This paper provides background information on cognitive  aspects of post-quantum security. It explores the security threats against communication security and particularly against key exchange that is enabled by the development of quantum computers. The applied and theoretical aspects of quantum-cryptographic technologies are considered.

The interrelated elements that make up to the concept and content determined by the application of quantum cryptography are analysed. The systematic analysis of quantum algorithms, quantum cryptography and quantum hashing are presented. The development of specialized quantum computers, focused on solving cryptographic problems is justified. Terms which must be taken into account in the selection of elliptic curves for cryptographic applications are determined. The proper concept vehicle over is brought, in particular the concepts of singularity and super singularity are determined for elliptic curves and theoretical positions, lying in their basis, are examined.