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Quantitative information flow, relations and polymorphic types. (English) Zbl 1101.68560
Summary: 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.

MSC:
68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)
94A15 Information theory (general)
03B40 Combinatory logic and lambda calculus
68P25 Data encryption (aspects in computer science)
94A17 Measures of information, entropy
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