Trustworthy Systems

Additive and multiplicative notions of leakage, and their capacities


Carroll Morgan, Mário Alvim, Konstantinos Chatzikokolakis, Annabelle McIver, Catuscia Palamidessi and Geoffrey Smith




Macquarie University

Winner of the 2015 NSA Best Scientific Cybersecurity Paper Award


Protecting sensitive information from improper disclosure is a fundamental security goal. It is complicated, and difficult to achieve, often because of unavoidable or even unpredictable operating conditions that can lead to breaches in planned security defences. An attractive approach is to frame the goal as a quantitative problem, and then to design methods that measure system vulnerabilities in terms of the amount of information they leak. A consequence is that the precise operating conditions, and assumptions about prior knowledge, can play a crucial role in assessing the severity of any measured vunerability.

We develop this theme by concentrating on vulnerability measures that are robust in the sense of allowing general leakage bounds to be placed on a program, bounds that apply whatever its operating conditions and whatever the prior knowledge might be. In particular we propose a theory of channel capacity, generalising the Shannon capacity of information theory, that can apply both to additive- and to multiplicative forms of a recently- proposed measure known as g-leakage. Further, we explore the computational aspects of calculating these (new) capacities: one of these scenarios can be solved efficiently by expressing it as a Kantorovich distance, but another turns out to be NP-complete.

We also find capacity bounds for arbitrary correlations with data not directly accessed by the channel, as in the scenario of Dalenius’s Desideratum.

BibTeX Entry

    address          = {{Vienna}, {Austria}},
    author           = {Morgan, Carroll and Alvim, Mário and Chatzikokolakis, Konstantinos and McIver, Annabelle and
                        Palamidessi, Catuscia and Smith, Geoffrey},
    booktitle        = {{Computer} {Security} {Foundations}},
    keywords         = {quantitative information flow, channel capacity, confidentiality, dalenius desideratum},
    month            = jul,
    pages            = {308--322},
    paperurl         = {},
    title            = {Additive and multiplicative notions of leakage, and their capacities},
    year             = {2014}