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On a large class of non-linear coding methods based on Boolean invertible matrices

Karanikas Costas (Aristotle University of Thessaloniki, Department of Informatics, Thessaloniki, Greece)
Atreas Nikolaos D. (Aristotle University of Thessaloniki, Department of Informatics, Thessaloniki, Greece)

The main target of this work is to construct a large enumerated class of non- linear coding methods, based on a discrete invertible transform called Riesz Product, which is associated to a class of Boolean invertible matrices of order m × m. The particular class of matrices is uniquely determined by a couple of permutations of the first m natural numbers {1, 2, ..., m}, so for any m = 1, 2, 3, ..., we get at least (m!)2 different non-linear coding methods. The resulting encoding/decoding method is very fast and requires low memory. It can be used both as a new encryption tool or as a Boolean random generator. .

Keywords: Non-linear coding, Boolean invertibile matrices, permutations, Riesz products