The　difference　expansion　based　(DE-based)　reversible　data　hiding　schemes　suit　different　types　of　vector　maps　respectively,　and　show　good　performance,　both　in　capacity　and　invisibility.　In　addition,　the　schemes　are　strictly　reversible.　The　potential　applications　of　the　data　hiding　schemes　may　include　map　data　authentication,　secret　communication,　and　so　on.　However,　a　loophole　exists　in　the　DE-based　data　hiding　schemes.　Through　analyzing　the　DE-based　embedding　behavior　and　the　effect　of　embedding　on　the　histogram　of　coordinate　differences　or　Manhattan　distance　differences,　this　paper　finds　unusual　gaps　in　the　histogram　which　reveal　the　presence　of　secret　data.　Furthermore,　by　deducing　and　analyzing　the　coordinate　or　Manhattan　distance　difference　histogram　of　a　stego-map,　we　can　get　a　formula　of　the　estimated　embedding　rate,　and　estimate　the　length　of　hidden　data　through　the　use　of　Laplace　curve　fitting　function.　Adopted　practical　map　datum,　computing　results　show　that　this　paper＇s　scheme　is　applicable　to　the　vector　maps　represented　by　polygons　or　polygonal　lines.　Moreover,　it　is　possible　to　extend　this　paper＇s　scheme　to　some　other　data　sets,　e.g.,　3D　polygonal　meshes,　or　images.