Quantitative Information Flow, Relations and Polymorphic Types

David Clark, Sebastian Hunt, Pasquale Malacaria

Research output: Contribution to journalArticlepeer-review

105 Citations (Scopus)


This paper uses Shannon's information theory to give a quantitative definition of information flow in systems that transform inputs to outputs. For deterministic systems, the definition is shown to specialize to a simpler form when the information source and the known inputs jointly determine all inputs uniquely. For this special case, the definition is related to the classical security condition of non-interference and an equivalence is established between non-interference and independence of random variables. Quantitative information flow for deterministic systems is then presented in relational form. With this presentation, it is shown how relational parametricity can be used to derive upper and lower bounds on information flows through families of functions defined in the second-order lambda calculus.
Original languageEnglish
Pages (from-to)181-199
Number of pages19
JournalJournal of Logic and Computation
Issue number2
Publication statusPublished - Apr 2005


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