Understanding Database Reconstruction Attacks on Public Data

There exists a solution universe of all the possible solutions to this set of constraints. If the solution universe contains a single possible solution, then the published statistics completely reveal the underlying confidential data--provided that noise was not added to either the microdata or the tabulations as a disclosure-avoidance mechanism. If there are multiple satisfying solutions, then any element (person) in common among all of the solutions is revealed. If the equations have no solution, either the set of published statistics is inconsistent with the fictional statistical agency's claim that it is tabulated from a real confidential database or an error was made in that tabulation. This doesn't mean that a high-quality reconstruction is not possible.