A Complete Symbolic Bisimulation for Full Applied Pi Calculus

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A Complete Symbolic Bisimulation for Full Applied
Pi Calculus

• Jia Liu and Huimin Lin
• Institute of Software, Chinese Academy of
  Sciences
• Accepted for SOFSEM2010

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Outline

• Background
• Motivation
• Symbolic Semantics
• Conclusion

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Applied Pi Calculus

• M. Abadi and C. Fournet , 2001
• Description and analysis of cryptographic
  protocols
• Communication, Concurrency and Scope extrusion
• Primitive Functions f, enc, dec
• Equational Theory

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Syntax
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Active Substitution M/x

• x can be regarded as an alias of term M
• Floats and applies to the process coming into
  contact with it
• Partial environment knowledge
• Special mechanism for outputting compound messages

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Structural Equivalence
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Operational Semantics
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Example
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Labeled Bisimilarity

• Static Equivalence
• Labeled Bisimilarity
• Labeled bisimilarity coincides with barbed
  equivalence.

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Problem

• Automated Verification
• Infinite number of possible behaviors of the
  attacker
• Symbolic theory more amenable and efficient

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Symbolic Theory

• Symbolic Theory
• basic idea a variable with constraints
• value-passing CCS originally proposed by
  M.Hennessy and H.Lin
• Pi-Calculus by M.Boreale and R.De Nicola and
  independently by H.Lin
• Symbolic Transition Relation
• Symbolic Bisimilarity

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Symbolic Semantics for Applied Pi Calculus

• Structural Equivalence
• Unexpectedly technically difficult
• general data structure
• mobility
• mechanism of alias

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Related Work

• S. Delaune, S. Kremer and M. D. Ryan , Symbolic
  Bisimulation for the Applied Pi- Calculus,
  FSTTCS07
• Intermediate Representation
• Circumventing the difficulties caused by
• Intermediate Processes a selected but sufficient
  subset
• Bridging the gap between symbolic semantics and
  concrete semantics

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Deficiencies

• Complicated
• sound but incomplete absence of
  partition of constraints, informally,
• Finite fragment of the calculus infinitely many
  name binders

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Symbolic Semantics

• Symbolic Bisimilarity
• sound and complete w.r.t
• Infinite Fragment of Applied Pi

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Intermediate Representation
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Transformation

• transforming
  an extended process to an inter. extended process
  by
• Pulling all name binders to the top level
• Applying active substitutions
• Eliminating variable restrictions

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Transformation(cont.)

• Recursions
• Infinitely many binders
• on-the-fly

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Constraints

• Constraint

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Trails

• Trail

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Formulas

• Formulas
• Satisfiability
• for formulas to stand alone'

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Partition

• the set of substitutions which
  respect and satisfy .
• A collection of formulas is a partition of
  under if

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Symbolic Operational Semantics
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Symbolic Operational Semantics(cont.)
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Example
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Updating Trails
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Example
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Symbolic Bisimulation
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Soundness and Completeness
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Example
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Conclusion

• We have presented a general symbolic framework
  for the applied pi calculus in which a sound and
  complete notion of symbolic bisimulation is
  devised.
• Moreover, our framework accommodates recursions,
  hence our result is for the full applied
  pi-calculus.

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Thanks!