- Email: [email protected]
Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology
ARTICLE IN PRESS
Optics and Lasers in Engineering 45 (2007) 761–765 www.elsevier.com/locate/optlaseng
Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology Yong-Ying Wang, Yu-Rong Wang, Yong Wang, Hui-Juan Li, Wen-Jia Sun Optics Department, School of Information Science and Engineering, Shandong University, Jinan 250100, Shandong Province, China Received 15 November 2006; received in revised form 13 January 2007; accepted 18 January 2007
Abstract A new method of optical image encryption with binary Fourier transform computer-generated hologram (CGH) and pixel-scrambling technology is presented. In this method, the orders of the pixel scrambling, as well as the encrypted image, are used as the keys to decrypt the original image. Therefore, higher security is achieved. Furthermore, the encrypted image is binary, so it is easy to be fabricated and robust against noise and distortion. Computer simulation results are given to verify the feasibility of this method and its robustness against occlusion and additional noise. r 2007 Elsevier Ltd. All rights reserved. Keywords: Optical image encryption/decryption; Computer-generated hologram; Pixel-scrambling technology
1. Introduction Optical technology for information security has received increasing interest in the past decade [1–10]. Several methods and algorithms, such as double random phase encoding [1], the coding method based on iterative phase retrieval algorithm [2–5], virtual optics [6,7], have been proposed. Some researchers [8–10] use pixel scrambling with other methods to encrypt image. In Refs. [8,9], a method using pixel random technology and optical systems based on the fractional Fourier transform (FRT) is proposed, in which a reference beam is necessary to record the complex data after each FRT operation, and spatial light modulators with the functions of modulating both amplitude and phase are used to display the signal. It is very hard to perform by optical implementation at present. Meng [10] uses pixel random technology and iterative Fresnel-transform algorithm to encrypt image. He adopts more phase masks to encrypt the original image in order to increase its security and decrease the errors caused by the quantization of phase masks owing to limitations in the fabrication procedure. The more number of phase masks Corresponding author. Tel.: +86531 8836 1208.
E-mail address: [email protected] (Y.-Y. Wang). 0143-8166/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2007.01.003
he uses, the better decrypted image can be retrieved, at the same time the higher accuracy of alignment is needed. This method is more complicated and hard to be implemented optically. Therefore, it can be only used in digital image encryption. In this paper, a new method of optical image encryption with pixel scrambling and binary Fourier transform CGH is proposed. In this method, the encrypted image is an amplitude-only image composed of only two values, one or zero. By comparison, binary images are simplest to be fabricated, replicated and transferred, and this structure can increase the robustness to noise and distortion caused by some processing. In the decryption process, only the intensity of the image needs to be recorded and displayed, which can be easily performed by optical apparatus. The present method has significant potential for verification, anti-counterfeiting application and encryption security. The principle and procedure of the proposed image encryption method based on binary Fourier transform CGH and pixel-scrambling technology are described in Section 2. The computer simulation results and the examination of robustness against occlusion and additional noise are provided in Section 3. Conclusions are presented in Section 4.
