Correlated tuple data release via differential privacy

Abstract

Privacy preserving methods supporting for tuple data release have attracted the attention of researchers in multidisciplinary fields. Among the advanced methods, differential privacy (DP), introducing independent Laplace noise, has become an influential privacy mechanism owing to its provable and rigorous privacy guarantee. Nonetheless, in practice, tuple data to be protected are always correlated while independent noise may cause undesirable information disclosure than expected. Recent researches attempt to optimize the sensitivity function of DP with consideration of the correlation strength between data – but have a drawback in a substantial growth of noise level. Therefore, for correlated tuple data release, how to decrease the noise level incurred by correlation strength is yet to be explored. To remedy this problem, this paper exploits the degradation of DP in expected privacy levels for correlated tuple data and proposes a solution to mitigate it. We first demonstrate a filtering attack, presenting a possibility of using the different dependence between original outputs and perturbations to sanitize a certain level of noise to extract individual’s sensitive information. Secondly, we introduce the notion of correlated tuple differential privacy (CTDP) to preserve expected privacy for correlated tuple data and further propose a generalized Laplace mechanism (GLM) to achieve privacy guarantees in CTDP. Then we design a practical iteration mechanism, including an update function, to conduct GLM when facing large scale queries. Finally, experimental evaluation on real-world datasets over multiple fields show that our solution consistently outperforms state-of-the-art mechanisms in data utility while providing the same privacy guarantee as other approaches for correlated tuple data.

Introduction

In data-driven applications, such as location based services (LBSs), disease surveillance and social networks, etc., information sharing is necessary for data owners to obtain better services. For example, in location based applications, behaviors trend towards uploading one’s precise position to service provider can be used to get better shopping recommendations and route planning services. In disease surveillance case, sharing personal physical condition can prevent the outbreak of some diseases.

As the above examples suggest, information sharing has outstanding benefits for knowledge discovery and acquisition. But the shared data may contain individual’s sensitive information (e.g., personal home address, health condition). Untreated data may disclose individual’s privacy while data owners may not be willing to publish their true data values because of privacy considerations. Therefore, privacy preserving data release (PPDR) has become a substantial issue in data sharing and mining [1], [2].

Early privacy preserving schemes inherently rely on the security guarantee of designed algorithms, where the security is difficult to be theoretically proved and analyzed. To remedy this problem, DP proposed by Dwork [3], [4] has a solid mathematical foundation, and no restrictions on the background knowledge of the adversary. It is a kind of privacy protection method which strictly defines the strength of protection and data utility. Due to the fact that DP can provide a complete theoretical guarantee of privacy security and better data availability, it has become a significant PPDR framework in recent years.

DP mechanism assumes that the records in the dataset are independent with each other and adds independent and identically distributed (IID) Laplace noise to the query results to guarantee its rigorous definition. However, this assumption becomes weak in correlated tuple records. IID Laplace noise can be sanitized from the query results and will not achieve expected privacy degree in correlated tuple records. For example, the relationships of members in the same family may provide helpful background knowledge for violating users’ privacy information [5], as illustrated in Fig. 1 and Example 1.

Example 1

Consider a database including six people with their records of inspection results. An adversary could ascertain their relationships by using a web crawler algorithm. The database publishes users’ data to the third party via differential privacy technology to protect the 6th person’s health information. Given query results, such as “the number of persons uninfected with flu”, an adversary may attempt to infer the health condition of the 6th person. He/she can launch an attack by asking “how many persons in this database are uninfected among the first five and all of the persons respectively?”. In order to protect the 6th person’s health information, a small IID Laplace noise is added to the true queries and the noisy values around the true answer 4 (e.g., 3 or 5) are answered. However, if the attacker knows the relationships of users that user 2, 4, 5 and 6 are the members of the same family, then the attacker learns that they have the same health condition and can infer that the 6th person is uninfected.

The above example illustrates that IID Laplace noise in the standard DP can not achieve expected privacy guarantee in correlated tuple data release. A user’s sensitive information can still be forecast and inferred according to the relationships of users. The goal of this paper is to allow third parties (who may be untrustworthy) to analyze and mine beneficial information from published records, while preserving the privacy of the tuple data collected from individuals.

Current approaches attempt to solve this problem from two natural solutions: one category is based on correlated model and the other category redefines the sensitivity function of DP with consideration of correlation levels. The first approaches establish models to describe the relations of the correlated tuple data, e.g., a Gaussian model that reflects the tuple data correlations, and a Markov [6] or Bayesian [7], [8] model that represents the transition probability distribution of the publishing process. After establishing a model, mechanisms generate noise that conforms to the model and add it to the query result. In the second category, the number of correlated tuple data or correlation coefficient matrix are utilized to describe the correlation levels, which are designated as the weight to redefine the sensitivity function to determine the noise level added into the original outputs.

