In this paper, we propose a privacy-preserving pattern recognition method that uses encrypted sparse representations in L0 norm minimization. We prove, theoretically, that the proposal has exactly the same dictionary and sparse coefficient estimation performance as the Label Consistent K-Singular Value Decomposition (LC-KSVD) algorithm for non-encrypted signals. It can be directly implemented by the LC-KSVD algorithm without any modification. Finally, we demonstrate its excellent recognition performance and security strength for the face recognition task using the Extended YaleB database.