Geometric Shape Effects in Redundant Keys used to Encrypt Data Transformed by Finite Discrete Radon Projections

The Finite discrete Radon Transform (FRT) represents digital data exactly and without redundancy. Redundancy can however be injected into the FRT by reserving part of the image area to be replaced by a key that contains pixels of known, fixed values. The resulting image redundancy can be used to watermark values into the image, or as an encryption key that must be known if the image data is to be recoverable from a subset of transmitted projections. This paper looks at the affect the geometry of the selected key areas has on the interaction between the FRT projections of the key area and those of the data area. A method is proposed to measure this interaction of projected values. Results for simple key geometries are obtained. These give some insight into the design of key shapes that optimise the coupling of projected key and image values.