Analyses of the consistent eavesdropping attack of several eavesdroppers on the ping-pong protocol with entangled pairs of qubits

Abstract

In this paper the analyses of the eavesdropping attack of two or more eavesdroppers on the original ping-pong protocol with entangled pairs of qubits is carried out. General recursive expression for probability d of attack detection for any number n of eavesdroppers that allows to calculate this probability through the corresponding probability when n – 1 eavesdroppers attack is obtained. It is shown that an increase in the number of attackers in the quantum channel leads to an increase in the probability of detecting these attacks by legitimate users. The expressions for the maximum eavesdroppers' amount of information during a consistent attack of two and three eavesdroppers are obtained. It is indicated that the maximum eavesdroppers' amount of information determined by the same expression as in the case of one eavesdropper's attack, only the value of d is varying. It is shown that the ping-pong protocol with pairs of entangled qubits is vulnerable to eavesdropping attack of several eavesdroppers not more than to one eavesdropper's attack.