Internet Security CSCE 813 Communicating Sequential Processes

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Internet Security CSCE 813Communicating
Sequential Processes
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Reading

• Today
• Modelling and analysis of security protocols
  Chapter 1
• Next Class
• Modelling and analysis of security protocols
  Chapter 1 and 2

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CSP Objectives

• Model dynamics
• Model and analyze concurrency
• E.g., calculation intensive systems, distributed
  applications
• Support parallelism

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CSP

• Notation for describing systems of parallel
  agents that communicate by passing messages
  between them
• Formal study of systems
• Concurrency
• Security
• Mathematical notation for describing interaction
• Different components influence each other

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CSP Components

• Processes
• Operators
• Communication visible events ?
• Invisible (internal) event ?
• CSP allows to describe the states in which
  processes might be ? allows to work out what
  actions are immediately possible for the process
  and what the result states of the actions are

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Message Passing

• Synchronous both processes MUST be ready to
  communicate
• Non-buffered sends and receives
• Explicit naming of source and destination
  processes

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Messages
Send (B, message)
Receive (A, message)
Process A
Process B
Input command ltsource-processgt ?lttarget
valuegt e.g., keyboard?m Output command
ltdestination processgt!lttarget valuegt e.g.,
screen?average
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Communication

• Process P executes and input command specifying
  process Q as its source AND
• Process Q executes an output command specifying
  process P as its destination AND
• The target variable in the input statement
  matches the value in the output statement

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Program Equivalence

• Two programs P1 and P2 are equivalent if they
  produce patterns of visible actions that cannot
  be distinguished by an observer.
• Only the communications of a program matters!

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Communication

• Prefix given a process P and a communication a
  in ?, a ? P is a program that
• Performs a then
• Behaves as P
• Given in, out in ? what is
• in ? out ? P
• Process Stop no visible or non-visible action
• Given a in ? what is a ? Stop

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Build Processes

• Consider Given a,b,c in ?
• Proc a ? b ? c ? Stop
• Proc finite succession of choices before
  stopping
• Procs environment might choose not to accepted
  any of a,b,c, so it might get stuck before Stop

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Build Processes

• Recursion processes go on forever
• Looping back to a state they have been before
• Alt to ? fro ? Alt
• Dalt to ? fro ? to ? fro ? Dalt
• Malt1 to ? Malt2
• Malt2 fro ? Malt1
• Nalt to ? fro ? Dalt
• 1, 2, 5, and (3,4) are equivalent programs

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Prefix

• Offering a single action
• Offering of choice any set of visible actions
• If A ? ? , ?x A ? P(x) represent all the
  actions in A
• x is the parameter of P -- parameters can be
  used in events or manipulated
• When a ? A is chosen, it behaves like P(a)
• Example always prepared to offer any event from
  A ? ?
• RUNA ?x A ? RUNA

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Compound events

• Coding Machine example
• CM1(s) ?x L ? off ? CM1 (s,x)
• CM1(s,off) Stop
• CM1(s,x) crypt(s,x) ? CM1(newstate(s,x)) (x ?
  L)
• Action channel name followed by zero or more
  data components
• Coding Machine example without off
• CM2(s) in?x ? out!crypt(s,x) ?
  CM2(newstate(s,x))

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Choice Operators

• Deterministic finite state machine over finite ?
• e.g., Pi ? X Ai ? Pi(x)
• Choice operator ?
• Gives the option between the actions of two
  processes then
• Behaves like the one chosen

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Choice Operator

• Example Choice
• if A B ? C then
• ?x A ? P(x) (?x B ? P(x)) ? (?x C ? P(x)
  )
• Stop and equivalence
• if A A ? Ø then
• ?x A ? P(x) (?x A ? P(x)) ? Stop
• that is P ? P ? Stop
• If B Ø then ?x B ? P(x) ? Stop

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Choice Operator

• Revisit if A B ? C then
• ?x A ? P(x) (?x B ? P(x)) ? (?x C ? P(x)
  )
• If B and C are disjoint together they give all
  the choices in A
• What happens if B and C overlap?
• Given processes P and Q, what does P ? Q mean?
• Choosing an action x ? B ? C what is the result
  of
• (?x B ? P(x)) ? (?x C ? Q(x) )
• CSP allows the implementor to make a choice
  between the two sides
• After action x, the process may behave as P(x) or
  Q(x), the environment has no control over it.

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Non-determinism

• Program acts nondeterministically if it is
  unpredictable
• The program is allowed to make internal decision
  that affect how it behaves as viewed from the
  outside
• Implementation is allowed to choose
• E.g.,
• (a ? a ? Stop) ? (a ? b ? Stop)

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Non-Deterministic Choice

• P ? Q
• behaves like P or like Q
• User has no control over which
• Can be implemented using two internal actions
• Implementer is not required to implement this way
  (can choose either P or Q or (P or Q))
• Useful for model degree of unpredictability, like
  communication medium that transmits data
  correctly or loose it.

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Non-Deterministic Choice

• P ? Q and P ? Q have identical traces sequences
  of visible communications
• In most circumstances it cannot be told whether a
  non-deterministic choice was made by observing
  the process.
• What is the difference between
• (a ? P) ? Stop and (a ? P) ? Stop ?

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Parallel Operators

• Put sequential processes parallel
• System state state of each component
• Number of possible states increases exponentially
  with the size of the network
• How to put processes together for parallel
  network?
• How to check whether such a network satisfies a
  specification?

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Parallel Combination

• Just an other process to which any of the
  previous operators can be applied.
• Each parallel process is equivalent to a
  sequential one (with infeasibly large number of
  states)
• CSP processes influence each other by affecting
  what communications they can perform.

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Parallel Combination

• Synchronize all visible actions
• P Q can perform a ? ? only when P and Q can
• (?x A ? P(x)) (?x B ? Q(x))
• ?x A? B ? (P(x) Q(x))

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Parallel Combinations

• Interfaces parallel operator P X Q
• Synchronize all events in X
• Example
• P ?x A ? P(x)
• Q ?x B ? Q(x)
• P X Q ?x X ? A ? B ? (P(x) Q(x))
• ? ?x A \ X ? (P(x) X Q)
• ? ?x B \ X ? (PX Q(x))

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Alphabet Controlled

• P X Y Q
• Each process is given control of a particular set
  of events
• No process is ever permitted to communicate
  outside of its own alphabet
• Interface between two processes intersection of
  their alphabet

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CSP Operators

• Stop process does nothing
• a ? P event prefix
• ?xA ? P event prefix choice
• P ? Q choice between two processes
• P ? Q nondeterministic choice
• P Q lockstep parallel
• P X Q interface parallel
• P X Y Q synchronizing parallel

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Next Class CSP CH 1 finishModeling security
protocols in CSP