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.
This paper considers the problem of providing security to statistical databases against disclosure of confidential information. Security-control methods suggested in the literature are classified into four general approaches: conceptual, query restriction, data perturbation, and output perturbation. Criteria for evaluating the performance of the various security-control methods are identified. Security-control methods that are based on each of the four approaches are discussed, together with their performance with respect to the identified evaluation criteria. A detailed comparative analysis of the most promising methods for protecting dynamic-online statistical databases is also presented. To date no single security-control method prevents both exact and partial disclosures. There are, however, a few perturbation-based methods that prevent exact disclosure and enable the database administrator to exercise "statistical disclosure control." Some of these methods, however introduce bias into query responses or suffer from the 0 1 query-set-size problem (i.e., partial disclosure is possible in case of null query set or a query set of size 1). We recommend directing future research efforts toward developing new methods that prevent exact disclosure and provide statistical-disclosure control, while at the same time do not suffer from the bias problem and the 0 1 query-set-size problem. Furthermore, efforts directed toward developing a bias-correction mechanism and solving the general problem of small query-set-size would help salvage a few of the current perturbation-based methods.