A little knowledge goes a long way: faster detection of compromised data in 2-D tables

A reexamination is made of the problem of protecting sensitive data in an n by n table of integer statistics, when the nonsensitive data are made public along with the row and column sums for the table. Consideration is given to the problem of computing the tightest upper bounds on the values of sensitive (undisclosed) cells. These bounds, together with tightest lower bounds (which can be efficiently computed), define precisely the smallest intervals that an adversary can deduce for the missing sensitive cell values. Small intervals compromise the security of the undisclosed data, and in some cases violate laws on public data disclosure. It is observed that the number of initial needed bounds can be reduced from O(n log n) to 2n-1 by exploiting a recent result of C.K. Cheung and T.C. Hu (1988)