ARTICLE IN PRESS Y.-Y. Wang et al. / Optics and Lasers in Engineering 45 (2007) 761–765
762
2. Image encryption method
2.2. Pixel scrambling and inverse pixel scrambling
2.1. Binary Fourier transform CGH [11,12]
Pixel scrambling [8–10] is equal to divide the original image into several subsections and displace the position of the parts. It means that the gray or red–green–blue value of the point (x, y) is exchanged with that of (x0 , y0 ) according to a special order. One could not get any useful information from the pixel-scrambled image, but the original image can be restored by the inverse operation. We take a 3 3 numerical matrix as an example. First, we construct a matrix M that is a random permutation of the integers from 1 to 9 (3 3). The principle of pixel scrambling is depicted in Fig. 2. The Roman numerals and the Arabic numerals in Fig. 2(a) denote the order of the parts in the original image and matrix M, which is the order of the original image parts in the image after pixel scrambling, respectively. In Fig. 2(b) we can see that the scrambled image looks like noise and you could not get the original image from it. Fig. 3 shows the process of corresponding inverse pixel scrambling. Fig. 3(a) is the scrambled image. In Fig. 3(b) the Arabic numerals denote
In the method developed by Lohmann, the hologram plane is divided into smaller rectangles each containing an aperture. An example of a Lohmann cell is shown in Fig. 1. In each cell, there is a transparent rectangle on an opaque background. The width of the rectangle is a constant. The height of the (m, n)th rectangle is determined by the value of amplitude. The position of the (m, n)th rectangle inside the cell is determined by the value of phase. Therefore, the expression for binary Fourier transform CGH becomes Hðu; vÞ ¼
XX m
pmn
ymn ; ¼ 2p
n
l mn
u ðm þ pmn Þ du v n dv rect , W du l mn dv 0 F , ¼ 0 mn F rect
mn max
where |Fmn| and ymn denote the amplitude and the phase distribution of the Fourier spectrum, respectively. The values of pmn are defined in the interval [0, 1], and 0plmnp1. The function rect(x/a) is defined as 1 for |x|pa/2 and as 0 otherwise, the value of W is a constant. In order to get brightness of image, the value of W is 12 [12]. Meanwhile, we use modular over-flow correction [13] to avoid reconstruction image distorted. Finally, we can obtain a binary Fourier transform CGH. Because we want to receive the intensity of the original image, display the binary image H(u, v) on SLM which is illuminated by a plane wave, then compute the inverse Fourier transform, the intensity of the original image can be obtained through the intensity distribution of the firstorder diffraction.
b
I (8)
1mn
V
III
VII
VIII
IV
II
IX
I
VI
II (6) III (2) Pixel scrambling
IV(5)
V (1)
VI(9) Random
VII (3) VIII (4) IX (7)
Fig. 2. The process of pixel scrambling: (a) the original image and (b) the image after pixel scrambling.
a
b V
III
VII
VIII
IV
II
IX
I
VI
Inverse Pixel scrambling
W
n
a
I (8)
II (6)
III (2)
IV(5)
V (1)
VI(9)
VII (3) VIII (4) IX (7)
Fig. 3. The process of inverse pixel scrambling: (a) the scrambled image and (b) the image after inverse pixel scrambling.
f (x,y)
PS1
f '(x,y)
FT
F (u,v)
PS2
F'(u,v)
Encode
H'(u,v)
pmn
H'(u,v)
m Fig. 1. Structure of the (m, n)th cell in binary hologram.
IPS2
H (u,v)
IFT
h (x,y)
IPS1
h'(x,y)
first-order diffraction of the output intensity
Fig. 4. Diagram of the encryption and decryption processes.
ARTICLE IN PRESS Y.-Y. Wang et al. / Optics and Lasers in Engineering 45 (2007) 761–765
the order of the parts in the image after pixel scrambling. We can get the original image after inverse pixel scrambling. In the process of pixel scrambling, if the parts of the image are more disorderly, in other words, the size of each part is much smaller, the security of the image will be higher, but at the same time, the calculation will be much larger.
763
2.3. The process of the encryption and decryption Suppose f (x, y) is the complex amplitude distribution in the object plane. The size of the original image is s s. We divide f (x, y) into several parts and the size of each part is Ds1 Ds1, then we scramble the parts of f (x, y) using the corresponding parameters according to
Fig. 5. (a) The original image, (b) the image after pixel scrambling, (c) the encrypted image, (d) the decrypted image without the first step inverse pixel scrambling, (e) the decrypted image without the second step inverse pixel scrambling and (f) the correct decrypted image.
Fig. 6. Set of encrypted images covered by a zero-value square which the area values are 30%, 40% and 50% of the encrypted image, respectively: (a) pixel-scrambling technology, (c) the method in this paper, (b) and (d) the corresponding decrypted images of (a) and (c).
