Differential Privacy and Applications

Abstract

The right to privacy is considered as a fundamental right. Data privacy generally concerns whether and how data is shared with a third party, how it is collected and stored, as well as the laws governing data sharing in areas such as health care, education and financial services [3]. The problem of defining the right to privacy gained special importance with the development of information technology. The first definition of privacy is given in Warren and Brandeis’s 1890 seminal book, “The Right to Privacy” [9] and it is inspired by new photographic and printing technologies and their influence on citizens’ personal life. From that moment, new technologies raised new privacy concerns and brought new meanings of the notion “privacy”. Although technology has developed data privacy problems, technology can also help solve them. In order to deal with these problems, we must formalize them first. Jeannette M. Wing highlighted the importance of formal methods in the domain of data privacy in [6]. Mathematical formulations of different notions of privacy are highly important for guiding the development of privacy preserving technologies. One of the best-known mathematical formulations of privacy is Differential Privacy proposed by Cynthia Dwork. The idea is to start with a statistical database and an adversary who wants to learn some of the sensitive data from the database. Differential privacy relies on incorporating random noise so that everything an adversary receives is noisy and imprecise. Unlike the early pro- posed techniques of anonymization, the differential privacy is not a property of a database, it is a property of queries, functions applied on a database. Definition 1 [1] Let ε > 0 . A mechanism M is ε-differentially private iff for every pair of adjacent databases D, D′and for every S ⊆range(M): Pr[M(D) ∈S] ≤exp(ε)Pr[M(D′) ∈S], where the probability space is over the coin flips of the mechanism M. In [4] we have compared different models for privacy preserving. In this paper we deal in more detail with the concept of differential privacy and it’s applications. One of the recent applications is differential privacy on graphs [2] implemented in social media and recommendation systems [5]. Another current application is in the domain of location privacy and processing of geolocation data like [7]. Finally, we discuss the latest ideas for application in the blockchain technology [8].