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

Abstract

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. .