We examine Euclidean distance-preserving data perturbation as a tool for privacy-preserving data mining. Such perturbations allow many important data mining algorithms e.g. hierarchical and k-means clustering), with only minor modification, to be applied to the perturbed data and produce exactly the same results as if applied to the original data. However, the issue of how well the privacy of the original data is preserved needs careful study. We engage in this study by assuming the role of an attacker armed with a small set of known original data tuples (inputs). Little work has been done examining this kind of attack when the number of known original tuples is less than the number of data dimensions. We focus on this important case, develop and rigorously analyze an attack that utilizes any number of known original tuples. The approach allows the attacker to estimate the original data tuple associated with each perturbed tuple and calculate the probability that the estimation results in a privacy breach. On a real 16-dimensional dataset, we show that the attacker, with 4 known original tuples, can estimate an original unknown tuple with less than 7 error with probability exceeding 0.8.
Samarati and Sweeney @cite_18 @cite_34 developed the k-anonymity framework wherein the original data is perturbed so that the information for any individual cannot be distinguished from at least k-1 others. Values from the original data are generalized (replaced by a less specific value) to produce the anonymized data. This framework has drawn lots of attention because of its simple privacy definition. A variety of refinements have been proposed, see discussions on k-anonymity in various chapters in @cite_24 . None of these approaches consider Euclidean distance preserving perturbation as we do.
@cite_24 @cite_18 @cite_34
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We focus primarily on the use of additive and matrix multiplicative data perturbation techniques in privacy preserving data mining (PPDM). We survey a recent body of research aimed at better understanding the vulnerabilities of these techniques. These researchers assumed the role of an attacker and developed methods for estimating the original data from the perturbed data and any available prior knowledge. Finally, we briefly discuss research aimed at attacking k-anonymization, another data perturbation technique in PPDM. Today's globally networked society places great demands on the dissemination and sharing of information. While in the past released information was mostly in tabular and statistical form, many situations call for the release of specific data (microdata). In order to protect the anonymity of the entities (called respondents) to which information refers, data holders often remove or encrypt explicit identifiers such as names, addresses, and phone numbers. Deidentifying data, however, provides no guarantee of anonymity. Released information often contains other data, such as race, birth date, sex, and ZIP code, that can be linked to publicly available information to reidentify respondents and inferring information that was not intended for disclosure. In this paper we address the problem of releasing microdata while safeguarding the anonymity of respondents to which the data refer. The approach is based on the definition of k-anonymity. A table provides k-anonymity if attempts to link explicitly identifying information to its content map the information to at least k entities. We illustrate how k-anonymity can be provided without compromising the integrity (or truthfulness) of the information released by using generalization and suppression techniques. We introduce the concept of minimal generalization that captures the property of the release process not distorting the data more than needed to achieve k-anonymity, and present an algorithm for the computation of such a generalization. We also discuss possible preference policies to choose among different minimal generalizations.