A Note on a Conjecture of Kam and Ullman Concerning Statistical Databases

A statistical database is d collection of records about which certain queries may be answered. In [l] Kam and Ullman considered security problems in a particular model of statistical database. The purpose of the present note is to prove a conjecture raised there. In the model of Kam and Ullman [I], a statistical clarahose F is a function from strings of k bits (keys) to sntegers. An (s, k)query (0 < s < k) is 2 sequence in d 0, 1, *jk with exactly s O’s and 1’s. The * is a ‘don’t -care’ symbol, and we shall say that a key nta’ches a query if the key and the query agree in all except those positions where the query has *‘s. The resporrse of a database F to a query Q is defined to be the vabz