Oriol Farràs

Oriol Farràs, Jordi Ribes-González, Sara Ricci

Privacy-preserving data splitting is a technique that aims to protect data privacy by storing different fragments of data in different locations. In this work we give a new combinatorial formulation to the data splitting problem. We see the data splitting problem as a purely combinatorial problem, in which we have to split data attributes into different fragments in a way that satisfies certain combinatorial properties derived from processing and privacy constraints. Using this formulation, we develop new combinatorial and algebraic techniques to obtain solutions to the data splitting problem. We present an algebraic method which builds an optimal data splitting solution by using Gröbner bases. Since this method is not efficient in general, we also develop a greedy algorithm for finding solutions that are not necessarily minimal sized.

Oriol Farràs, Josep Domingo-Ferrer, Alberto Blanco-Justicia

Cryptographic primitives are essential for constructing privacy-preserving communication mechanisms. There are situations in which two parties that do not know each other need to exchange sensitive information on the Internet. Trust management mechanisms make use of digital credentials and certificates in order to establish trust among these strangers. We address the problem of choosing which credentials are exchanged. During this process, each party should learn no information about the preferences of the other party other than strictly required for trust establishment. We present a method to reach an agreement on the credentials to be exchanged that preserves the privacy of the parties. Our method is based on secure two-party computation protocols for set intersection. Namely, it is constructed from private matching schemes.

Klara Stokes, Oriol Farràs

Anonymous database search protocols allow users to query a database anonymously. This can be achieved by letting the users form a peer-to-peer community and post queries on behalf of each other. In this article we discuss an application of combinatorial configurations (also known as regular and uniform partial linear spaces) to a protocol for anonymous database search, as defining the key-distribution within the user community that implements the protocol. The degree of anonymity that can be provided by the protocol is determined by properties of the neighborhoods and the closed neighborhoods of the points in the combinatorial configuration that is used. Combinatorial configurations with unique neighborhoods or unique closed neighborhoods are described and we show how to attack the protocol if such configurations are used. We apply k-anonymity arguments and present the combinatorial configurations with k-anonymous neighborhoods and with k-anonymous closed neighborhoods. The transversal designs and the linear spaces are presented as optimal configurations among the configurations with k-anonymous neighborhoods and k-anonymous closed neighborhoods, respectively.