Systems, methods, and physical computer-readable storage media for performing geometric data compression and geometric data decompression and/or geometric data encryption and geometric data decryption. A virtual geometric compression object is generated within a computer system by defining a plurality of discrete elements arranged in a geometric shape and assigning one or more data bit values to each of the plurality of discrete elements. The virtual geometric compression object is used by the computer system to compress sequences of uncompressed data bits into compression definitions. A compression definition defines a path through the virtual geometric compression object corresponding to a sequence of uncompressed data bits. In a reverse manner, for data decompression, at least a portion of a virtual geometric compression object is generated and a compression definition is used to extract a corresponding sequence of uncompressed data bits from the portion of the virtual geometric compression object.