Security in P2P Networks: Language Theoretic Approach

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Security in P2P Networks Language Theoretic
Approach

• Katalin Lázár
• kati_at_elte.hu
• Eötvös Loránd University
• Department of Information Systems
• Budapest, Hungary

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Content

• P2P Networks
• Language Theoretic Approach
• Outlook
• Potentials for non-combinatorial testing

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P2P Networks

• Internet is witnessing a revolution
• P2P networking
• enables true distributed computing,
• creates networks of computing resources that can
  exhibit very high availability and fault
  tolerance.
• Every entity, referred to as a peer, has equal
  status.
• A peer group is a collection of peers that have
  agreed upon a common set of services.
• Message sending.
• Pipes.

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Language Theoretic Approach

• Motivation
• Interactions between agents (peers) can be
  described by language theoretic tools
• Grammar systems theory

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Notations
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Multisets
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Multisets
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Lindenmayer Systems
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Lindenmayer Systems
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Context Conditions
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P2P Networks Language Theoretic Approach

• Language theoretic model
• network of parallel language processors
• language processors - peers
• string collections behaviour of the system
• language processors form teams, send and receive
  information through collective and individual
  filters (context conditions)

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P2P Networks Definition
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P2P Networks Definition
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Notation
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Configuration Transmission

• a state (or a configuration) of TciNMPF0L a
  system
• function configuration transmissions
• rewriting step communication step (collective
  and individual filters, their combination)
• a new string collection consists of such elements
  that are able to penetrate the output filter of
  the sender and the input filter of the receiver
• computation sequence of configuration
  transmissions

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Configuration
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Rewriting Step
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Communication Step
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TCP/IP Handshake
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TCP/IP Handshake
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TCP/IP Handshake
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TCP/IP Handshake
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SYNflood Attack
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SYNflood Attack
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SYNflood Attack
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SYNflood Attack
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Information Dynamics
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Information Dynamics
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Information Dynamics in P2P Networks

• Relationship with the growth functions of
  developmental systems, decidability problems
• The growth function is either exponential or
  polynomially bounded, which is decidable.
• The decidability of sequence and language
  equivalence problems
• it is decidable for two P2P networks whether they
  function in the same manner concerning the
  dynamics of information
• The saturation of information in P2P networks

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Information Dynamics in P2P Networks

• In theory, a well-defined input filter system
  can protect the network against overloading and
  faults stemming from the function of the system,
  in a sense that certain pieces of information are
  not allowed to penetrate the filters. Faults
  emerging during the function of the network may
  substantially influence how such a system works.
  Faults should not superpose each other. In P2P
  there is a new type of fault, its opposite is
  called trust based system.
• Simple trick motivated by Internet crawler
  experiments
• Peers have a one-step buffer, which serves for
  registering and continuously evaluating the peers
  that send faulty (e.g., delayed or erroneous) or
  faultless messages to the given peer. Trust based
  system selection of trusted friends. We found
  selection the most efficient for scale-free small
  world networks
• Good news
• The introduction of a buffer does not have an
  influence on the mathematical results regarding
  the developmental systems, since the buffer can
  be regarded as a special multiset string
  processor, whose rewritings are identical
  rewritings and messages contain some information
  about the peers that send faulty messages to the
  peer the given buffer belongs to. We call the
  buffer apprentice peer.

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Information Dynamics in P2P Networks

• Potentials of our apprentice peers
• Maintenance of long-term adaptive information
• maintenance of list of friends
• prevention of propagation of faulty information
  in the network
• concept is flexible
• generalizes beyond one-step buffers
• allows for hierarchical construction

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Outlook

• Direct importance for P2P
• P2P systems is attached to the language
  theoretical model presented.
• We described a method how an automatism can be
  built in the development of P2P systems.
• Problems of P2P
• Nowadays softwares possess all characteristics of
  complex systems and are difficult (sometimes
  impossible) to test.
• Furthermore, no compiler exists that could check
  at a higher level the logical consistency of a
  software using rule-based systems

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Outlook

• Indirect importance for P2P
• If the P2P system can be formulated as a grammar
  system, then it will be
• consistent as warranted by the grammar
• adaptive as warranted by our apprentice method
• Local testing of units (if they satisfy the
  grammar) becomes satisfactory
• avoid combinatorial explosion
• P2P system can self-optimize itself in a robust
  manner

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References

• R. Flenner et al. Java P2P Unleashed. Sams
  Publishing, 2001.
• E. Csuhaj-Varjú, A. Salomaa Networks of Parallel
  Language Processors. In Gh. Paun and A. Salomaa
  (Eds.) New Trends in Formal Languages, Control,
  Cooperation and Combinatorics. Lecture Notes in
  Computer Science, Vol. 1218, 1997, pp. 299-318.
• K. Lázár, E. Csuhaj-Varjú, A. Lorincz
  Peer-to-Peer Networks a Language Theoretic
  Approach (submitted)