Abstract
We examine the use of model-checking in the analysis of information leakage in social networks. We take previous work on the formal analysis of digital crowds and show how a variation on the formalism can naturally model the interaction of people and groups of followers in intersecting social networks. We then show how probabilistic models of the forwarding and reposting behaviour of individuals can be used to analyse the risk that information will leak to unwanted parties. We illustrate our approach by analysing several simple examples.
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Notes
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Though note that these could be included.
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In [25], the formulas \(M^{\uparrow i} \varphi \) and \(M^{\downarrow i}\varphi \) have also subscripts that denote the nature of the communication, i.e., whether it expresses a question, a statement, or an order, but we here only use statements and thus omit subscripts.
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Prism allows models to be created as Discrete Time Markov Chains (DTMCs), Continuous Time Markov Chains (CTMCs) and Markov Decisions Procedures (MDPs). Since our models had no continuous or non-deterministic aspects that would have required more complex models we opted to use the simplest of these (DTMCs) in modelling. We opted for a representation based on Markov Chains since they capture stochastic processes well and it seemed plausible that models of information leakage in social networks might need to be cyclic. If the possibility of cyclic models could be ruled out then Bayesian Networks would also be a plausible candidate formalism.
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We use the notation \(P^{=n}\) to indicate that there is a probability of n that something will occur.
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Acknowledgments
This work was partially funded through EPSRC Grants EP/L024845 (“Verifiable Autonomy”) and EP/N007565 (“Science of Sensor System Software”). The authors would also like to thank Dagstuhl for their facilities and hospitality, something that provided the impetus for this work.
Access to Data. The Prism models used in this work will are available in the University of Liverpool’s Data Catalogue at DOI:10.17638/datacat.liverpool.ac.uk/163.
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Dennis, L.A., Slavkovik, M., Fisher, M. (2017). “How Did They Know?”—Model-Checking for Analysis of Information Leakage in Social Networks. In: Cranefield, S., Mahmoud, S., Padget, J., Rocha, A. (eds) Coordination, Organizations, Institutions, and Norms in Agent Systems XII. COIN COIN 2016 2016. Lecture Notes in Computer Science(), vol 10315. Springer, Cham. https://doi.org/10.1007/978-3-319-66595-5_3
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