Praneeth Kumar Vippathalla

Sophie Taylor, Praneeth Kumar Vippathalla, Justin Coon

The fundamental trade-off between privacy and utility remains an active area of research. Our contribution is motivated by two observations. First, privacy mechanisms developed for one-time data release cannot straightforwardly be extended to sequential releases. Second, practical databases are likely to be useful to multiple distinct parties. Furthermore, we can not rule out the possibility of data sharing between parties. With utility in mind, we formulate a new privacy-utility trade-off problem to adaptively tackle sequential data requests made by different, potentially colluding entities. We consider both expected distortion and mutual information as measures to quantify utility, and use mutual information to measure privacy. We assume an attack model whereby illicit data sharing, which we call collusion, can occur between data receivers. We develop an adaptive algorithm for data releases that makes use of a Blahut-Arimoto-style algorithm. We show that the resulting data releases are optimal when expected distortion quantifies utility, and locally optimal when mutual information quantifies utility. Numerical experiments on real data demonstrate that the proposed adaptive algorithm can exploit previously released information to reduce cumulative leakage under collusion without sacrificing much, if any utility. Finally, we discuss how our findings may extend to applications in machine learning.

Sophie Taylor, Praneeth Vippathalla, Justin Coon

We study differentially private data release, where a database is accessed through successive, possibly adaptive queries and mechanisms. Existing composition theorems and privacy filters combine worst case per-round privacy parameters, leaving room for more refined accounting based on realised leakage, which we term realisation-level accounting. We propose a realisation-level filtering approach to determine stopping times for data releases, and design one such filter. Despite technical challenges arising from conditioning on realisations and stopping time, we prove that the filter guarantees $(ε, δ)$-differential privacy, with $ε$ and $δ$ chosen by the data handler. Through numerical evidence, we demonstrate that realisation-level filtering provides a path to better utility beyond mechanism-level methods. Furthermore, our proposed filter applies to arbitrary mechanisms, including those that are badly behaved under Rényi differential privacy.

Praneeth Kumar Vippathalla, Chung Chan, Navin Kashyap et al.

In this paper, we explore the connection between secret key agreement and secure omniscience within the setting of the multiterminal source model with a wiretapper who has side information. While the secret key agreement problem considers the generation of a maximum-rate secret key through public discussion, the secure omniscience problem is concerned with communication protocols for omniscience that minimize the rate of information leakage to the wiretapper. The starting point of our work is a lower bound on the minimum leakage rate for omniscience, $R_{\mathop{\mathrm{L}}}$, in terms of the wiretap secret key capacity, $C_{\mathop{\mathrm{W}}}$. Our interest is in identifying broad classes of sources for which this lower bound is met with equality, in which case we say that there is a duality between secure omniscience and secret key agreement. We show that this duality holds in the case of certain finite linear source (FLS) models, such as two-terminal FLS models and pairwise independent network models on trees with a linear wiretapper. Duality also holds for any FLS model in which $C_{\mathop{\mathrm{W}}}$ is achieved by a perfect linear secret key agreement scheme. We conjecture that the duality in fact holds unconditionally for any FLS model. On the negative side, we give an example of a (non-FLS) source model for which duality does not hold if we limit ourselves to communication-for-omniscience protocols with at most two (interactive) communications. We also address the secure function computation problem and explore the connection between the minimum leakage rate for computing a function and the wiretap secret key capacity.