Optical Image Encryption and Data Hiding using Double Random Phase Encoding and Advanced Encryption Standard on Chaotic Baker Mapped Image

Optical Image Encryption and Data Hiding using Double Random Phase Encoding and Advanced Encryption Standard on Chaotic Baker Mapped Image

Deepak Thomas

Department of Electronics and Communication Nehru Institute of Engineering and Technology, Coimbatore, India

T. Prabu

Department of Electronics and Communication Nehru Institute of Engineering and Technology,

Coimbatore, India

Abstract In every communication channel or methodology now a days, there is a necessity of secure transmission from sender to the authentic receiver. In this paper a new technique for optical image encryption based on Chaotic Baker Map, Advanced Encryption Standard (AES) and Double Random Phase Encoding (DRPE) is presented. This technique is implemented in three layers to enhance the security level of the classical DRPE. At first layer a pre-processing is performed with the Chaotic Baker Map on the original image. Then AES algorithm is used to encrypt the image for the security and confidentiality of the image. A message is also stored in the pixels of the image. After AES encryption the classical DRPE is done. DRPE is done using two random phase masks, one in the input plane and the other in the Fourier plane, to encrypt the primary image in to stationary white noise. MATLAB simulation experiments show that the proposed technique enhances the security level of the DRPE, and at the same time has a better immunity to noise. Histogram analysis is performed to check the effectiveness of the method.

Index TermsOptical Image, DRPE, AES, Chaotic Baker Map

1. INTRODUCTION

   The term Digital Image Processing (DIP) generally refers to the processing of a two-dimensional picture by a digital computer. In a broader context, it implies digital processing of any two-dimensional data. The image is converted to digital form using a scanner or digitizer and then process it. It is the numerical representations of objects to a series of operations in order to obtain a desired result. It starts with one image and produces a modified version of the same. It is therefore a process that takes an image into another.

   A digital image is an array of real numbers represented by a finite number of bits. The principle advantage of Digital Image Processing methods is its versatility, repeatability and the preservation of original data precision. Encryption is the process of transforming a piece of information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The output is known as the cipher text. The reverse process

   of transforming cipher text to plaintext is known as decryption.

   The optical encryption techniques play an important role in several fields like medical or biometric images for storage and transmission, video conferencing over optical fiber, military applications, online banking systems, governmental services, identity cards, satellite images etc. Care has to be taken while dealing with images. Problems occur with unauthorized use by hackers. Optical encryption provides a better and safe way for image communication. To retrieve the original optical information at the receiver side, the encryption method and keys are essentially required.

   In this paper, first Chaotic Baker Map is applied to the input image. It is a unit square map. It is applied to image dividing the image to different parts. Then data hiding is carried out in the encoded image. After data hiding Advanced Encryption Standard is applied and then Double Random Phase Encoding is done. DRPE method uses two random phase masks, one is used in the input plane and the other in the Fourier plane. DRPE is used to encrypt the primary image into stationary white noise. To meet the high levels of security, DRPE with Chaoticmap pre-processing and AES is proposed in this paper.

   The remaining sections of this paper are organized as follows. Section II gives an explanation of the chaotic Baker map and the data hiding technique used in the pre-processing step. Section III gives an explanation of the AES and then the section IV explains the DRPE method used. Section V discusses the proposed technique with required block diagrams. Section VI presents the simulation results. Finally, Section VII gives the conclusion.

2. CHAOTIC BAKERMAP AND DATA HIDING

   The baker's map is used in many deterministic dynamical systems, due to its action on the space of functions defined on the unit square. The baker's map defines an operator on the space of functions, which known as the transfer operator of the map. In the baker's map the Eigen functions and Eigen values of the transfer operator is easily determined.

   p1 p2	p3 p4 p5 p6	p7 p8
   p9 p10	p11 p12 p13 p14	p15 p16
   p17 p18	p19 p20 p21 p22	p23 p24
   p25 p26	p27 p28 p29 p30	p31 p32
   p33 p34	p35 p36 p37 p38	p39 p40
   p41 p42	p43 p44 p45 p46	p47 p48
   p49 p50	p51 p52 p53 p54	p55 p56
   p57 p58	p59 p60 p61 p62	p63 p64

   chaotic randomization of an 8X8 matrix with a secret key S=[2,4,2].

   Data hiding is done with the help of image pixels. The Least Significant Bit (LSB) of each pixel is changed to store the required message.Thus a byte of message is stored within eight pixels with ine bit of data in the LSB of each pixel. The length of the message is calculated and the first byte of data is the message length.This data hiding is done to the chaotic bakered image and the next stage of image encryption is carried out.

   III .AES ALGORITHM

   p31	p23	p15	p7	p32	p24	p16	p8
   p63	p55	p47	p39	p64	p56	p48	p40
   p11	p3	p12	p4	p13	p5	p14	p6
   p27	p19	p28	p20	p29	p21	p30	p22
   p43	p35	p44	p36	p45	p37	p46	p38
   p59	p51	p60	p52	p61	p53	p62	p54
   p25	p17	p9	p1	p26	p18	p10	p2
   p57	p49	p41	p33	p58	p50	p42	p34

   Advanced Encryption Standard (AES) allows a data length of 128 bits. In AES there are four basic operation blocks which performs substitution of bytes, shifting rows, mixing columns and adding round key. The AES operates on array of bytes which is organized as a 4*4 matrix that is called the state. The algorithm begins with an Add round key stage followed by ninerounds of four stages each and a tenth round of three stages which is carried out for both encryption and decryption. The flow of the AES encryption algorithm is shown in Figure 2.

