On the Sensitivity of the Gamma of the Quantum Cryptographic System AKM2017 to Changes in the Session Key

Abstract

The quantum cryptographic system AKM2017 is considered. The results of the analysis of the dependence of the degree of difference between the encryption and decryption gamut on the degree of difference between the corresponding session keys are presented. The equality of these degrees of distinction is revealed and substantiated. For an arbitrarily fixed encryption session key, the distribution of session decryption keys by classes is revealed and described, depending on the value of the degree of difference between the encryption and decryption gamuts. One class is made up of all session decryption keys, leading to the same value of the degree of difference between the encryption and decryption gamuts. A geometric interpretation of the specified distribution by classes is given in the form of placement along circles (class is a circle) on the surface of a sphere of unit radius centered at the origin of the Euclidean rectangular coordinate system in a three-dimensional linear space over the field of real numbers. The stated results can be used to solve the problems of optimizing the values of the parameters of accuracy and reliability of the functioning of variants of practical implementations of the quantum cryptographic system AKM2017, for example, when setting up a session decryption key, which makes it possible to guarantee a predetermined small value of the mathematical expectation of the number of incorrectly decrypted binary plain text.