Text encryption based on chaotic mappings and information matrices

Abstract

The relevance of the work is due to the widespread implementation of data encryption, including text messages, in numerous areas of civil and military applications. A review of traditional methods of encryption of textual information and methods developed based on promising development directions (cellular automata, neural networks, chaotic mapping) is presented. The work is devoted to developing an algorithm for text encryption using information matrices and systems with deterministic chaos. Following the proposed encryption algorithm, the original text is transformed into a 2D array of data – the information matrix. The elements of this matrix are the text characters. The position of the information matrix element is uniquely related to the position of the source text character, and the value of the element is determined by the binary code of the open text alphabet character. A 3D chaotic system is used to encrypt the information matrix. The essential dependence of the chaotic mapping on the initial conditions and its transitivity property allows for simultaneous mixing and diffusion of the information matrix elements. By the example of Ressler’s 3D chaotic system, we investigated the stability criteria of the proposed encryption algorithm to static cryptanalysis (correlation coefficients between the elements of the encrypted information matrix, entropy, probability distribution of element values) and differential cryptoanalysis (percentage of changed elements and the average change of intensity). The computational experiments showed sufficiently good (close to theoretically achievable values) stability criteria and 100 % correspondence between the decoded text and the original text. Computational experiments were performed using the developed programs in Python and Java.