Although various prioritization solutions towards mitigating differentially private release for correlated tuple data have been proposed, current schemes are still afflicted with the following challenges:

• Rigorous restriction: Model based methods assume that the dependence of tuple data conforms to a specific model, e.g., a Gaussian or Markov model. However, this is a rigorous assumption in real-world applications. In fact, the tuple data forms in reality are diverse and can rarely be described by a single model. Noise generated by a specific model that does not tally with the realistic model will not only limit its scope of use but also reveal privacy.

• Low-level utility: The measure to resize sensitivity function of DP considering tuple data correlations need to be carefully conducted since the tiny change of correlation may have a serious effect on the noise. Because the stronger the correlations of tuple data are, the seriously larger the correlated sensitivity function will be than that of independent records. However, larger sensitivity function will directly lead to the increase of noise level and destroy data utility.

These challenges imply that a novel mechanism for differentially private release of correlated tuple data is in high demand. With respect to the first challenge, to lift the rigorous model restriction, we attempt to explore a generalized mechanism applicable for any dependent form of tuple data. To this end, we propose a generalized Laplace mechanism that can handle arbitrary correlated forms of tuple data. This mechanism ensures differential privacy while addressing any data forms. For the second challenge, observed that whether a perturbation preserves privacy depends on (i) how much perturbation is added, and (ii) how the perturbation is added. State-of-the-art schemes mainly improve their algorithms from the first aspect and introduce extra noise to offset the privacy leakage caused by IID Laplace noise. Based on this observation, we try to address this challenge from the second aspect and explore how the perturbation should be added. Our idea is that if the correlation of perturbation is “similar” with that of query results, an adversary can not sanitize the perturbation and the privacy leakage can be alleviated. Therefore, there is no need to generate extra noise to compensate for the sanitized part.

Based on these considerations, we propose an effective differentially private release solution for correlated tuple data, including a novel concept of “correlated tuple differential privacy” (CTDP) and a generalized Laplace mechanism (GLM) to conduct CTDP. To the best of our knowledge, CTDP is the first differential privacy technique for correlated tuple data release that renders the dependence between noise and outputs indistinguishable (similar) to an adversary. Our contributions are fourfold:

• Filtering Attack: In our previous work, we have demonstrated the possibility of a filtering attack on individual sensitive information by utilizing the different dependence between original outputs and perturbation from the aspect of signal processing. The inference attack shows that some of the IID Laplace noise can be sanitized by a linear filter, leading to a reduction of privacy degree in practice. In this paper, we generalizes this attack method to test whether individual’s sensitive privacy can be inferred using the difference of correlations between original data and published data, as described in Section 4.

• Correlated Differential Privacy: To defend against inference attack launched by adversaries who have prior knowledge about the correlation of tuple data, we first formalize the notion of CTDP and then, we show the possibility of achieving CTDP guarantees by augmenting a generalized Laplace mechanism (GLM), which makes the correlation of the noise similar with that of original outputs intended to be protected. GLM allows a differential privacy guarantee for dependent tuple data while no additional noise is required, maintaining the same noise scale as in standard DP.

• Iteration Mechanism: Since the queries in practice are always continuous and large scale, to make the correlation between noise and original outputs keep consistent under continuous queries, we propose a practical and efficient iteration mechanism. We first initialize a Laplace variable, and then regenerate a new variable according to the property of bivariate GLM when answering a new query each time. By this means, we apply GLM to practice when answering continuous large quantities of queries.

• Experimental Evaluation: Extensive evaluation involving different query functions over multiple large-scale real-world datasets illustrates that our solution consistently outperforms state-of-the-art mechanisms in data utility while providing the same privacy guarantee as other approaches for correlated tuple data.

The remainder of this paper is organized as follows. In Section 2, we briefly introduce the related work associated with our work. Then notations and preliminaries adopted in this work are described in Section 3. Section 4 demonstrates a possible filtering attack to obtain an estimate of individual’s sensitive data. Our solution that consists of a formal notion CTDP and a generalized Laplace mechanism to achieve privacy guarantee of CTDP is described in Section 5. Section 6 proposes an iteration mechanism to address continuous queries, including an update function for repeat queries. Details of theoretical analysis and data utility are demonstrated in Section 7. Experimental evaluation is conducted in Section 8, followed by the conclusions and future works in Section 9.