Image Encryption using Quad Phase Masks in ... - IEEE Xplore

Image Encryption using Quad Phase Masks in Fractional Fourier Domain and Case Study Monika Dahiya

Sanatan Sukhija

Hukum Singh

Computer Science and Engineering

Computer Science and Engineering

Applied Science and Humanities

ITM University, Gurgaon

ITM University, Gurgaon

ITM University, Gurgaon

[email protected]

[email protected]

[email protected]

Abstract— A Technique for the encryption of the image is proposed using the random phase masks and fractional Fourier transform. The method uses four random phase masks and two fractional orders that act as the encryption key. The encryption scheme transmits the data to the authorised user maintaining its integrity and confidentiality. Numerical simulations results have been carried out to validate the algorithm and its Mean Square Error (MSE) is calculated. Furthermore, an image is divided in to four sections and on each of the section of the image different algorithms are applied and then there encryption and the decryption time is studied and also their MSE are calculated and compared to find an algorithm which is most optimal. Keywords— Encryption; Decryption; Random Phase Encoding; Fourier Transform; Fractional Fourier Transform.

I. INTRODUCTION With the development that has been made in the multimedia technologies, the information security of the images has become an important subject. We are living in the age of information where maintaining the integrity and confidentiality of information is a great concern. In today’s world it has become more important to secure the images during transmission. So, Encryption is the process in which sender wants to send an information to the receiver, he takes an input information and apply some algorithms on the information called the encryption algorithms and converts it into an unintangible information. This information sent to the receiver can be termed as the encrypted information. Then, this information is transmitted over some channel to the recipient. The receiver receives the encrypted image. Then the receiver applies the decryption algorithm to obtain the actual image that the sender intended to send. Many encryption algorithms have been proposed [1-8]. Among them Double Random Phase Encoding (DRPE) method has been widely used. The DRPE scheme uses two random phase masks that are statistically independent in the input domain and the Fourier domain respectively to encrypt the input image in to a stationary white noise [1]. An enhancement to this technique is the Fractional Fourier Transform. Fractional Fourier Transform enhances the key space of the algorithm as it uses the fractional orders. Other researchers have also made significant contributions in this

c 978-1-4799-2572-8/14/$31.00 2014 IEEE

area [8-9]. Madhusudan Joshi and Keher Singh[10] have given the encryption of the colored images by splitting the colored image in to RGB components. Zhang and Karim[11] have proposed encryption of the colored image using single channel. Inspired by the Double Random Phase Encoding and Fractional Fourier Transform, we have proposed a method that combines the Double Random Phase Encoding algorithm and the Fractional Fourier Transform to encrypt and decrypt the image. Since, this method uses four random phase keys, one in the input domain, two in the Fourier domain and one in the fractional Fourier domain. Now to decrypt the image we need two fractional orders and three decrypting keys, the correct knowledge of all these five parameters lead to correct decryption. Results have being studied to what happens if incorrect decryption keys or incorrect fractional orders are used in the decryption. Numerical Simulation results have been studied and the Mean Square Error between the primary (input) image and the decrypted image is calculated. Then, we will further take a colored input image and divide the image in to four sections. And then, to first part of the colored image, we will encrypt this colored image by dividing it in to the Red, Green, Blue component [10] . Then, we will consider the second part of the image and initially convert the colored image in to the greyscale image and then encrypt the image using Fractional Fourier Transform[9] Further, taking the third part of the image we will apply the algorithm that we will be discussing in this paper. Then, finally on fourth part of image convert the colored image in to an indexed image initially and then encrypting the image using the Fractional Fourier Transform [11] . II. PRINCIPLE OF ENCRYPTION AND DECRYPTION Fractional Fourier Transform (FRT) is the enhancement to the Fourier Transform. 1-D notations have been considered for notifying the symbols. Let xm and xp be the coordinates of the input plane and the output pth fractional plane respectively. The FRT of the function f(xm) of the order p can be defined as [12]-

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