ARTICLE IN PRESS 764
Y.-Y. Wang et al. / Optics and Lasers in Engineering 45 (2007) 761–765
the method in Section 2.2 to obtain a scrambled image f 0 (x, y) ¼ PS1{f (x, y)}, where PS1 denotes pixel scrambling. The Fourier transform of the scrambled image is F (u, v) ¼ FT{f 0 (x, y)}, where FT denotes Fourier transform. We divide F (u, v) into several parts and the size of each part is Ds2 Ds2, then we scramble the parts of F (u, v) in the same way to obtain a scrambled frequency F 0 (u, v) ¼ PS2 {F(u, v)}. Finally, we code F 0 (u, v) into binary image H 0 (u, v) by method of detour phase coding. The binary image H 0 (u, v) is the encrypted image. Because the pixel scrambling of the input domain and Fourier domain are random in the process of encryption, computing the inverse Fourier transform of encrypted image directly cannot get any useful information. In this method, the size of the original image, the orders of the pixel scrambling in the input and Fourier planes, as well as the binary image, are used as the keys to recover the original image. If impostors copy the binary image without getting the corresponding parameters, they cannot obtain the useful information. Let us discuss the decryption process. First, we should scramble inversely the parts of the binary image H 0 (u, v) using the corresponding parameters, H(u, v) ¼ IPS2{H 0 (u, v)}, where IPS2 denotes inverse pixel scrambling. The binary image H(u, v) is displayed on SLM, which is illuminated by a plane wave and inverse Fourier transformed, then we record the first-order diffraction h(x, y) of the output intensity distribution by CCD and finally inversely scramble the parts of the h(x, y) to get the original image h0 (x, y) ¼ IPS1{h(x, y)}. Fig. 4 shows the encryption and decryption processes.
Fig. 7. The encrypted images with adding zero-mean Gaussian white noise of variance 0.3 and 0.5, respectively: (a) pixel-scrambling technology, (c) the method in this paper, (b) and (d) the corresponding decrypted images of (a) and (c).
3. Computer simulation results and discussion In this section, we apply the method discussed in Section 2 to construct CGH as the encrypted image. The sizes of the original image and the scrambling subsection in the input plane are 64 64 pixels and 4 4 pixels, respectively. M1 ¼ (64/4) (64/4) ¼ 256, and the size of pixel scrambling in Fourier plane is 4 4 pixels, M2 ¼ (64/ 4) (64/4) ¼ 256. The binary Fourier transform CGH has 512 512 pixels, and each cell is 8 8 pixels. In the CGH encoding process, the quantization levels of amplitude and phase are nine and eight, respectively. All of them can be generated by computer. Fig. 5(a) is the original image and Fig. 5(b) is the image after pixel scrambling in the input plane. Before Fourier transformation, the image is multiplied by a phase function exp[ij(x, y)] in which j(x, y) has random value between 0 and 2p in order to smooth the Fourier frequency. Fig. 5(c) shows the encrypted image. Figs. 5(d) and (e) are decrypted images without the first step inverse pixel scrambling and the second step inverse pixel scrambling, respectively. Fig. 5(f) is the correct decrypted image with the correct inverse pixels scrambling. In Fig. 5, we can draw a conclusion that the security of this method is rather higher. If the impostors copy the
encryption image without the corresponding parameters M1 and M2, they cannot get any information of the original image. The robustness of the method is also examined. We compare this method with the image encryption method, which is only based on pixel-scrambling technology. In the first example of distortions illustrated in Figs. 6(a) and (c), the images encrypted by pixel-scrambling technology and our method, respectively, are covered by a zero-value square, where the area values vary from 30% to 50% of the encrypted image. The corresponding decrypted images are shown in Figs. 6(b) and (d), respectively. From these figures, we can see that the image based on our method will be retrieved even if half of the encrypted image pixels have been lost. In another example illustrated in Figs. 7(a) and (c), the additive zero-mean Gaussian noise of variance 0.3 and 0.5, respectively, are added to the encrypted images based on two methods, Figs. 7(b) and (d) are the corresponding images revealed from the encrypted images, respectively. Compared with the pixel-scrambling technology, our method has higher degree of robustness to distortions and noise.
