F-TPE: Flexible Thumbnail-Preserving Encryption Based on Multi-Pixel Sum-Preserving Encryption

Abstract

People are accustomed to utilizing mobile phones to capture images and uploading them to the cloud due to various incomparable advantages such as saving the storage space on the device. In this context, privacy concerns are raised since images may contain some sensitive information. Encrypting images by traditional schemes can alleviate privacy leak, but the usability is often deprived since it is tough to browse them on the cloud. Recently, Tajik <i>et al.</i> proposed an ideal <i>thumbnail-preserving encryption</i> (TPE) scheme to achieve the balance of usability and privacy by leveraging a two-pixel substitution encryption method while the Markov chain is utilized to prove the security. However, the connectivity of Markov chain in this scheme is weak since the length of pixel groups in the encryption process is only two, leading to a long mixing time of achieving the stationary distribution of Markov chain. To this end, we firstly propose a method of <i>multi-pixel sum-preserving encryption</i> (MP-SPE) that realizes the encipherment of vectors of arbitrary length. Then, with the help of MP-SPE, a novel flexible ideal TPE scheme (F-TPE) is designed and the connection of Markov chain is improved. The experiments have demonstrated that the proposed scheme can effectively attain the balance between usability and privacy. In addition, F-TPE takes much less time in encrypting compared with the existing work.