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Table of contents
1 Introduction
1.1 Concurrent and Probabilistic Processes
1.2 Differential Privacy
1.3 This thesis: Differential Privacy in Concurrent Systems
1.3.1 Modular reasoning
1.3.2 Bisimulations for differential privacy
1.3.3 Complete proof systems
1.3.4 Generalized bisimulation metrics
1.4 Plan of the Thesis and Contributions
1.5 Publications
2 Preliminaries
2.1 Probability Spaces
2.2 Probabilistic Automata
2.3 Probabilistic Process Algebra
2.4 Probabilistic bisimilarity
2.5 Pseudometrics
2.6 Differential Privacy
3 Modular Reasoning in a Probabilistic Process Calculus
3.1 Preliminaries
3.1.1 CCSp with secret labels
3.1.2 Process terms as channels
3.1.3 Differential Privacy in CCSp with secret labels
3.1.4 The Crowds protocol
3.1.5 Relation between differential privacy and anonymity
3.2 Modular Reasoning
3.3 Trust and Legitimacy in Crowds
3.3.1 Examples
3.3.2 The CCSp code for the extended Crowds protocol
3.3.3 An anonymity-preservation property
3.4 Degradation of privacy by trust
3.4.1 An adjacency relation based on trust
3.4.2 False negatives in Theorem 3.3.2
3.5 Users’ preference levels in Crowds
3.6 Related work
3.7 Conclusion
4 Bisimulations for Differential Privacy
4.1 Preliminaries
4.1.1 Admissible scheduler
4.1.2 Differential privacy under admissible scheduler
4.2 The accumulative bisimulation
4.3 The amortised bisimulation
4.4 Comparing the two bisimulations
4.4.1 Relations with conventional probabilistic bisimilarity
4.5 Congruence
4.6 An application to the Dining Cryptographers Protocol
4.7 Conclusion
5 Complete Proof Systems for Amortised Probabilistic Bisimulations
5.1 A simple probabilistic process algebra
5.2 Amortised probabilistic bisimulation
5.2.1 Basic properties
5.3 Weak amortised probabilistic bisimulation
5.3.1 Basic properties of 4
5.3.2 Amortised observational congruence
5.4 Proof system A1 for amortised bisimulation
5.5 Proof system A2 for amortised observational congruence
5.6 Conclusion
6 Generalized Bisimulation Metrics
6.1 Preliminaries
6.2 A general family of Kantorovich liftings
6.3 A general family of bisimilarity pseudometrics
6.3.1 Bisimilarity as 0-distance
6.3.2 Relation with trace distributions
6.4 The multiplicative variant
6.4.1 Transformations of the linear-fractional program
6.4.2 Application to differential privacy
6.5 Non-expansiveness
6.6 Conclusion
7 Conclusion
Bibliography
Index
