Due to the identification functionality, identity authentication is the first and primary security step in many information systems. There exist many works dedicated to giving secure identity authentication. However, most of the existing schemes suffer from at least one of the following problems: heavy account management, single point of failure, and privacy leakage. To tackle these challenges, we propose two blockchain-based identity authentication schemes in this paper. One is based on the famous Diffie-Hellman key exchange protocol and is efficient but with user-verifier interaction. The other utilizes the ring signature, which is non-interactive with a small computational cost. Besides the traditional security properties, such as unforgeability and identity anonymity, our proposed schemes can hold non-transferability, i.e., the verifier cannot prove the user's identity authentication to any third party. At last, the extensive experimental results demonstrate that our proposals are practical and efficient.