  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.
