To address the low security and identity authentication difficulties of education resource sharing, this paper proposed a cross-domain identity authentication scheme based on blockchain technology and certificateless signature. The user security, cross-domain authentication, traceability of malicious users, and non-tamperable registration information were realized during the identity authentication process by the sharing of high security and no need for key escrow in the certificateless signature technology with blockchain distributed networks. First, intra-domain blockchain and cross-domain blockchain were design to facilitate the cross-domain authentication by a blockchain-based identity authentication model. Then, user safety and traceability of malicious users were guaranteed by certificateless signature and trapdoor hash functions in the authentication phase. Through the analysis, this scheme meets the security attributes such as mutual authentication and user identity security. Compared with other schemes, it has advantages in computing overhead and communication overhead. The scheme can better meet the computing environment with limited computing power on the user side.