We present a cryptographic scheme for encrypting 2-D gray scale images by using a large family of fractals. This scheme is based on a transposition of the image elements implemented by a generator of 2-D hierarchical scanning patterns producing a large subset of the (n2)! possible orders defined on a 2-D image of n × n elements. Each pattern defines a distinct order of pixels and can be described by an expression, which is considered as the key of the transposition. This transposition cipher can easily be combined with various substitution ciphers, producing efficient product ciphers operating on pictorial data. Two such ciphers are constructed and their effects on real gray value images are shown. Encryption and decryption algorithms are derived from a parallel algorithm implementing the creation of the family of scanning patterns.
Nikolaos G. Bourbakis,
"Image encryption method using a class of fractals," Journal of Electronic Imaging 4(3), (1 July 1995). https://doi.org/10.1117/12.208654