In this paper, we propose L0 norm optimization in a scrambled sparse representation domain and its application to an Encryption-then-Compression (EtC) system. We design a random unitary transform that conserves L0 norm isometry. The resulting encryption method provides a practical orthogonal matching pursuit (OMP) algorithm that allows computation in the encrypted domain. We prove that the proposed method theoretically has exactly the same estimation performance as the nonencrypted variant of the OMP algorithm. In addition, we demonstrate the security strength of the proposed secure sparse representation when applied to the EtC system. Even if the dictionary information is leaked, the proposed scheme protects the privacy information of observed signals.

In this paper, we propose a secure computation of sparse coding and its application to Encryption-then-Compression (EtC) systems. The proposed scheme introduces secure sparse coding that allows computation of an Orthogonal Matching Pursuit (OMP) algorithm in an encrypted domain. We prove theoretically that the proposed method estimates exactly the same sparse representations that the OMP algorithm for non-encrypted computation does. This means that there is no degradation of the sparse representation performance. Furthermore, the proposed method can control the sparsity without decoding the encrypted signals. Next, we propose an EtC system based on the secure sparse coding. The proposed secure EtC system can protect the private information of the original image contents while performing image compression. It provides the same rate-distortion performance as that of sparse coding without encryption, as demonstrated on both synthetic data and natural images.

In this paper, we propose secure dictionary learning based on a random unitary transform for sparse representation. Currently, edge cloud computing is spreading to many application fields including services that use sparse coding. This situation raises many new privacy concerns. Edge cloud computing poses several serious issues for end users, such as unauthorized use and leak of data, and privacy failures. The proposed scheme provides practical MOD and K-SVD dictionary learning algorithms that allow computation on encrypted signals. We prove, theoretically, that the proposal has exactly the same dictionary learning estimation performance as the non-encrypted variant of MOD and K-SVD algorithms. We apply it to secure image modeling based on an image patch model. Finally, we demonstrate its performance on synthetic data and a secure image modeling application for natural images.

A privacy-preserving support vector machine (SVM) computing scheme is proposed in this paper. Cloud computing has been spreading in many fields. However, the cloud computing has some serious issues for end users, such as the unauthorized use of cloud services, data leaks, and privacy being compromised. Accordingly, we consider privacy-preserving SVM computing. We focus on protecting visual information of images by using a random unitary transformation. Some properties of the protected images are discussed. The proposed scheme enables us not only to protect images, but also to have the same performance as that of unprotected images even when using typical kernel functions such as the linear kernel, radial basis function (RBF) kernel and polynomial kernel. Moreover, it can be directly carried out by using well-known SVM algorithms, without preparing any algorithms specialized for secure SVM computing. In an experiment, the proposed scheme is applied to a face-based authentication algorithm with SVM classifiers to confirm the effectiveness.