k^m-anonymization Meets Differential Privacy under Sampling

Abstract

Various models for evaluating anonymity have been proposed so far. Among them, k-anonymity is widely known as a typical anonymity measure, guaranteeing that at least k individuals in a database have the same values. Unfortunately, it is difficult to create highly useful anonymized data satisfying k-anonymity for high-dimensional data because of the curse of dimensionality. Several approaches relaxing k-anonymity have been proposed, such as k^m-anonymity, to overcome the problem. On the other hand, we have another privacy protection metric, developed by Dwork et al., called differential privacy. However, the complete protection index for differential privacy, i.e., the level of noise that can satisfy the desired privacy, has not been clarified. This paper shows relationships between k^m-anonymity and differential privacy under sampling, proposed by Li et al., that is, a weak notion of differential privacy. Numerical experiments are then performed to give relations among the parameters of k^m-anonymity and differential privacy under sampling. These experiments also show relationships between k-anonymity and k^m-anonymity as k-anonymity is a special case of k^m-anonymity in some sense.