МАТЕМАТИЧНА МОДЕЛЬ СИМТЕРИЧНОЇ КРИПТОГРАФІЧНОЇ СИСТЕМИ ЗАХИСТУ МОВНОЇ ІНФОРМАЦІЇ НА ОСНОВІ ДИФЕРЕНЦІАЛЬНИХ ПЕРЕТВОРЕНЬ

Анотація

Among known cryptographic systems, in practice, symmetric cryptographic systems are most often used to protect speech information. Such systems, when encrypting speech information, implement stream encryption of outgoing traffic. At the same time, the rapid development of quantum and post-quantum technologies, methods and means of cryptanalysis determines the urgent need for their further development. One of the promising approaches, which is not sufficiently covered in the professional literature today, is considered to be an approach based on the methods of integral cryptography. According to the basic principles of integral cryptography, a mathematical model in the form of an integral Fredholm equation of the first kind can be used as the basis of a cryptographic algorithm for a symmetric cryptographic system of speech information protection. The main difference and at the same time the advantage of cryptographic systems based on Fredholm integral equations of the first kind is their guaranteed theoretical and practical cryptographic stability. The guaranteed theoretical cryptographic stability and speed of such a symmetric cryptographic system is provided by the application of the method of differential transformations of Academician of the National Academy of Sciences of Ukraine G. Pukhov. Practical crypto-resistance is ensured by the practical unsolvability of the inverse incorrect decryption problem. It is suggested to use the regularization method of Professor A. Tikhonov to decipher the cyphergram obtained from speech information. Thus, the proposed mathematical model of a symmetric cryptographic system based on differential transformations is a further development of modern information technologies for cryptographic protection of speech information in Ukraine.