  This paper investigates a quantum version of McEliece public-key encryption
(PKE) scheme, and analyzes its security. As is well known, the security of
classical McEliece PKE is not stronger than the onewayness of related classical
one-way function. We prove the security of quantum McEliece PKE ranks between
them. Moreover, we propose the double-encryption technique to improve its
security, and the security of the improved scheme is proved to be between the
original scheme and the quantum one-time pad.