   SubBytes

   Cipher Key

   Plain Text ADD Round Key

   Fig.1. Chaotic Randomization of an 8X8 Matrix with a Secret Key S=[2,4,2]

   The chaotic Baker map is a well-known tool of image encryption. It is a tool based on permutation which performs the randomization of a square matrix of dimensions M x M . It is done by changing the pixel positions based on a secret key. In this technique a pixel is assigned to another pixel position in a bijective way. The Baker map is denoted by

   B(v1,v2, vk ) (1)

   where the sequence of k integers, is chosen such that each

   Shift Rows

   Mix Columns

   ADD Round Key

   (n-1)

   Rounds

   integer vi divides M , and

   M i =v1+v2++ vi

   Shift Rows

   The pixel at indices (l,s), is mapped to

   (2)

   SubBytes

   Round Keys

   Final Round

   Final Round Keys

   B(n ……n

   ) l,s

   ADD Round Key

   1 k

   M

   i

   (l M

   v

   )s mod M , vi (ss mod M )M

   i

   v M v

   (3)

   Cipher Text

   i i i

   where Mi l Mi vi and 0 s M

   The square matrix M x M is divided into k rectangles of width vi and number of elements M. Then the elements in each rectangle are rearranged to a row in the permuted rectangle. After that the rectangles are taken from right to left beginning with upper rectangles, and then lower ones. Then the scan begins from the bottom left corner towards upper elements which is done in each rectangle. Figure 1 shows

   Fig. 2. Design flow of AES Encryption Algorithm

   In the tenth round mixing of columns is not included. The first nine rounds of the decryption algorithm are governed by the four stages which includes, inverse shift rows, inverse substitute bytes, add round key and inverse mix columns. Again in the tenth round the inverse mix columns stage is not included. The AES decryption algorithm is explained in Figure 3.

   Final Round Keys

   Cipher Text ADD Round Key

   Inv Shift Rows Inv SubBytes

   Round Keys

   Inv Mix Columns ADD Round Key

   Cipher Key

   Inv SubBytes Inv Shift Rows

   ADD Round Key

   Plain Text

   (n-1)

   Rounds

   Final Round

   fixed polynomial. Figure 5 shows the resultant output state. And in the inverse mix columns transformation, every column of the state array is considered as a polynomial.

   Mix column

   a0,0	a0,1	a0,2	a0,3
   a1,0	a1,1	a1,2	a1,3
   a2,0	a2,1	a2,2	a2,3
   a3,0	a3,1	a3,2	a3,3

   b0,0	b0,1	b0,2	b0,3
   b1,0	b1,1	b1,2	b1,3
   b2,0	b2,1	b2,2	b2,3
   b3,0	b3,1	b3,2	b3,3

   Fig.5. Mix Column Operation

3. DRPE

Double Random Phase Encoding (DRPE) is used to encrypt an input image. The input image is rearranged by two random phase masks, one located at the input plane and the other one at the Fourier plane in a 4f optical system. The encryption and decryption keys used are conjugate to each other. So DRPE is regarded as a symmetrical key system. To

Fig.3. Design flow of AES Decryption Algorithm

The substitute bytes operation is a non linear byte substitution method using a substation table or S-box which is shown in Figure 4. Here each byte from the input state is replaced by another byte from S table. The substitution is invertible. Inverse substitute bytes is the reverse operation of the substitute bytes transformation. In the inverse substitute bytes operation the inverse S-box is applied to

reconstruct the input image at the receiver side, decryption keys or random phase masks are required to be sent through a secure channel. The decryption process uses the same Fourier Random Phase Mask (RPM) as in the encryption process.

In the DRPE method first consider a primary intensity image f (x, y), where x and y denote the spatial domain coordinates. Also and denote the Fourier domain coordinates. (x, y)denote the encrypted image,

each byte of the state.

and

n(x, y)

and

m(x, y), denote two independent white

S-Box

sequences uniformly distributed in 0, 2.

To encode f (x, y)into a white stationary sequence, two RPMs are used,

n (x, y) exp2i n(x, y)

m (x, y) exp2i m(x, y)

(4)

h(x, y) m(x, y)

is a phase function uniformly

distributed in 0, 2.The second RPM, m (v,),is the

Fourier transform of the function

h(x, y),

Fig.4. Substitute Bytes Operation

In the shift rows transformation, the first row of the state array remains unchanged and the bytes in the second, third and forth rows are cyclically shifted by one, two and three bytes to the left respectively. Inverse shift rows is the inverse of the shift rows operation in which the first row of the state array remains unchanged. And the bytes in the second, third and forth rows are cyclically shifted by one, two and three bytes to the right, respectively. In the mix columns transformation, every column of the state array is considered as a polynomial and they are multiplied with a

FT h(x, y) h(v,) m (v,) exp2i m(v,)

(5)

The encryption process consists of multiplying the primary image by the rst RPM n (x, y). The result is then convolved with the function h(x, y). The encrypted function is a complex function with amplitude and phase. It is given by the following expression:

n m

(x, y) f (x, y) (x, y) FT 1 (v,) (6)

where the symbol ( ) denotes convolution. The encrypted function has a noise-like appearance that does not reveal the content of the primary image. In the decryption

f (x, y)

fB x, y

process, (x, y)

is Fourier transformed, multiplied by the

complex conjugate of the second RPM m (v,)that acts as

a key, and then inverse Fourier transformed. As a result, the output is

Original Image

AES

encryption

Chaotic Baker

Data

m

FT 1 FT (x, y) (v,)

Encrypted Image

= FT 1 FT f (x, y) (x, y) (v,) (v,)

n m m

= f (x, y) n (x, y)