ARTICLE IN PRESS Y.-Y. Wang et al. / Optics and Lasers in Engineering 45 (2007) 761–765
4. Conclusions We have proposed an image encryption method based on pixel-scrambling technology and binary Fourier transform CGH. The binary encrypted image has the structure that is simplest to be fabricated, and its robustness to distortions and noise is increasing. The decryption process can be carried out optically by using spatial light modulator with the function of modulating amplitude. Computer simulations are performed to verify the validity of the proposed method. This method has significant potential for verification, anti-counterfeiting application and encryption security. Acknowledgments The authors acknowledge the support by the Natural Science Foundations of Shandong Province, China, Grant No. Y2004G01. References [1] Refregier P, Javidi B. Optical image encryption based on input plane and Fourier plane random encoding. Opt Lett 1995;20(7):767–9.
765
[2] Wang RK, Chatwin C. Random phase encoding for optical security. Opt Eng 1996;35(9):2464–9. [3] Li Y, Kreske K, Rosen J. Security and encryption optical systems based on a correlator with significant output images. Appl Opt 2000;39(29):5295–301. [4] Chang HT. Image encryption using separable amplitude-based virtual image and iteratively retrieved phase information. Opt Eng 2001;40(10):2165–71. [5] Situ G, Zhang J. Image hiding with computer-generated phase codes for optical authentication. Opt Commun 2005;245:55–65. [6] Peng X, Yu L, Cai L. Double lock for image encryption with virtual optical wavelength. Opt Express 2002;10(1):41–5. [7] Peng X, Cui Z, Tan T. Information encryption with virtual-optics imaging system. Opt Commun 2002;212(4–6):235–45. [8] Hennelly B, Sheridan JT. Optical image encryption by random shifting in fractional Fourier domains. Opt Lett 2003(28):269–71. [9] Zhao J, Lu H, Song X, Li J, Ma Y. Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique. Opt Commun 2005;249:493–9. [10] Meng X-F, Cai L-Z, Yang X-L, Shen X-X, Dong G-Y. Information security system by iterative multiple-phase retrieval and pixel random permutation. Appl Opt 2006(45):3289–97. [11] Brown BR, Lohmann AW. Complex spatial filtering with binary masks. Appl Opt 1966;5(6):967–9. [12] Lohmann AW, Paris DP. Binary Fraunhofer holograms, generated by computer. Appl Opt 1967;6(10):1739–48. [13] Dallas WJ. Magnitude-coupled phase quantization. Appl Opt 1974;13(10):2274–9.
Optics and Lasers in Engineering 45 (2007) 761–765 www.elsevier.com/locate/optlaseng
Optical image encryption based on binary Fourier transform computer-generated hologram and pixel scrambling technology Yong-Ying Wang, Yu-Rong Wang, Yong Wang, Hui-Juan Li, Wen-Jia Sun Optics Department, School of Information Science and Engineering, Shandong University, Jinan 250100, Shandong Province, China Received 15 November 2006; received in revised form 13 January 2007; accepted 18 January 2007
Abstract A new method of optical image encryption with binary Fourier transform computer-generated hologram (CGH) and pixel-scrambling technology is presented. In this method, the orders of the pixel scrambling, as well as the encrypted image, are used as the keys to decrypt the original image. Therefore, higher security is achieved. Furthermore, the encrypted image is binary, so it is easy to be fabricated and robust against noise and distortion. Computer simulation results are given to verify the feasibility of this method and its robustness against occlusion and additional noise. r 2007 Elsevier Ltd. All rights reserved. Keywords: Optical image encryption/decryption; Computer-generated hologram; Pixel-scrambling technology
1. Introduction Optical technology for information security has received increasing interest in the past decade [1–10]. Several methods and algorithms, such as double random phase encoding [1], the coding method based on iterative phase retrieval algorithm [2–5], virtual optics [6,7], have been proposed. Some researchers [8–10] use pixel scrambling with other methods to encrypt image. In Refs. [8,9], a method using pixel random technology and optical systems based on the fractional Fourier transform (FRT) is proposed, in which a reference beam is necessary to record the complex data after each FRT operation, and spatial light modulators with the functions of modulating both amplitude and phase are used to display the signal. It is very hard to perform by optical implementation at present. Meng [10] uses pixel random technology and iterative Fresnel-transform algorithm to encrypt image. He adopts more phase masks to encrypt the original image in order to increase its security and decrease the errors caused by the quantization of phase masks owing to limitations in the fabrication procedure. The more number of phase masks Corresponding author. Tel.: +86531 8836 1208.
