The problem of the release of anonymized microdata is an important topic in
the fields of statistical disclosure control (SDC) and privacy preserving data
publishing (PPDP), and yet it remains sufficiently unsolved. In these research
fields, k-anonymity has been widely studied as an anonymity notion for mainly
deterministic anonymization algorithms, and some probabilistic relaxations have
been developed. However, they are not sufficient due to their limitations,
i.e., being weaker than the original k-anonymity or requiring strong parametric
assumptions. First we propose Pk-anonymity, a new probabilistic k-anonymity,
and prove that Pk-anonymity is a mathematical extension of k-anonymity rather
than a relaxation. Furthermore, Pk-anonymity requires no parametric
assumptions. This property has a significant meaning in the viewpoint that it
enables us to compare privacy levels of probabilistic microdata release
algorithms with deterministic ones. Second, we apply Pk-anonymity to the post
randomization method (PRAM), which is an SDC algorithm based on randomization.
PRAM is proven to satisfy Pk-anonymity in a controlled way, i.e, one can
control PRAM's parameter so that Pk-anonymity is satisfied. On the other hand,
PRAM is also known to satisfy ε-differential privacy, a recent
popular and strong privacy notion. This fact means that our results
significantly enhance PRAM since it implies the satisfaction of both important
notions: k-anonymity and ε-differential privacy.Comment: 22 pages, 4 figure