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We examine Euclidean distance-preserving data perturbation as a tool forprivacy-preserving data mining. Such perturbations allow many important datamining algorithms e.g. hierarchical and k-means clustering), with only minormodification, to be applied to the perturbed data and produce exactly the sameresults as if applied to the original data. However, the issue of how well theprivacy of the original data is preserved needs careful study. We engage inthis study by assuming the role of an attacker armed with a small set of knownoriginal data tuples (inputs). Little work has been done examining this kind ofattack when the number of known original tuples is less than the number of datadimensions. We focus on this important case, develop and rigorously analyze anattack that utilizes any number of known original tuples. The approach allowsthe attacker to estimate the original data tuple associated with each perturbedtuple and calculate the probability that the estimation results in a privacybreach. On a real 16-dimensional dataset, we show that the attacker, with 4known original tuples, can estimate an original unknown tuple with less than 7%error with probability exceeding 0.8.

Breaching Euclidean Distance-Preserving Data Perturbation Using Few Known Inputs