In this Paper, we investigate the security of Zhang, Li and Guo quantum keydistribution via quantum encryption protocol [$\text{Phys. Rev. A} \textbf{64},24302 (2001)$] and show that it is not secure against some of Eve's attacks andwith the probability one half she gets all of keys without being detected bythe two parties. The main defect in this protocol is that there is an attackstrategy by which Eve can change the previously shared Bell state between Aliceand Bob to two Bell states among herself and Alice and Bob. Hence, we show thatwith probability $1/d$ its generalization to $d$-dimension systems is notsecure and show that its extension to the case of more partners based on thereusable GHZ states is not secure and with probability one half Eve gets all ofkeys without being detected by the two parties. In what follows, we show how ingoing to higher dimensions those protocols can be repaired.
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机译：在本文中，我们研究了通过量子加密协议[$ \ text {Phys。 Rev. A} \ textbf {64}，24302（2001）$]，并显示它对于夏娃的某些攻击是不安全的，并且有一半的概率她获得了所有密钥而没有被双方发现。该协议的主要缺陷在于，存在一种攻击策略，通过该策略，夏娃可以将先前在Alice和Bob之间共享的Bell状态更改为她自己以及Alice和Bob之间的两个Bell状态。因此，我们证明，在概率为$ 1 / d $的情况下，将其推广到$ d $维系统是不安全的，并表明将其扩展到基于可重用的GHZ状态的更多合作伙伴的情况是不安全的，并且有一半的夏娃获得了所有密钥而没有被两方发现。在下面的内容中，我们显示了如何将这些协议扩展到更高的维度。
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