The paper studies the relevance of the issues of encrypting confidential data for their transmission over unsecured channels of information and communication networks. An analysis of encrypted information exchange on the Internet based on the Google service was carried out in terms of the volume of encrypted web traffic. It is concluded that the difference in traffic volumes between countries is due to the popularity of the types of devices used, the geographic access infrastructure, as well as the availability of software that provides modern types of encryptions. The role of the HTTPS protocol in ensuring the security of working with resources on the Internet is substantiated. The NIST security requirements for modern information and communication systems in the post-quantum period are analyzed. It is determined that within a short period of time the power of computing devices increases exponentially, which entails an increase in the implementation of both already known and new attacks on cryptographic algorithms that ensure the strength of security services in networks. Based on the results of this study, the results of a comparative analysis of the complexity of classical and quantum algorithms were demonstrated. The classification of special attacks was considered according to the signs of influence on computing processes, according to access to systems and means, as well as according to the specifics of the attacks themselves. Solutions submitted for participation in the NIST competition for the definition of security standards through electronic digital signature mechanisms, encryption algorithms and key encapsulation are analyzed. The results of the analysis are presented in the form of a scheme of security and stability of the proposed protocols and algorithms. It is recommended to use TLS protocols to ensure the integrity and authenticity of users when establishing communication sessions with websites. A scheme of the process of authenticated encryption and authentication of an encrypted message transmitted over a TLS connection has been developed. A process scheme has been developed for authentication encryption and decryption of information when establishing a communication session in TLS protocols. A comparative analysis of the characteristics of the TLS 1.3 and TLS 1.2 protocols was carried out.