Nikolaenko S. Methods of security amplification for quantum direct communication protocols

An object of research is the process of transmission and interception of information in quantum communication channel. An objective is to develop of methods for improving noise immunity and security to one and more eavesdropping attacks of quantum direct communication protocols. Research methods. To develop mathematical models of non-coherent eavesdropping attack and two more attacks of eavesdropper on ping-pong protocol, to develop a new method of increasing security of these protocols used methods of quantum mechanics, quantum and classical information theory, classical cryptography and cryptanalysis. To perform time estimations implementing methods to increasing security of ping-pong protocols used methods of procedural programming. To develop a method for the implementation of error-correcting coding ping-pong protocols in depolarizing quantum channel used methods in quantum and classical information theory, classical error-correcting coding, simulation. Theoretical and practical results: Mathematical models of several eavesdropper attacks on ping-pong protocol with two-and three-qubit entangled states, which allow you to perform quantitative assessment of security to this attack protocol depending of protocol parameters and parameters of systems eavesdroppers. XOR encryption for increasing security of ping-pong protocols, the practical implementation of that increasing security of protocols to eavesdropping attacks. Simulation models and software for simulation of ping-pong protocols two-qubit entangled states using the XOR encryption and reversible hashing for increasing security to eavesdropping attacks. Simulation results information transmission ping-pong protocol with pairs of entangled qubits in quantum depolarizing channel using a binary error-correcting Fire code (60.44), including statistical information confirming the correction of error bursts, if the probability of depolarization of qubits in the quantum channel does not exceed 7 %, which corresponds to the modern experi-mental situation in the transmission of photons at a distance of about 150 km. Scientific novelty : For the first time the mathematical models of sequential incoherent eavesdropping attack of two or more eavesdroppers on the protocols with entangled two- and three-qubit states is developed on the basis of the quantum and classical information theory, which allowed to perform security estimation of these protocols to such attacks. For the first time the method of security amplification for the ping-pong protocols based on XOR encryption of message are proposed for any of ping-pong protocol that allowed to improve the security of these protocols to eavesdropping attacks. Also the method of reversible hashing by LUP-decomposition is modified. Assessment of the computational complexity of the proposed methods of security amplification for the ping-pong protocols with entangled two-qubit states is performed, that allowed to evaluate the effect of the improving security procedures on protocols performance on the whole and to give recommendations for the choice of methods for security amplification. For the first time the method of error correction Fire Сode of ping-pong protocol with two entangled qubit states is used, thus noise immunity of these protocols is improved. The results of studies are implemented in such organizations: Odessa National Academy of Telecommunications named after A.S. Popov and National Aviation University, Kiev.