The systems and methods of this invention watermark an original data file using dimensional compression and expansion. The original data file extends along a given dimension and has portions that extend along that given dimension. The information is embedded into the data file by selectively dimensionally compressing or expanding a size of each of some or all of the portions along the given dimension, which can be space or time. The portions of the data file are selectively dimensionally expanded or compressed according to a given encoding scheme. This encoding scheme can use the kind of modification, the relationships between the type of modification between adjacent portions, or the duration or degree of compression or expansion to store a portion of the embedded information. The portions of the embedded information can be individual bits of binary or trinary information, or can be a portion of analog information.