||In this paper, we propose a method to estimate secure sparse representations in L0 norm minimization, and evaluate the effectiveness of the proposed scheme. With the advent of the big data era, digital content continues to increase. Sparse coding is attracting attention as an information processing model for extracting significant information from a large amount of data. It has been applied to a number of fields including image processing and data analysis, and its effectiveness is recognized. On the other hand, cloud computing is spreading in many fields including image processing and data analysis. However, the cloud computing has some serious issues for end users, such as unauthorized use and leak of data, and privacy compromise, due to unreliability of providers and some accident. We propose a method to estimate secure sparse coefficients from encrypted observed signals while keeping them secure. Simulation results show that it can estimate the encrypted sparse coefficients and unauthorized users can not decode observed signals even in leaking of dictionaries.