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An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm Bing Zhang a , Jun Sang *a , Mohammad. S. Alam b a School of Software Engineering, Chongqing University, Chongqing, China, 401331; b Department of Electrical and Computer Engineering, University of South Alabama, Mobile, AL, USA, 36688-0002 Abstract An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks 1 M and 2 M via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt 2 M into 2' M . Finally, a host image was enlarged by extending one pixel into 2 2 pixels and each element in 1 M and 2' M was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2 2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing. Keywords: image hiding, cascaded iterative Fourier transform (CIFT), public key, RSA 1. Introduction Since the double random phase encoding technique was proposed by Refregier and Javidi in 1995 [1], the optical technique based image encryption [2, 3] and information hiding [4, 5] has been widely used. Due to the rapid development of the Internet, a large amount of data needs to be transferred and for data security the information hiding method has a very high value these years [6, 7]. In this paper, we proposed an image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm. Cascaded iterative Fourier transform was used to convert one secret image into two phase-only masks, while the RSA algorithm was used to encrypt one of the masks. Computer simulations show that the method has a very good robustness and performance. This paper is organized as follows: in Section 2, the proposed image hiding method is briefly introduced and analyzed. Section 3 performs the numerical simulation experiment. In Section 4, the final conclusions are presented. * corresponding author: [email protected] Optical Pattern Recognition XXIV, edited by David Casasent, Tien-Hsin Chao, Proc. of SPIE Vol. 8748, 87480H · © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2018257 Proc. of SPIE Vol. 8748 87480H-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/03/2013 Terms of Use: http://spiedl.org/terms

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An image hiding method based on cascaded iterative Fourier

transform and public-key encryption algorithm

Bing Zhanga, Jun Sang

*a, Mohammad. S. Alam

b

aSchool of Software Engineering, Chongqing University, Chongqing, China, 401331; bDepartment of Electrical and Computer Engineering, University of South Alabama,

Mobile, AL, USA, 36688-0002

Abstract

An image hiding method based on cascaded iterative Fourier transform and public-key encryption

algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks

1M and 2M via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key

encryption algorithm RSA was adopted to encrypt 2M into 2'M . Finally, a host image was

enlarged by extending one pixel into 2 2 pixels and each element in 1M and 2'M was

multiplied with a superimposition coefficient and added to or subtracted from two different elements in

the 2 2 pixels of the enlarged host image. To recover the secret image from the stego-image, the

two masks were extracted from the stego-image without the original host image. By applying

public-key encryption algorithm, the key distribution was facilitated, and also compared with the image

hiding method based on optical interference, the proposed method may reach higher robustness by

employing the characteristics of the CIFT algorithm. Computer simulations show that this method has

good robustness against image processing.

Keywords: image hiding, cascaded iterative Fourier transform (CIFT), public key, RSA

1. Introduction

Since the double random phase encoding technique was proposed by Refregier and Javidi in 1995

[1], the optical technique based image encryption [2, 3] and information hiding [4, 5] has been widely

used. Due to the rapid development of the Internet, a large amount of data needs to be transferred and

for data security the information hiding method has a very high value these years [6, 7].

In this paper, we proposed an image hiding method based on cascaded iterative Fourier transform

and public-key encryption algorithm. Cascaded iterative Fourier transform was used to convert one

secret image into two phase-only masks, while the RSA algorithm was used to encrypt one of the

masks. Computer simulations show that the method has a very good robustness and performance.

This paper is organized as follows: in Section 2, the proposed image hiding method is briefly

introduced and analyzed. Section 3 performs the numerical simulation experiment. In Section 4, the

final conclusions are presented.

*corresponding author: [email protected]

Optical Pattern Recognition XXIV, edited by David Casasent, Tien-Hsin Chao, Proc. of SPIE Vol. 8748, 87480H · © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2018257

Proc. of SPIE Vol. 8748 87480H-1

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2. The proposed method

2.1 Transform the secret image with the cascaded iterative Fourier transform

The cascaded iterative Fourier transform (CIFT) algorithm [8, 9] is an algorithm based on DRPE

technology. Suppose ( , )f x y is the secret image that to be encrypted. For CIFT, two uniformly

distributed random arrays 0

1P and 0

2P (valued between and ) are selected. Then, the

following iteration is applied.

1

1 2( , ) { {exp[ ( , )]}exp[ ( , )]}.k k kx y F F jP x y jP u v (1)

1

3 1 2( , )exp[ ( , )] { {exp[ ( , )]}exp[ ( , )]}.k k k kf x y jP x y F F jP x y jP u v (2)

( , ), ( , ) 0( , ) .

( , ), ( , ) 0

k

k

f x y if f x yg x y

f x y if f x y

(3)

1 32

1

{ ( , )exp[ ( , )]}( , ) ( ).

{exp[ ( , )]}

k kk

k

F g x y jP x yP u v angle

F jP x y

(4)

1 1 1

1 3 2( , ) [ { { ( , )exp[ ( , )]}exp[ ( , )]}].k k k kP x y angle F F g x y jP x y jP u v (5)

where 0,1,2,...k ; F and 1F are represent the Fourier transform and the inverse Fourier

transform; ( , )x y and ( , )u v are represent the space coordinate and frequency coordinate;

3 ( , )kP x y is the thk iterative phase on the output plane, i.e., the phase of ( , )k x y ; ( , )kf x y is

an approximate amplitude image reconstructed from the thk iteration.

Because of high convergence speed of CIFT algorithm, ( , )kf x y will convergent to ( , )f x y

after about twenty iterations.

