The multiple-parameter discrete fractional Hadamard transform

Abstract

Discrete fractional Hadamard transform (DFrHaT) is a generalization of the Hadamard transform, which has been widely used in signal processing. In this paper, we present the multiple-parameter discrete fractional Hadamard transform (MPDFrHaT), which has multiple order parameters instead of only one in DFrHaT. The proposed MPDFrHaT is shown to possess all of the desired properties of DFrHaT. In fact, it will reduce to DFrHaT when all of its order parameters are the same. We also propose a novel encryption technique, double random amplitude (DRA) encoding scheme, by cascading twofold random amplitude filtering. As a primary application, we exploit the multiple-parameter feature of MPDFrHaT and double random amplitude encoding scheme for digital image encryption in the MPDFrHaT domain. Results show that this method can enhance data security.