Efficient outsourced extraction of histogram features over encrypted images in cloud

JPEG steganalysis mainly includes feature extraction and classification [1, 2], and thus the quality of the extracted features has an important influence on the detection performance of classifiers. With the development of JPEG steganalysis, the dimension of extracted features is greatly increased for improving the detecting performance [3]. In recent years, histogram calculation is widely used to create high-dimensional image features for JPEG steganalysis. In [4], the 8000-dimensional discrete cosine transform residual (DCTR) features which utilized 64 filters were proposed, where the decompressed JPEG image was convoluted with each filter and then the first-order residuals were obtained from subsampling images. Further, Song et al. [2] proposed a feature extraction method based on two dimensional (2D) Gabor filters, where the decompressed JPEG image was decomposed with different scales and orientations, and then the image features were extracted from the filtering coefficients. Compared with DCTR features, the 2D Gabor filters can obtain the embedding changes from more scales and orientations, and thus the 17000-dimensional Gabor filters residual (GFR) features were more effective. These two kinds of features are the most important methods of histogram calculation for JPEG steganalysis until now. It is well known that for massive JPEG images, feature extraction based on histogram calculation is very difficult to be executed in a client due to limited ability. Therefore, it is very important for a client to decrease the computational load without decreasing the detection performance during feature extraction. Securely outsourced computation may be a feasible method to achieve this goal, which could outsource the task of a client to a cloud server and realize histogram feature extraction efficiently for massive JPEG images. Currently, there are a lot of work for outsourcing expensive operations to an untrusted server. Ren et al. [5] constructed an outsourced scheme of modular exponentiations (MExps) based on a single server, where the client could verify the computation results with a probability of 1. Chen et al. [6] first proposed an efficient outsourced scheme for bilinear pairing, where the client does not need to execute any expensive operation. Ren et al. [7] presented another outsourced scheme, which simultaneously improved efficiency and checkability based on a single server. Wang et al. [8] proposed an outsourced image recovery service architecture under the compressed sensing framework. Ren et al. [9] proposed an outsourced feature extraction scheme based on the co-occurrence matrix, where the original images were protected from the server by using a projection of one to many with trapdoor, and the client could verify and obtain true results of extracted feature.