Implementation of the discrete wavelet transform and multiresolution analysis in the encrypted domain

Abstract

Signal processing in the encrypted domain is a new technology for protecting valuable signals from insecure signal processing. Although there has been some research in the area, this field of research is still in its infancy. In this paper, we propose a scheme for implementing discrete wavelet transform (DWT) and multi-resolution analysis (MRA) in a homomorphic encrypted domain. We first suggest a framework for performing DWT and inverse discrete wavelet transform (IDWT) in the encrypted domain and then conduct an analysis of data expansion and quantization errors on the framework. In order to solve the problem of data expansion, which is very important in practical applications, we then present a novel method for reducing data expansion in the case that both DWT and IDWT are performed. With the proposed method, multi-level DWT/IDWT can be performed with less data expansion in a homomorphic encrypted domain. We address the case of a two-dimensional Haar wavelet transform and give some experiments to demonstrate the advantages of our improved method. To the best of our knowledge, this is the first paper on the implementation of DWT and MRA in the encrypted domain.