54 research outputs found
Differential Privacy versus Quantitative Information Flow
Differential privacy is a notion of privacy that has become very popular in
the database community. Roughly, the idea is that a randomized query mechanism
provides sufficient privacy protection if the ratio between the probabilities
of two different entries to originate a certain answer is bound by e^\epsilon.
In the fields of anonymity and information flow there is a similar concern for
controlling information leakage, i.e. limiting the possibility of inferring the
secret information from the observables. In recent years, researchers have
proposed to quantify the leakage in terms of the information-theoretic notion
of mutual information. There are two main approaches that fall in this
category: One based on Shannon entropy, and one based on R\'enyi's min entropy.
The latter has connection with the so-called Bayes risk, which expresses the
probability of guessing the secret. In this paper, we show how to model the
query system in terms of an information-theoretic channel, and we compare the
notion of differential privacy with that of mutual information. We show that
the notion of differential privacy is strictly stronger, in the sense that it
implies a bound on the mutual information, but not viceversa
Differential Privacy: on the trade-off between Utility and Information Leakage
Differential privacy is a notion of privacy that has become very popular in
the database community. Roughly, the idea is that a randomized query mechanism
provides sufficient privacy protection if the ratio between the probabilities
that two adjacent datasets give the same answer is bound by e^epsilon. In the
field of information flow there is a similar concern for controlling
information leakage, i.e. limiting the possibility of inferring the secret
information from the observables. In recent years, researchers have proposed to
quantify the leakage in terms of R\'enyi min mutual information, a notion
strictly related to the Bayes risk. In this paper, we show how to model the
query system in terms of an information-theoretic channel, and we compare the
notion of differential privacy with that of mutual information. We show that
differential privacy implies a bound on the mutual information (but not
vice-versa). Furthermore, we show that our bound is tight. Then, we consider
the utility of the randomization mechanism, which represents how close the
randomized answers are, in average, to the real ones. We show that the notion
of differential privacy implies a bound on utility, also tight, and we propose
a method that under certain conditions builds an optimal randomization
mechanism, i.e. a mechanism which provides the best utility while guaranteeing
differential privacy.Comment: 30 pages; HAL repositor
Measuring Information Leakage using Generalized Gain Functions
International audienceThis paper introduces g-leakage, a rich general- ization of the min-entropy model of quantitative information flow. In g-leakage, the benefit that an adversary derives from a certain guess about a secret is specified using a gain function g. Gain functions allow a wide variety of operational scenarios to be modeled, including those where the adversary benefits from guessing a value close to the secret, guessing a part of the secret, guessing a property of the secret, or guessing the secret within some number of tries. We prove important properties of g-leakage, including bounds between min-capacity, g-capacity, and Shannon capacity. We also show a deep connection between a strong leakage ordering on two channels, C1 and C2, and the possibility of factoring C1 into C2 C3 , for some C3 . Based on this connection, we propose a generalization of the Lattice of Information from deterministic to probabilistic channels
A Quantitative Information Flow Analysis of the Topics API
Third-party cookies have been a privacy concern since cookies were first
developed in the mid 1990s, but more strict cookie policies were only
introduced by Internet browser vendors in the early 2010s. More recently, due
to regulatory changes, browser vendors have started to completely block
third-party cookies, with both Firefox and Safari already compliant.
The Topics API is being proposed by Google as an additional and less
intrusive source of information for interest-based advertising (IBA), following
the upcoming deprecation of third-party cookies. Initial results published by
Google estimate the probability of a correct re-identification of a random
individual would be below 3% while still supporting IBA.
In this paper, we analyze the re-identification risk for individual Internet
users introduced by the Topics API from the perspective of Quantitative
Information Flow (QIF), an information- and decision-theoretic framework. Our
model allows a theoretical analysis of both privacy and utility aspects of the
API and their trade-off, and we show that the Topics API does have better
privacy than third-party cookies. We leave the utility analyses for future
work.Comment: WPES '23 (to appear
A Formal Model for Polarization under Confirmation Bias in Social Networks
We describe a model for polarization in multi-agent systems based on Esteban
and Ray's standard family of polarization measures from economics. Agents
evolve by updating their beliefs (opinions) based on an underlying influence
graph, as in the standard DeGroot model for social learning, but under a
confirmation bias; i.e., a discounting of opinions of agents with dissimilar
views. We show that even under this bias polarization eventually vanishes
(converges to zero) if the influence graph is strongly-connected. If the
influence graph is a regular symmetric circulation, we determine the unique
belief value to which all agents converge. Our more insightful result
establishes that, under some natural assumptions, if polarization does not
eventually vanish then either there is a disconnected subgroup of agents, or
some agent influences others more than she is influenced. We also prove that
polarization does not necessarily vanish in weakly-connected graphs under
confirmation bias. Furthermore, we show how our model relates to the classic
DeGroot model for social learning. We illustrate our model with several
simulations of a running example about polarization over vaccines and of other
case studies. The theoretical results and simulations will provide insight into
the phenomenon of polarization.Comment: arXiv admin note: substantial text overlap with arXiv:2104.11538,
arXiv:2012.0270
A novel analysis of utility in privacy pipelines, using Kronecker products and quantitative information flow
We combine Kronecker products, and quantitative information flow, to give a
novel formal analysis for the fine-grained verification of utility in complex
privacy pipelines. The combination explains a surprising anomaly in the
behaviour of utility of privacy-preserving pipelines -- that sometimes a
reduction in privacy results also in a decrease in utility. We use the standard
measure of utility for Bayesian analysis, introduced by Ghosh at al., to
produce tractable and rigorous proofs of the fine-grained statistical behaviour
leading to the anomaly. More generally, we offer the prospect of
formal-analysis tools for utility that complement extant formal analyses of
privacy. We demonstrate our results on a number of common privacy-preserving
designs
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