A proof of security of quantum key distribution in probabilistic clone scheme

A probabilistic clone/resend attack strategy is proposed in this paper. Detailed analysis on the security of quantum key distribution under this attack strategy shows that the maximum information leaking to Eve is 83.4%, and the bit error rate of the sifted key is 16.6%. However, by either discarding the key distribution according to the security criteria of quantum bit error rate for quantum key distribution protocol or distilling a secret key with the privacy amplification technique, the quantum key distribution still has an asymptotic perfect security. Simulations on the procedure of quantum key distribution under the proposed attack strategy show the same results.