  We present a classification of quantum public-key encryption protocols. There
are six elements in quantum public-key encryption: plaintext, ciphertext,
public-key, private-key, encryption algorithm and decryption algorithm.
According to the property of each element which is either quantum or classical,
the quantum public-key encryption protocols can be divided into 64 kinds. Among
64 kinds of protocols, 8 kinds have already been constructed, 52 kinds can be
proved to be impossible to construct and the remaining 4 kinds have not been
presented effectively yet. This indicates that the research on quantum
public-key encryption protocol should be focus on the existed kinds and the
unproposed kinds.
