Quantum public-key cryptosystem includes unconditionally secure quantum public-key cryptographic algorithm and computationally secure quantum public-key cryptographic algorithm. This paper presents a quantum Niederreiter public-key cryptosystem by using quantum stabilizer LDPC codes. Constructed key based on quantum LDPC codes directly. Take advantage of the sparsity of LDPC codes. Compared with McEliece public-key cryptosystem, Encoding complexity is reduced. Its security relies on the fact that NPC problem can not be solved on quantum Turing machines.
A quantum public-key cryptosystem without quantum channels between any two users using non-orthogonal states is provided in this paper. Every user keeps a set of quantum particles in non-orthogonal states in a key management center (KMC) as the public key while he or she keeps the states of them as the private key. By the help of KMC users can accomplish secret communication and message authentication. The laws of quantum physics guarantee the unconditional security of this cryptosystem. No entangled states or complex quantum operations are needed. On the other hand there are no quantum channels needed to connecting any two users. So the public-key cryptosystem is easier to carry out and more robust in practice.