Mathematical methods for privacy protection

Abstract

This is the age of tremendous development of information technologies that is followed by fast appearance of new disciplines and their application in all parts of everyday life and society. Privacy is one of the most important problems that relates to information technologies. The notion of privacy has a different meaning for everyone. The 20th century brought technological advance that increased the availability and the usage of information, [11], which, in return, led to appearance of new meanings of the term “privacy”. Basically, privacy is the ability and possibility to control the way of accessing the data and it’s distribution, [12, 7]. The age that we live in can be called information age. Nowadays, different activities that were private in the earlier age, leave digital trace, that can be used to learn about individual’s interests, characteristics, beliefs, but also about his/her personal information; e.g. phone number, address and even various medical data. Today, almost everyone is an everyday user of e-mail, messaging services (SMS, Skype, Viber, etc.), social networks (Facebook, Twitter, Instagram, etc.), different search engines (Google, Bing), that are used to get answers to everyday, but also to sensitive questions, and e-services (Booking, Amazon, eBay) that are used for online shopping. The usage of this services creates digital trace of the individuals, commercial entities and government institutions in various countries that users may or may not be aware of. Internet of things is a paradigm that is, in this age, as common as the above mentioned services. This paradigm consists of usage of a large number of sensors, mostly with a help of wireless networks, in order to gather various data like temperature, energy consumption, but also different medical data that comes from the patients. It is clear that the privacy of medical data is important, but on the first glance, privacy of the data like energy consumption may seem unimportant. However, if that data privacy can be compromised, it could, for example, lead to obtaining information about when a certain object is full with people, and when it is not, which could lead to easier planning of an intrusion.Cloud computing is another common paradigm nowadays, that represents the computer infrastructure that gives constant access to shared resource pool (storage, services, applications) via network, most commonly via internet. In cloud computing, user data, that is processed (e.g. Google docs), or only stored (e.g. Dropbox), are located on a remote computer that is usually not in the ownership of the user. In this scenario, the question of privacy is even more important, especially since the data can be very sensitive, because other users can be malicious and can compromise the data privacy on the cloud. However, users are not the only one that can endanger privacy. Cloud providers can be malicious as well, or at least curious, so they may access the data of their users. Moreover, they can delegate and disseminate the users’ data to a third party which can further use it. A taxonomy to understand privacy violations is thus sorely needed, [9]. All of the above mentioned paradigms and activities have one thing in common - the data (digital trace or user’s data) is kept on the provider’s side in a permanent way, that makes them practically impossible to be deleted. Taking into account that there are already well-developed methods for processing large data, that can be used to find various sensitive information, it is clear that the privacy problem is an important topic, and it will continue to be so in the future. Mathematical models and formal methods have become the base tools in computer science for developing reliable software and hardware. New paradigms of information technologies, such as internet of things, cloud computing, blockchain, also require reliability that can only be provided by mathematical models. Basic directions of mathematical methods application to data privacy are: - computational models for privacy, based on computational models for distributed and concurrent systems [5]; - formal methods for privacy, based on logic, type systems and verification,[10]; - differential privacy, [3] and probabilistic methods of reasoning, [13], [8]; - cryptographic methods for privacy, [6]; - application in social networks, databases, medical data, linked data, [4]; - open data, [2]; - legal aspects of privacy in information systems, [1]. The complexity of this problem requires multidisciplinary teams of mathematicians, computer scientists, information scientists, lawyers, sociologists and psychologists [1, 2]. It is necessary to encourage mathematical and multidisciplinary researches that are relevant to privacy protection, since that will be one of the biggest challenges of the modern society.