E-mail address: [email protected] (Y.-Y. Wang). 0143-8166/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2007.01.003
he uses, the better decrypted image can be retrieved, at the same time the higher accuracy of alignment is needed. This method is more complicated and hard to be implemented optically. Therefore, it can be only used in digital image encryption. In this paper, a new method of optical image encryption with pixel scrambling and binary Fourier transform CGH is proposed. In this method, the encrypted image is an amplitude-only image composed of only two values, one or zero. By comparison, binary images are simplest to be fabricated, replicated and transferred, and this structure can increase the robustness to noise and distortion caused by some processing. In the decryption process, only the intensity of the image needs to be recorded and displayed, which can be easily performed by optical apparatus. The present method has significant potential for verification, anti-counterfeiting application and encryption security. The principle and procedure of the proposed image encryption method based on binary Fourier transform CGH and pixel-scrambling technology are described in Section 2. The computer simulation results and the examination of robustness against occlusion and additional noise are provided in Section 3. Conclusions are presented in Section 4.
ARTICLE IN PRESS Y.-Y. Wang et al. / Optics and Lasers in Engineering 45 (2007) 761–765
762
2. Image encryption method
2.2. Pixel scrambling and inverse pixel scrambling
2.1. Binary Fourier transform CGH [11,12]
Pixel scrambling [8–10] is equal to divide the original image into several subsections and displace the position of the parts. It means that the gray or red–green–blue value of the point (x, y) is exchanged with that of (x0 , y0 ) according to a special order. One could not get any useful information from the pixel-scrambled image, but the original image can be restored by the inverse operation. We take a 3 3 numerical matrix as an example. First, we construct a matrix M that is a random permutation of the integers from 1 to 9 (3 3). The principle of pixel scrambling is depicted in Fig. 2. The Roman numerals and the Arabic numerals in Fig. 2(a) denote the order of the parts in the original image and matrix M, which is the order of the original image parts in the image after pixel scrambling, respectively. In Fig. 2(b) we can see that the scrambled image looks like noise and you could not get the original image from it. Fig. 3 shows the process of corresponding inverse pixel scrambling. Fig. 3(a) is the scrambled image. In Fig. 3(b) the Arabic numerals denote
In the method developed by Lohmann, the hologram plane is divided into smaller rectangles each containing an aperture. An example of a Lohmann cell is shown in Fig. 1. In each cell, there is a transparent rectangle on an opaque background. The width of the rectangle is a constant. The height of the (m, n)th rectangle is determined by the value of amplitude. The position of the (m, n)th rectangle inside the cell is determined by the value of phase. Therefore, the expression for binary Fourier transform CGH becomes Hðu; vÞ ¼
XX m
pmn
ymn ; ¼ 2p
n
l mn
u ðm þ pmn Þ du v n dv rect , W du l mn dv 0 F , ¼ 0 mn F rect
mn max
where |Fmn| and ymn denote the amplitude and the phase distribution of the Fourier spectrum, respectively. The values of pmn are defined in the interval [0, 1], and 0plmnp1. The function rect(x/a) is defined as 1 for |x|pa/2 and as 0 otherwise, the value of W is a constant. In order to get brightness of image, the value of W is 12 [12]. Meanwhile, we use modular over-flow correction [13] to avoid reconstruction image distorted. Finally, we can obtain a binary Fourier transform CGH. Because we want to receive the intensity of the original image, display the binary image H(u, v) on SLM which is illuminated by a plane wave, then compute the inverse Fourier transform, the intensity of the original image can be obtained through the intensity distribution of the firstorder diffraction.
