A cryptosystem based on a mathematical model of chaotic oscillations generated on the basis of differential equations

Анотація

At the present time, when widespread and easily accessible technical means are used for the transmission and storage of any data, the protection of information from violations of its confidentiality, integrity, and accessibility is one of the most important problems. The transmitted data can be influenced by the transmission environment or external (information system) environment, as well as various actions of attackers aimed at interception, damage to information. Encryption of transmitted data is one of the methods of protection against malicious attacks. This article is devoted to justification of the use of cryptosystems based on mathematical model of the chaos generator, proposed by Leon Chua in 1983, describing the principles of implementing cryptoalgorithm and prospects of its application. Chaos generator cryptosystems have a number of advantages over symmetric systems and public key systems (the latter are usually used in the form of hybrid cryptosystems when encrypting information), the main problem of which is the length of the key, and as a result - its repeatability. The length of the key obtained from the chaos generator is practically unlimited and each generator can create different processes, which, with a slight change in the initial conditions, make it difficult to determine the structure of the generator. There were described the problems of traditional cryptosystems, the theory of cryptostability, absolutely and computationally stable ciphers, a separate theoretical method for solving the problem of increasing the cryptostability of hybrid computationally stable systems by including a mathematical model of the chaos generator as a key generator for encrypting the data that is transmitted. The scientific novelty of this study is the developed method of applying the mathematical model of the chaos generator "Chua scheme" as the main component of the hybrid cryptosystem, where the chaos generator is used as a source of public and private keys of the asymmetric encryption algorithm and the key of the symmetric algorithm, which is directly used for data encryption. Recommendations and requirements for the implementation of the cryptosystem on the chaos generator "Chua scheme" are described.

Keywords: chaos generator, mathematical model, Chua circuit, encryption, cryptography, information security, deterministic chaos.