We propose a new computationally efficient privacy-preserving identification framework based on layered sparse coding. The key idea of the proposed framework is a sparsifying transform learning with ambiguization, which consists of a trained linear map, a component-wise nonlinearity and a privacy amplification. We introduce a practical identification framework, which consists of two phases: public and private identification. The public untrusted server provides the fast search service based on the sparse privacy protected codebook stored at its side. The private trusted server or the local client application performs the refined accurate similarity search using the results of the public search and the layered sparse codebooks stored at its side. The private search is performed in the decoded domain and also the accuracy of private search is chosen based on the authorization level of the client. The efficiency of the proposed method is in computational complexity of encoding, decoding, "encryption" (ambiguization) and "decryption" (purification) as well as storage complexity of the codebooks.