Auditing Boolean attributes

We study the problem of auditing databases which support statistical sum queries to protect the security of sensitive information; we focus on the special case in which the sensitive information is Boolean. Principles and techniques developed for the security of statistical databases in the case of continuous attributes do not apply here. We prove certain strong complexity results suggesting that there is no general efficient solution for the auditing problem in this case. We propose two efficient algorithms: The first is applicable when the sum queries are one-dimensional range queries (we prove that the problem is NP-hard even in the two-dimensional case). The second is an approximate algorithm that maintains security, although it may be too restrictive. Finally, we consider a "dual" variant, with continuous data but an aggregate function that is combinatorial in nature. Specifically, we provide algorithms for two natural definitions of the auditing condition when the aggregate function is MAX.