We propose a quantum public-key encryption (QPKE) protocol for an unknown multi-qubit state based on qubit-wise teleportation. The private-key is a computational Boolean function, whereas the public-key is a pair of a random bit string and a quantum state. A private-key corresponds to an exponential number of public-keys. Security analysis showed that the proposed protocol has information-theoretic security from attacks for the private-key and the encryption. A multi-partite quantum secret state sharing protocol is presented based on the proposed multi-qubit-oriented QPKE protocol. Such secret state sharing protocol is information-theoretically secure.