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.