Image Encryption with Discrete Fractional Cosine Transform and Chaos

We present a new method for image encryption with discrete factional cosine transform (DFrCT) and chaos. DFrCT holds the particular properties which the conventional discrete cosine transform (DCT) hasnpsilat, that is its fraction. Chaos functions have extreme sensitivity to the initial conditions. Logistic map is a simple equation of chaos functions. XOR is first operated between the original image and logistic map. Then the chaotic image is transformed with DFrCT two times using different keys successively by rows and by columns. Based on this method, the image can encrypted effectively, also, the transmission of the encrypted image with DFrCT and chaos is faster than with fractional Fourier transform (DFrFT) and chaos. The computer simulations are presented to verify the validity of the proposed method, such as the mean square error (MSE) between the original images and the decrypted images.

I. Introduction

With the rapid development of Internet and the wide application of multimedia technology, people can communicate the digital multimedia information with others conveniently in the internet. In many cases, we hope our image data which are transmitted on the network do not be browsed or processed by illegal receivers. Therefore, the security of digital images attracts much attention recently, and many different methods for image encryption have been proposed. Such as the method for image encryption with fractional Fourier transform (FrFT) [1], and the technique for image encryption using fractional Fourier transform and radial Hilbert transform (RHT) [2]. Another method for optical image encryption using fractional Fourier transform and chaos was proposed by Narendra Singh [3]. Zhao et al proposed an optical image encryption method using fractional Hartley transform [4]. Wu et al proposed a method for image encryption with discrete fractional cosine transform (DFrCT) [5].