To solve the privacy image problem stored in cloud, we propose a compressive sensing (CS) based image compression, authentication, encryption algorithm in cloud, which can implement computation outsourcing to get rid of the expensive storage and computation costs. To achieve these goals, combined with the logistic-tent-sine chaotic map, a logistic-tent-sine chaotic map (LTSS) is proposed for it has larger chaotic ranges and better chaotic behaviors than simple 1D chaotic map such as a logistic chaotic map. Then, the LTSS chaotic system is employed for image protection algorithm in cloud, which contains three parts: data owner, cloud services and data user. The primary role of the data owner part is to compress and encrypt the image while embedding the owner’s Palmprint discriminative and binary features for authentication. The low-frequency part of the image is encrypted using the proposed Binary Data Cyclic Encryption algorithm (BDCE) while the owner’s palmprint features are embedded for authentication of the data owner. The high-frequency data are randomized for compression by the CS and following encrypted by the Double Random Phase Encoding (DRPE). For the cloud services, authentication services depend on the key and palmprint features and the high computational compressed sensing reconstruction is implemented in cloud can reduce the user burden. For data users, a user should provide the correct key and right palmprint, and then obtain an image available from the cloud service. The algorithm has better quality compared with the common compressive sensing based algorithms and robust to noise and occlusion for using the discrete wavelet transform. What is more, theoretical analysis and empirical evaluations show that the proposed algorithm can resist to exhaustive attack, differential attack and classical attacks.