Імітаційне моделювання методів для генерування потоку великорозмірних перестановок при їх ізоморфних представленнях матрицями

Abstract

The methods and processes of generation of a flow of permutation matrices of significant dimension in their new isomorphic representations are considered and modeled. The need and relevance of the development of methods for the formation of a stream of large-scale permutations and the peculiarities and advantages of their application for cryptographic transformations, image encryption, masking (hiding) of video files, implementation of protocols for agreement by a group of participants of the master secret key-permutation in matrix-type cryptosystems are substantiated. Three options for generating a stream of permutation matrices are proposed. It is shown that simple element-by-element modulo operations and shifts performed in the initial permutations isomorphically represented by matrices, and multiple permutations of elements in these permutations (equivalent to raising the corresponding permutation matrices to the power), make it possible, based on these basic operations, procedures, to generate the required number of shared secret permutation matrix keys in streaming mode. The results of modeling the methods and processes of generating the flow of large-sized permutation matrices in general, their algorithmic steps, and operations are given.