Confused Modulo Projection based Somewhat Homomorphic Encryption -- Cryptosystem, Library and Applications on Secure Smart Cities

With the development of cloud computing, the storage and processing of massive visual media data has gradually transferred to the cloud server. For example, if the intelligent video monitoring system cannot process a large amount of data locally, the data will be uploaded to the cloud. Therefore, how to process data in the cloud without exposing the original data has become an important research topic. We propose a single-server version of somewhat homomorphic encryption cryptosystem based on confused modulo projection theorem named CMP-SWHE, which allows the server to complete blind data processing without \emph{seeing} the effective information of user data. On the client side, the original data is encrypted by amplification, randomization, and setting confusing redundancy. Operating on the encrypted data on the server side is equivalent to operating on the original data. As an extension, we designed and implemented a blind computing scheme of accelerated version based on batch processing technology to improve efficiency. To make this algorithm easy to use, we also designed and implemented an efficient general blind computing library based on CMP-SWHE. We have applied this library to foreground extraction, optical flow tracking and object detection with satisfactory results, which are helpful for building smart cities. We also discuss how to extend the algorithm to deep learning applications. Compared with other homomorphic encryption cryptosystems and libraries, the results show that our method has obvious advantages in computing efficiency. Although our algorithm has some tiny errors ($10^{-6}$) when the data is too large, it is very efficient and practical, especially suitable for blind image and video processing.