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Solving the privacy problem of users in the consortium blockchain becomes the key to accelerate the implementation of the practical application of blockchain. A set of anonymous identity authentication scheme based on PKI is designed based on Hyperledger Fabric platform, a typical representative of the consortium blockchain. By splitting the private key d into two parts, different roles use each private key to generate the joint signature of the anonymous certificate to achieve the separation of permissions in the process of certificate generation and solve the single point attack problem in the process of anonymous certificate tracking. The analysis shows that the improved scheme can achieve higher security than the original scheme with lower computing and storage overhead.