In this paper, we consider a privacy preserving encoding framework for identification applications covering biometrics, physical object security and the Internet of Things (IoT). The proposed framework is based on a sparsifying transform, which consists of a trained linear map, an element-wise nonlinearity, and privacy amplification. The sparsifying transform and privacy amplification are not symmetric for the data owner and data user. We demonstrate that the proposed approach is closely related to sparse ternary codes (STC), a recent information-theoretic concept proposed for fast approximate nearest neighbor (ANN) search in high dimensional feature spaces that being machine learning in nature also offers significant benefits in comparison to sparse approximation and binary embedding approaches. We demonstrate that the privacy of the database outsourced to a server as well as the privacy of the data user are preserved at a low computational cost, storage and communication burdens.