With the application and promotion of biometric technology, biometrics has become more and more important to identity authentication. In order to ensure the privacy of the user, the biometrics cannot be stored or manipulated in plaintext. Aiming at this problem, this paper analyzes and summarizes the scheme and performance of the existing biometric authentication system, and proposes an iris-based ciphertext authentication system based on fully homomorphic encryption using the FV scheme. The implementation of the system is partly powered by Microsoft's SEAL (Simple Encrypted Arithmetic Library). The entire system can complete iris authentication without decrypting the iris feature template, and the database stores the homomorphic ciphertext of the iris feature template. Thus, there is no need to worry about the leakage of the iris feature template. At the same time, the system does not require a trusted center for authentication, and the authentication is completed on the server side directly using the one-time MAC authentication method. Tests have shown that when the system adopts an iris algorithm with a low depth of calculation circuit such as the Hamming distance comparison algorithm, it has good performance, which basically meets the requirements of real application scenarios.