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.
We propose two interactive identification protocols based on a general construction of quantum public-key
cryptosystem. Basic protocol contains set-up phase and authentication phase. Participants do operation with
quantum computing of Boolean function in two-round transmission of authentication phase. Basic one only
ensures completeness and soundness, but leaks information about private-key. We modify basic protocol with
random string and random Boolean permutation. After modification, both transmitted states in two-round
transmission can be proved to be ultimate mixed states. No participant or attacker will get useful information
about private-key by measuring such states. Modified protocol achieves property of zero-knowledge.