Quantum computation and quantum information
Quantum computation and quantum information
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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Recently, Zhang, Li and Guo (ZLG) suggested a new approach to quantum key distribution by usinga shared Bell state which acts as quantum key in order to encode and decode classical information.Subsequently, others extended ZLG protocol to d-dimensional systems and to quantum secret sharingbased on reusable GHZ states. However, Gao et al. have shown that if Eve employs a special strategyto attack, these protocols become insecure. Afterwards, they repair ZLG protocol so that their eavesdroppingstrategy becomes inefficient. In this paper, we investigate the security of ZLG quantum keydistribution protocol and show that it is not secure against Eve's attacks and with probability of one halfshe gets all of the keys without being detected by the two parties. In this eavesdropping strategy, Evetransforms the previously shared Bell state between Alice and Bob to two Bell states among herselfand the parties. Moreover, we briefly show that ZLG's repairing by Gao et al's is not efficient againstof our attack and Eve can choose an appropriate rotation angle and measurement bases which help herto do eavesdropping. Afterwards, we discuss generalization of ZLG protocol to d-dimensional systemsand show that with probability 1/d, Eve gets all of keys. We show that quantum secret sharing basedon reusable GHZ states is also not secure and with probability one half, Eve gets all of keys. We repairthem by going to higher dimensional shared EPR or GHZ states. Finally, we compare ZLG protocolwith ours and show that the ZLG protocol and its extensions are less robust against the channel noisewith respect to ours.