Linear spaces and transversal designs: k-anonymous combinatorial configurations for anonymous database search

TL;DR

This paper explores how combinatorial configurations like linear spaces and transversal designs can be used to enhance anonymity in database search protocols by ensuring k-anonymity through their neighborhood properties.

Contribution

It introduces the use of combinatorial configurations with k-anonymous neighborhoods for anonymous database search, identifying optimal structures like transversal designs and linear spaces.

Findings

Transversal designs and linear spaces are optimal k-anonymous configurations.

Protocols can be attacked if configurations with unique neighborhoods are used.

k-anonymity can be achieved through specific combinatorial configurations.

Abstract

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.