2.2 Encrypt one of the obtained masks with RSA

The iteration process yields two phrase-only masks 1( , )P x y and 2 ( , )P u v . One mask

1( , )P x y is chosen and encrypted with the public-key encryption algorithm RSA. After the encryption,

1( , )P x y becomes 1 '( , )P x y .

2.3 Embed the secret image into the host image

In this step, the host image ( , )H x y is enlarged by extending one pixel into 2 2 pixels, and

( , )H x y becomes '( , )H x y . Then the two masks are embedded as follows.

Proc. of SPIE Vol. 8748 87480H-2

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'

fÔf

.dir111

I I IM ir 16 tr\ ...

w,

1

1

2

2

'(2 1,2 1) '(2 1,2 1) '( , )

'(2 ,2 ) '(2 ,2 ) '( , )

'(2 ,2 1) '(2 ,2 1) ( , )

'(2 1,2 ) '(2 1,2 ) ( , )

H i j H i j t P i j

H i j H i j t P i j

H i j H i j t P i j

H i j H i j t P i j

(6)

Where t is the coefficient to embed the two masks. After embedding, the stego-image S( , )x y

is obtained.

3. Numerical simulations

Numerical simulations were conducted to verify the proposed method. The 256 256 image

Lena is chosen to be the secret image, which is shown in Fig.1.

Fig.1 the secret image

After encrypting the secret image with the CIFT algorithm described in Section 2.1, two

phase-only masks are obtained as Fig.2 shows.

Fig.2 the two phase-only masks

Proc. of SPIE Vol. 8748 87480H-3

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1'i`;4k

_,.

-c

Next, we choose the key of the RSA algorithm as:

public key: 2773, 847n d

private key: 2773, 63n e

After encrypting the mask 1( , )P x y with the RSA algorithm, 1( , )P x y becomes 1 '( , )P x y

shown in Fig.3.

Fig.3 the phase-only mask after encrypting with the RSA algorithm

Then, the two masks 1 '( , )P x y and 2 ( , )P u v are embedded into the host image (Fig.4) and the

stego-image shown in Fig.5 is obtained.

Fig.4 the host image

Proc. of SPIE Vol. 8748 87480H-4

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Fig.5 the stego-image

With the correct keys of the RSA algorithm, the secret image can be recovered, which is shown in

Fig.6.

Fig.6 the recovered secret image

By adding salt-pepper noise with density 0.02 to the stego-image, the stego-image is shown in

Fig.7(a). Due to the salt-pepper noise, the secret image recovered from the stego-image will be

somewhat different from the original secret image. However, it can still be recognized visually as

Fig.7(b) shows.

Proc. of SPIE Vol. 8748 87480H-5

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,;

' - ,-;L ' '

(a) (b)

Fig.7 adding salt-pepper noise with density 0.02 to the stego-image (a) the stego-image (b) the

recovered secret image

By cropping 1/16 of the top left corner of the stego-image, the stego-image is shown in Fig.8(a).

Due to the cropping operation, the secret image recovered from the stego-image will be somewhat

different from the original secret image. However, it can still be recognized visually as Fig.8(b) shows.

(a) (b)

Fig.8 cropping 1/16 of the top left corner of the stego-image (a) the stego-image (b) the recovered

secret image

4. Conclusions

An image hiding method based on cascaded iterative Fourier transform and public-key encryption

algorithm is proposed in this paper. With the CIFT algorithm, two random phase masks are obtained

from the secret image. Then, one of the masks is encrypted by the RSA algorithm. At last, these two

masks are embedded into a host image. Because of the RSA algorithm, the key distribution was

facilitated. The simulation experimental results demonstrate that the proposed method has a very good

robustness.

Proc. of SPIE Vol. 8748 87480H-6

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Acknowledgments

This work was supported by National Natural Science Foundation of China (No. 60972105). THE

AUTHOR GRATEFULLY ACKNOWLEDGES THE SUPPORT OF K.C.WONG EDUCATION

FOUNDATION, HONG KONG.

References

[1] P. Refregier, B. Javidi, "Optical image encryption based on input plane and Fourier plane random

encoding". Opt Lett. 20, 767–769 (1995).

[2] M. Osamu, J. Bahram, "Secure holographic memory by double-random polarization encryption".

Appl Opt. 43, 2915–2919 (2004).

[3] L.Z. Cai, M.Z. He, Q. Liu, X.L. Yang, "Digital Image Encryption and Watermarking by

Phase-Shifting Interferometry". Appl Opt. 43, 3078-3084(2004).

[4] S. Kishk and B. Javidi, "Information hiding technique with double phase encoding". Appl Opt. 41,

5462-5470(2002).

[5] H. Trichili, M. S. Bouhlel, L. Kamoun, "A review of watermarking techniques: Applications,

properties, and domains". J Test Eval. 31, 357–360 (2003).

[6] X. Zhou, D. Lai, S. Yuan, D. H. Li, J. P. Hu, "A method for hiding information utilizing

double-random phase-encoding technique," Optics and Laser Technology 39, 1360–1363 (2007)

[7] Kuang Tsan Lin, "Hybrid encoding method for hiding information by assembling double-random

phase-encoding technique and binary encoding method," Appl Opt 49, 3814-3820 (2010)

[8] Y. Y. Chen, X. Zhou, Y. L. Xiao, S. Yuan, X. L. Wu, "An improved watermarking method based on

double random phase encoding technique," Optics and Laser Technology 42,617–623 (2010).

[9] G. H. Situ, J. J. Zhang, "A cascaded iterative Fourier transform algorithm for optical security

applications," Optik 114, 473–477 (2003)

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