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Problem statement: In a previous research, we investigated the quantum key distribution of the well known BB84 protocol with several intercept and resend attacks. In the present research, we studied the effect of many eavesdroppers cloning attacks of the Bennett-Brassard cryptographic protocol on the quantum error and mutual information between honest parties and information with sender for each eavesdropper. Approach: The quantum error and the mutual information were calculated analytically and computed for arbitrary number of cloning attacks. Our objective in this study was to know if the number of the eavesdroppers and their angle of cloning act on the safety of information. Results: It was found that the quantum error and the secured/no secured transition depend strongly on the number of eavesdropper and their angle of attacks. The particular cases where all eavesdroppers collaborate were also investigated. Conclusion: Furthermore, the cloning attack’s quantum error is lower than the intercept and resends attacks one, which means that the cloning attacks is the optimal one for arbitrary number of eavesdropper

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The disturbance effect of a depolarizing channel on the security of the quantum key distribution of the four state BB84 protocol, with multiple sequential intercept-resend attacks of many eavesdroppers, has been studied. The quantum bit error rate and the mutual information are computed for an arbitrary number N of eavesdropper. It is found that the quantum error rate decreases when increasing the depolarizing parameter p characterizing the noise of the channel. For p<0.165, there exist, a special value tr p of p below which the information is secured, otherwise it is not secured. The value of tr p decreases when increasing the number of attacks. While, for p  0.165, the information is not secured independently of the eavesdropper's number. Phase diagrams corresponding to the securedunsecured information are also established.