Theoretical Results on De-Anonymization via Linkage Attacks

Consider a database D with records containing history of individuals' transactions, that has been de-identified, i.e., the variables that uniquely associate records with individuals have been removed from the data. An adversary de-anonymizes D via a linkage attack if using some auxiliary information about a certain individual in the database, it can determine which record of D corresponds to such individual. One example of this is given in the article Robust De-anonymization of Large Sparse Datasets, by Narayanan and Shmatikov [19], which shows that an anonymized database containing records with ratings of different movies rented by customers of Netflix, could in fact be de-anonymized using very little auxiliary information, even with errors. Besides the heuristic de-anonymization of the Netflix database, Narayanan and Shmatikov provide interesting theoretical results about database de-anonymization that an adversary can produce under general conditions. In this article we revisit these theoretical results, and work them further. Our first contribution is to exhibit different simple cases in which the algorithm Scoreboard, meant to produce the theoretical de-anonymization in [19], fails to do so. By requiring 1-sim to be a pseudo-metric, and that the algorithm producing the de-anonymization outputs a record with minimum support among the candidates, we obtain and prove deanonymization results similar to those described in [19]. We then consider a new hypothesis, motivated by the fact (observed in heuristic de-anonymizations) that when the auxiliary information contains values corresponding to rare attributes, the de-anonymization achieved is stronger. We formalize this using the notion on long tail [4], and give new theorems expressing the level of de-anonymization in terms of the parameters of the tail of the database D. The improvement in the deanonymization is reflected in the fact that when at least one value in the auxiliary information corresponds to a rare attribute of D, the size of auxiliary information could be reduced in about 50%, provided that D has a long tail. We then explore a microdata file from the Joint Canada/United States Survey of Health 2004 [22], where the records reflect the answers of the survey respondents. While many of the variables are related to health issues, some other variables a related to characteristics that individuals may disclose easily, such as physical activities (sports) or demographic characteristics. We perform an experiment with this microdata file and show that using only some non-sensitive attribute values