Quantum asymmetric cryptography with symmetric keys
  Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme, which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore, the state-estimation attack to a prior QPKC scheme is demonstrated. 
Fei Gao, Qiao-Yan Wen, Su-Juan Qin, Fu-Chen Zhu