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A database is compromised if a user can determine the data elements associated with keys which he did not know previously. If it is possible, compromise can be achieved by posing a finite set of queries over sets of data elements and employing initial information to solve the resulting system of equations. Assuming the allowable queries are linear, that is, weighted sums of data elements, we show how compromise can be achieved and we characterize the maximal initial information permitted of a user in a secure system. When compromise is possible, the initial information and the number of queries required to achieve it is surprisingly small.
Schwartz et al. (Fri,) studied this question.
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