Discrete fractional wavelet transform and its application to multiple encryption

Abstract

The fractional wavelet transform is a useful mathematical transformation that generalizes the most prominent tool in signal and image processing namely wavelet transform by rotation of signals in the time–frequency plane. The definition of discrete fractional wavelet transform is not reported yet in the literature. Therefore, a definition of the discrete fractional wavelet transform is consolidated by discretizing continuous fractional wavelet transform in the proposed work. Possible applications of the transform are in transient signal processing, image analysis, image transmission, biometrics, image compression etc. In this paper, image transmission is chosen as the primary application and hence a novel encryption scheme is proposed for securing multiple images during communication and transmission over insecure channel. The proposed multiple image encryption scheme is consolidated by fractional wavelet transform and chaotic maps. First, all the images are encrypted followed by their sharing. The sharing process is done considering numerical techniques by making the sharing process a system of linear equations. Experimental results and security analysis demonstrate the efficiency and robustness of the proposed primary application.