Krzysztof Grining

Dominik Bojko, Krzysztof Grining, Marek Klonowski

Probabilistic counters are well-known tools often used for space-efficient set cardinality estimation. In this paper, we investigate probabilistic counters from the perspective of preserving privacy. We use the standard, rigid differential privacy notion. The intuition is that the probabilistic counters do not reveal too much information about individuals but provide only general information about the population. Therefore, they can be used safely without violating the privacy of individuals. However, it turned out, that providing a precise, formal analysis of the privacy parameters of probabilistic counters is surprisingly difficult and needs advanced techniques and a very careful approach. We demonstrate that probabilistic counters can be used as a privacy protection mechanism without extra randomization. Namely, the inherent randomization from the protocol is sufficient for protecting privacy, even if the probabilistic counter is used multiple times. In particular, we present a specific privacy-preserving data aggregation protocol based on Morris Counter and MaxGeo Counter. Some of the presented results are devoted to counters that have not been investigated so far from the perspective of privacy protection. Another part is an improvement of previous results. We show how our results can be used to perform distributed surveys and compare the properties of counter-based solutions and a standard Laplace method.

Krzysztof Grining, Marek Klonowski

In 2011 Bhaskar et al. pointed out that in many cases one can ensure sufficient level of privacy without adding noise by utilizing adversarial uncertainty. Informally speaking, this observation comes from the fact that if at least a part of the data is randomized from the adversary's point of view, it can be effectively used for hiding other values. So far the approach to that idea in the literature was mostly purely asymptotic, which greatly limited its adaptation in real-life scenarios. In this paper we aim to make the concept of utilizing adversarial uncertainty not only an interesting theoretical idea, but rather a practically useful technique, complementary to differential privacy, which is the state-of-the-art definition of privacy. This requires non-asymptotic privacy guarantees, more realistic approach to the randomness inherently present in the data and to the adversary's knowledge. In our paper we extend the concept proposed by Bhaskar et al. and present some results for wider class of data. In particular we cover the data sets that are dependent. We also introduce rigorous adversarial model. Moreover, in contrast to most of previous papers in this field, we give detailed (non-asymptotic) results which is motivated by practical reasons. Note that it required a modified approach and more subtle mathematical tools, including Stein method which, to the best of our knowledge, was not used in privacy research before. Apart from that, we show how to combine adversarial uncertainty with differential privacy approach and explore synergy between them to enhance the privacy parameters already present in the data itself by adding small amount of noise.

Krzysztof Grining, Marek Klonowski, Piotr Syga

During Financial Cryptography 2012 Chan et al. presented a novel privacy-protection fault-tolerant data aggregation protocol. Comparing to previous work, their scheme guaranteed provable privacy of individuals and could work even if some number of users refused to participate. In our paper we demonstrate that despite its merits, their method provides unacceptably low accuracy of aggregated data for a wide range of assumed parameters and cannot be used in majority of real-life systems. To show this we use both precise analytic and experimental methods. Additionally, we present a precise data aggregation protocol that provides provable level of security even facing massive failures of nodes. Moreover, the protocol requires significantly less computation (limited exploiting of heavy cryptography) than most of currently known fault tolerant aggregation protocols and offers better security guarantees that make it suitable for systems of limited resources (including sensor networks). To obtain our result we relax however the model and allow some limited communication between the nodes.