We consider a problem in random matrix theory, which arises from computer science. The standard way to release the statistical summary of the information contained in a large data base is to publish its contingency table, which contains percentages of records having several given common entries. However, if the contingency table is released exactly, one can reconstruct the individual entries by solving a system of equations. The standard way to protect the privacy of individual records is to add a random noise to the contingency table. Determining the minimal necessary amount of such noise leads to the problem of estimating the smallest singular value of a special random matrix with dependent entries, which is generated from a random matrix with i.i.d. entries taking values 0 and 1.