An optimization problem in statistical databases

Let D = {a(1),..., a(n)} be a set of real numbers, and let S subset of {1,. .., n}. For an interval I subset of {1,..., n} we set SU M (I) = Sigma(i is an element of I) a(i). In this paper we solve the following problem which has been asked in connection with security of statistical databases: Find a largest family B of subintervals of {1,..., n} so that knowing the value o f SU M(I) for all I is an element of B does not enable one to calculate any element a(i) is an element of D, where i is an element of S.