METHOD FOR GENERATING A SEQUENCE OF REFINED FIBONACCI POLYNOMIAL MATRICES FOR DATA ENCRYPTION

Abstract

A method for generating the nth sequence of refined Fibonacci polynomial matrices of the mth order, whose elements are Fibonacci polynomials of order not higher than (m+n–2)th number is presented. The obtained Fibonacci matrices allow finding both their determinants and inverse matrices suitable for matrix encryption of block data. The shortcomings of the traditional approach to forming the structure of the elements of such matrices are revealed, primarily the number (k) of its different elements, which are Fibonacci polynomials of order not higher than (n–1). Such an insignificant number of elements is not only uninformative and transparent for the cryptanalyst, but also not stable with respect to cryptanalysis. The structure of the elements of Fibonacci polynomial matrices is specified, the number of which depends on the order of the matrix (m) and is k = m+1. The proposed structure of the elements of the nth sequence of Fibonacci polynomial matrices of the mth order has an interesting property, according to which it is possible to avoid using the recurrent matrix relation for their generation, and to form them only by the numbers of the sequence of Fibonacci polynomials, the specific values ​​of which depend on their location in the matrix and its column number. Software has been developed that allows generating both sequences of refined Fibonacci polynomial matrices of the mth order, and finding their determinants and inverse polynomial matrices of a similar order, suitable for both encrypting block messages and decrypting them.