Mammadov R. The security analysis against attacks of protocols of quantum cryptography

The object is information transfer processes by quantum communication channels and processes of interception of the information in the quantum channel. The subject is protocols of quantum keys distribution and protocols of quantum secure direct communication. The purpose is development of new protocols of quantum secure direct communication with increased information capacity, the analysis of their security to attacks, and also finding of the best protocols by criteria of security and information capacity in groups of similar protocols of quantum cryptography. Research methods: mathematical methods of quantum mechanics, the quantum and classical theory of the information, procedural programming methods, numerical experiment. Theoretical and practical results: 1. For the first time methods of quantum coding of the information and methods of the eavesdropping control are developed for three new ping-pong protocols of quantum secure direct communication between two users and three new protocols of a kind "two to one" with entangled four-qubit "omega"-, W- and "chi"-states. 2. For the first time mathematical models of eavesdropping attacks with use of auxiliary quantum systems on the developed ping-pong protocols are constructed. Expressions for quantity of the information which the eavesdropper can intercept, depending on protocol parameters and probability to detect attack at unitary control of eavesdropping are obtained. 3. The "intercept-resend" attack on the developed ping-pong protocols is analysed. It is shown that such attack is possible only on the protocol with four-qubit W-states, also such attack is not possible on protocols with four-qubit "omega"- and "chi"-states. 4. The comparative analysis of security, information capacity and a noise immunity of various ping-pong protocols, both developed in thesis, and offered by other authors is made. It is shown, what on these criteria the best among ping-pong protocols with the four-qubit entangled states are protocols with "omega"- and "chi"-states. 5. Methods of the analysis of security to various non-coherent attacks of three classes of quantum key distribution protocols with multidimensional quantum systems (qudits) are improved. Two methods comparative analysis of the security to non-coherent attacks, and also information capacity of these three classes of protocols is made. It is shown that under criteria of the security to non-coherent attacks and information capacity the best are the protocols of "preparation - measurement" kind using two mutually unbiased bases. Results of work are introducing into educational process of the educational centre of the Ministry of Communications and Information Technologies of the Republic Azerbaijan.