Algorithm for generating encryption keys in a symmetric cryptographic system for protecting speech information based on differential transformations

DOI: 10.31673/2409-7292.2024.040001

Abstract

The rapid evolutionary development of information technologies and the creation of quantum computers have become harbingers of the onset of the post-quantum cryptoperiod, during which classical symmetric and asymmetric cryptographic systems become particularly vulnerable. In the first case, Grover algorithms are used quite effectively to compromise symmetric cryptographic systems in the post-quantum period, in the second - Shor algorithms, respectively. Thus, potential vulnerabilities of known cryptographic systems can lead to a significant decrease in the level of security of protected objects, especially those of them that are classified as critical infrastructure objects or included in the national security and defense management circuit. Therefore, in order to develop guaranteed secure cryptographic information protection systems based on differential transformations, the cryptographic algorithms of which are based on Fredholm integral equations of the first kind, the article has developed a corresponding algorithm for generating encryption keys. It is proposed to use elementary functions as the initial data for generating encryption keys. For typical algebraic functions that meet the requirements for encryption keys based on differential transformations, their differential spectra have been constructed, and model examples have been given. The absence of similar solutions in the scientific literature for constructing an algorithm for generating encryption keys in a symmetric cryptographic system for protecting speech information based on differential transformations determines the priority of the scientific results obtained in the article.

Keywords: generation algorithm, encryption key, symmetric cryptographic system, differential transformations, differential spectrum, discrete.