According to the idea of zero trust, this paper proposed an anonymous identity authentication scheme based on hash functions and pseudo-random number generators, which effectively increased the anonymity and confidentiality when users use the mobile networks, and ensure the security of the server. This scheme first used single-packet authentication technology to realize the application stealth. Secondly, hash functions and pseudo-random number generators were used to replace public key cryptosystems and time synchronization systems, which improved system performance. Thirdly, different methods were set to save encrypted information on the user s mobile device and the server, which realized different forms of anonymous authentication and negotiates a secure session key. Through security analysis, function and performance comparison, the results showed that the scheme had better security, flexibility and practicality, while maintained good communication efficiency.