Progressive Image Restoration Based on CP-ABE With Constant-Size Ciphertext and Constant Bilinear Calculation

Sharing photos on an open social platform with one-to-many features increases the leakage risk of information of the shared photos. Ciphertext-policy attribute-based encryption (CP-ABE) is a one-to-many public key cryptosystem, and its access policy can be set by data owners. Therefore, if we share the protected image on the social platform and encrypt the restoration parameters of the shared image with CP-ABE, then only the accessor whose attribute set satisfies the access policy of CP-ABE can decrypt the ciphertext corresponding to his/her attribute level and then restore the image with the corresponding sharpness level. Consequently, image information protection is realized in a one-to-many scenario. However, for the existing CP-ABE, only when further shortening its ciphertext, reducing the number of bilinear pairing calculations during decryption, and ensuring flexible access policies is it beneficial for CP-ABE to be widely used in popular smart terminals that can run social software. Furthermore, existing algorithms for restoring images also have room for improvement in terms of time and space requirements. For this reason, we propose a progressive image restoration strategy based on the improved CP-ABE in this paper. For the improvement of CP-ABE, we design a new encryption scheme to achieve a shorter constant-size ciphertext, construct an auxiliary function to help the independent authority centers generate private keys for users in new ways, design a decryption algorithm with only one bilinear pairing calculation, and provide the update algorithms for attribute revocation. Subsequently, we build a distributed CP-ABE based on our improved CP-ABE, and the correctness and security of the proposed CP-ABE algorithm are also proven. In addition, we follow the tree access policy to support the access policy, including AND, OR, NOT and threshold operations simultaneously, to adapt to the requirement of some user attributes that undergo frequent changes. Moreover, based on the atmospheric scattering model, we adopt three algorithms to restore the protected image in the dehazing mode according to the sharpness parameters. Compared with the existing literature, we provide users with not only a flexible and efficient access control strategy, shorter constant-size ciphertext and fewer bilinear calculations but also multiple algorithms for restoring images. The experimental results for six privilege levels demonstrate the superiority of our algorithms in protecting image information.