Anonymous communication scheme based on quantum walk on Cayley graph

Abstract

Information security is the cornerstone and lifeblood of national security in the information society, and anonymous quantum communication is one of the important ways to protect information security. Using quantum walk randomness to effectively solve sensitive problems such as leakage of identity information. In this paper, an anonymous communication scheme based on quantum walks on the Cayley graph is proposed. First, both parties in the communication hide their identity information, and the sender Alice anonymously selects the receiver Bob through logic or operation. Secondly, the trusted third party and the communicating parties use the BB84 protocol to generate and distribute the security key. Alice encrypts the information sequence according to the security key to obtain the blind information; Bob uses the joint Bell state measurement and security key to sign and the trusted third party verifies the signature information. Third, the trusted third party calculates the position probability distribution function of Bob’s quantum walk via the Fourier transform, converts the position information corresponding to the maximum probability into a confirmation frame and sends it to Alice; Alice uses the quantum compression algorithm by decreasing dimensions to reduce the number of transmitted information bits(the length of the information bit can be reduced by up to 37.5%) and uses the security key to complete the information encryption and then transmit the information to the location indicated by the confirmation frame. Bob uses quantum walks to search the location node to obtain the transmission information and complete the anonymous quantum communication. Finally, the security analysis of the scheme is carried out, and the numerical simulation results of the Cayley graph of 200 nodes are given. At the 10-step walk, the maximal probability of the 6th node is 45.31%. According to the simulation results, the probability that Bob is eavesdropped on the specific location at his 10-step walk during the communication of this scheme is approximately 6 × 10<sup>–7</sup>%, so the receiver can avoid the identity information from the eavesdropping with a high probability, and the quantum network anonymity protocol is not broken.