A Complete Symbolic Bisimulation for Full Applied Pi Calculus Jia Liu and Huimin Lin Institute of Software, Chinese Academy of Sciences Accepted for SOFSEM2010

Outline Background Motivation Symbolic Semantics Conclusion

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:

Syntax

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

Structural Equivalence

Operational Semantics

Example

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

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

Symbolic Theory Symbolic Theory Symbolic Transition Relation: 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:

Symbolic Semantics for Applied Pi Calculus Structural Equivalence Unexpectedly technically difficult general data structure mobility mechanism of alias

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

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

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

Intermediate Representation

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

Transformation(cont.) Recursions Infinitely many binders “on-the-fly”

Constraints Constraint

Trails Trail:

Formulas Formulas Satisfiability for formulas to ``stand alone'‘

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

Symbolic Operational Semantics

Symbolic Operational Semantics(cont.)

Example

Updating Trails

Example

Symbolic Bisimulation

Soundness and Completeness

Example

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.

Thanks!