Dataset obfuscation refers to techniques in which random noise is added to the entries of a given dataset, prior to its public release, to protect against leakage of private information. In this work, dataset obfuscation under two objectives is considered: i) rank-preservation: to preserve the row ordering in the obfuscated dataset induced by a given rank function, and ii) anonymity: to protect user anonymity under fingerprinting attacks. The first objective, rank-preservation, is of interest in applications such as the design of search engines and recommendation systems, feature matching, and social network analysis. Fingerprinting attacks, considered in evaluating the anonymity objective, are privacy attacks where an attacker constructs a fingerprint of a victim based on its observed activities, such as online web activities, and compares this fingerprint with information extracted from a publicly released obfuscated dataset to identify the victim. By evaluating the performance limits of a class of obfuscation mechanisms over asymptotically large datasets, a fundamental trade-off is quantified between rank-preservation and user anonymity. Single-letter obfuscation mechanisms are considered, where each entry in the dataset is perturbed by independent noise, and their fundamental performance limits are characterized by leveraging large deviation techniques. The optimal obfuscating test-channel, optimizing the privacy-utility tradeoff, is characterized in the form of a convex optimization problem which can be solved efficiently. Numerical simulations of various scenarios are provided to verify the theoretical derivations.
