Necessary Condition for Maximum Usability of Sdb

A statistical database is a database in which only queries of statistical type are allowed, such as SUM, COUNT, MAX, MIN, MEAN. The security problem for a statistical database is to nd suitable control mechanisms so that while statistical information is provided, no sequence of queries is suucient to infer the values of protected elds of individual records. If such an inference is possible we say that the database has been compromised. Various types of compromise have been deened, including positive, negative and relative compromise, and many types of control mechanisms have been proposed for the protection against database compromise. One of the possible methods is the Audit Expert proposed by Chin and Oszoyoglu for the prevention of database compromise using SUM queries. At the heart of the Audit Expert is the query basis matrix which is used to determine whether a new query is`harmless' and so should be answered or whether it would lead to a compromise and so should be rejected. The usability (the ratio of answerable queries to all possible queries) of a statistical database running under the protection of Audit Expert depends on the query basis matrix. Miller et al (1991) found the maximum possible usability of a statistical database under static Audit Expert, and gave query basis matrices which achieve this maximum. In this paper we prove that there are no other basis matrices which achieve the maximum usability.