Hybrid Color and Grayscale Images Encryption Scheme Based on Quaternion Hartley Transform and Logistic Map in Gyrator Domain

Abstract

A hybrid color and grayscale images encryption scheme based on the quaternion Hartley transform (QHT), the two-dimensional (2D) logistic map, the double random phase encoding (DRPE) in gyrator transform (GT) domain and the three-step phase-shifting interferometry (PSI) is presented. First, we propose a new color image processing tool termed as the quaternion Hartley transform, and we develop an efficient method to calculate the QHT of a quaternion matrix. In the presented encryption scheme, the original color and grayscale images are represented by quaternion algebra and processed holistically in a vector manner using QHT. To enhance the security level, a 2D logistic map-based scrambling technique is designed to permute the complex amplitude, which is formed by the components of the QHT-transformed original images. Subsequently, the scrambled data is encoded by the GT-based DRPE system. For the convenience of storage and transmission, the resulting encrypted signal is recorded as the real-valued interferograms using three-step PSI. The parameters of the scrambling method, the GT orders and the two random phase masks form the keys for decryption of the secret images. Simulation results demonstrate that the proposed scheme has high security level and certain robustness against data loss, noise disturbance and some attacks such as chosen plaintext attack.