The problem of cyber security in the era of the creation of quantum computers is of particular relevance. Specifically, the data are at risk which are confidential or whose value depends on their integrity. In order to find a way out of the situation which happened in the article, a thorough comprehensive analysis of the current state of the known cryptosystems was carried out, based on a systematic approach. In particular, the advantages and disadvantages of models of cryptosystems which were created on the basis of cognitive cryptography are stated, the theory of dynamic chaos, constructive, quantum and post-quantum cryptography. The issue of cryptosystem models based on DNA algorithms is also raised, proxy cryptosystem models, attribute cryptosystems, packet and non-commutative cryptography. As a result of the research, it was found out that the greatest interest in terms of security today is integral cryptography. The lack of scientifically justified models of cryptosystems based on integrated cryptography has led to the development of one of these models. The model is developed on the basis of the proposed concept, which is based on the main principals of integral cryptography. As a result of the research, a generalized model of the cryptosystem was developed, which in the future is proposed to be called the cryptosystem of Fredholm. It is shown that the essence of the encryption and decryption procedures is reduced to solving the direct and inverse problem, which is described by the integral equation of Fredholm of the first-order. The article emphasizes in particular that compared to the known models of cryptosystems, the proposed model has a number of significant advantages. The first advantage is the guaranteed theoretical and practical cryptostability, which is due to the incorrectness of the inverse decryption problem. The second advantage of the proposed model is the absence of effective algorithms for cryptanalysis due to the lack of prevalence of integral cryptography in modern cyber security systems. The developed model serves the theoretical basis for the further development of appropriate cryptographic algorithms and research of their security parameters.