Research on protection of statistical databases from revelation of private or sensitive information has rarely examined situations where domain-dependent structure exits for a data attribute such that only a very few independent variables can characterize it. Such circumstances can lead to Diophantine (integer-solution) equations whose solution can lead to surprising or compromising inferences on quite large data populations. In many cases the Diophantine equations are linear, allowing efficient algorithmic solution. Probabilistic models can also be used to rank solutions by reasonability, further pruning the search space. Unfortunately, it is difficult to protect against this form of data compromise, and all countermeasures have disadvantages. (Author)