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

2. Outline
Background
Motivation
Symbolic Semantics
Conclusion

3. 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:

4. Syntax

5. 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

6. Structural Equivalence

7. Operational Semantics

8. Example

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

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

11. 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:

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

13. 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

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

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

16. Intermediate Representation

17. 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

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

19. Constraints
Constraint

20. Trails
Trail:

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

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

23. Symbolic Operational Semantics

24. Symbolic Operational Semantics(cont.)

25. Example

26. Updating Trails

27. Example

28. Symbolic Bisimulation

29. Soundness and Completeness

30. Example

31. 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.

32. Thanks!