the algorithm of the traitor
  detection process in the case of partially
  coinciding groups?
• How can we integrate the solutions we have just
  presented with some mechanisms of reputation
  evaluation?