Efficient Encrypted Images Filtering and Transform Coding with Walsh-Hadamard Transform and Parallel
Efficient Encrypted Images Filtering and Transform Coding with Walsh-Hadamard Transform and Parallelization
Since homomorphic encryption operations have high computational complexity, image applications based on homomorphic encryption are often time consuming, which makes them impractical. In this paper, we study efficient encrypted image applications with the encrypted domain Walsh-Hadamard transform (WHT) and parallel algorithms. We first present methods to implement real and complex WHTs in the encrypted domain. We then propose a parallel algorithm to improve the computational efficiency of the encrypted domain WHT. To compare the WHT with the discrete cosine transform (DCT), integer DCT, and Haar transform in the encrypted domain, we conduct theoretical analysis and experimental verification, which reveal that the encrypted domain WHT has the advantages of lower computational complexity and a shorter running time. Our analysis shows that the encrypted WHT can accommodate plaintext data of larger values. We propose two encrypted image applications using the encrypted domain WHT. To accelerate the practical execution, we present two parallelization strategies for the proposed applications. The experimental results show that the speedup of the homomorphic encrypted image application exceeds 12.
The existing homomorphic encryption operations are usually computationally expensive because the unbreakable property of the homomorphic cryptosystem partly results from the employment of a huge algebraic structure. The common cryptographic operations, such as module exponentiation, are much more computationally expensive than arithmetic operations in the plaintext domain. One of the important purposes of cloud computing is to store the users data in the cloud for the facility of access everywhere and easy distribution.
Cloud storage can provide the convenience for the further cloud computing. Various types of cloud storage services are provided by Amazon, Google, Baidu, Tecent, and Alibaba. To protect the security and privacy of users images, the users images should be stored in encrypted format. However, both cloud server and user may expect directly to perform processing on the encrypted images stored in cloud storage without decryption to prevent privacy leaking.
There have been many reports for this scenario, such as cloud-based secure health service, encrypted image feature extraction, privacy-preserving outsourced photo searching, secure forensic image recognition, etc. For example, in a privacy-preserving face recognition system, the encrypted face images will be performed filtering, feature extraction, and recognition. However, since there are a great amount of pixels in an image when applying these time-consuming homomorphic cryptographic operations, the required execution time is far beyond our expectations. For these reasons, the practical application of image processing with homomorphic encryption is greatly limited.
First, we suggest that it is preferable to use efficient and fast signal transforms whose performances are close to the commonly used signal transformations, such as DCT and DFT. Second, multi-core equipment is increasingly popular. A supercomputer may be composed of even thousands of CPU cores. We expect that the computing time will be reduced greatly if we succeed in parallelizing the algorithm to make use of more CPU cores. Specifically, in this paper, we focus on the investigation of WHT and CWHT and use them as the signal transforms in our encrypted image applications. Since the implementations of WHT and CWHT do not require any exponential operations, the encrypted domain WHT and CWHT are efficient. Furthermore, by analyzing the procedures of the encryption domain WHT/CWHT and their applications on encrypted images, we propose parallel strategies to accelerate the encrypted image applications. Our efficiency improvement makes the response of the cloud system rapid and improves the service experience.