Measuring privacy leakage in term of Shannon entropy

Abstract

Differential privacy is a privacy scheme in which a database is modified such that each users personal data are protected without affecting significantly the characteristics of the whole data. Example of such mechanism is Randomized Aggregatable Privacy-Preserving Ordinal Response (RAPPOR). Later it is found that the interpretations of privacy, accuracy and utility parameters in differential privacy are not totally clear. Therefore in this article an alternative definition of privacy aspect are proposed, where they are measured in term of Shannon entropy. Here Shannon entropy can be interpreted as number of binary questions an aggregator needs to ask in order to learn information from a modified database. Then privacy leakage of a differentially private mechanism is defined as mutual information between original distribution of an attribute in a database and its modified version. Furthermore, some simulations using the MATLAB software for special cases in RAPPOR are also presented to show that this alternative definition does make sense.