New Approach to Quantum Key Distribution Via Quantum Encryption

In this Paper, we investigate the security of Zhang, Li and Guo quantum key distribution 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 and with the probability one half she gets all of keys without being detected by the two parties. The main defect in this protocol is that there is an attack strategy by which Eve can change the previously shared Bell state between Alice and Bob to two Bell states among herself and Alice and Bob. Hence, we show that with probability $1/d$ its generalization to $d$-dimension systems is not secure and show that its extension to the case of more partners based on the reusable GHZ states is not secure and with probability one half Eve gets all of keys without being detected by the two parties. In what follows, we show how in going to higher dimensions those protocols can be repaired.