b
I (8)
1mn
V
III
VII
VIII
IV
II
IX
I
VI
II (6) III (2) Pixel scrambling
IV(5)
V (1)
VI(9) Random
VII (3) VIII (4) IX (7)
Fig. 2. The process of pixel scrambling: (a) the original image and (b) the image after pixel scrambling.
a
b V
III
VII
VIII
IV
II
IX
I
VI
Inverse Pixel scrambling
W
n
a
I (8)
II (6)
III (2)
IV(5)
V (1)
VI(9)
VII (3) VIII (4) IX (7)
Fig. 3. The process of inverse pixel scrambling: (a) the scrambled image and (b) the image after inverse pixel scrambling.
f (x,y)
PS1
f '(x,y)
FT
F (u,v)
PS2
F'(u,v)
Encode
H'(u,v)
pmn
H'(u,v)
m Fig. 1. Structure of the (m, n)th cell in binary hologram.
IPS2
H (u,v)
IFT
h (x,y)
IPS1
h'(x,y)
first-order diffraction of the output intensity
Fig. 4. Diagram of the encryption and decryption processes.
ARTICLE IN PRESS Y.-Y. Wang et al. / Optics and Lasers in Engineering 45 (2007) 761–765
the order of the parts in the image after pixel scrambling. We can get the original image after inverse pixel scrambling. In the process of pixel scrambling, if the parts of the image are more disorderly, in other words, the size of each part is much smaller, the security of the image will be higher, but at the same time, the calculation will be much larger.
763
2.3. The process of the encryption and decryption Suppose f (x, y) is the complex amplitude distribution in the object plane. The size of the original image is s s. We divide f (x, y) into several parts and the size of each part is Ds1 Ds1, then we scramble the parts of f (x, y) using the corresponding parameters according to
Fig. 5. (a) The original image, (b) the image after pixel scrambling, (c) the encrypted image, (d) the decrypted image without the first step inverse pixel scrambling, (e) the decrypted image without the second step inverse pixel scrambling and (f) the correct decrypted image.
Fig. 6. Set of encrypted images covered by a zero-value square which the area values are 30%, 40% and 50% of the encrypted image, respectively: (a) pixel-scrambling technology, (c) the method in this paper, (b) and (d) the corresponding decrypted images of (a) and (c).
ARTICLE IN PRESS 764
Y.-Y. Wang et al. / Optics and Lasers in Engineering 45 (2007) 761–765
the method in Section 2.2 to obtain a scrambled image f 0 (x, y) ¼ PS1{f (x, y)}, where PS1 denotes pixel scrambling. The Fourier transform of the scrambled image is F (u, v) ¼ FT{f 0 (x, y)}, where FT denotes Fourier transform. We divide F (u, v) into several parts and the size of each part is Ds2 Ds2, then we scramble the parts of F (u, v) in the same way to obtain a scrambled frequency F 0 (u, v) ¼ PS2 {F(u, v)}. Finally, we code F 0 (u, v) into binary image H 0 (u, v) by method of detour phase coding. The binary image H 0 (u, v) is the encrypted image. Because the pixel scrambling of the input domain and Fourier domain are random in the process of encryption, computing the inverse Fourier transform of encrypted image directly cannot get any useful information. In this method, the size of the original image, the orders of the pixel scrambling in the input and Fourier planes, as well as the binary image, are used as the keys to recover the original image. If impostors copy the binary image without getting the corresponding parameters, they cannot obtain the useful information. Let us discuss the decryption process. First, we should scramble inversely the parts of the binary image H 0 (u, v) using the corresponding parameters, H(u, v) ¼ IPS2{H 0 (u, v)}, where IPS2 denotes inverse pixel scrambling. The binary image H(u, v) is displayed on SLM, which is illuminated by a plane wave and inverse Fourier transformed, then we record the first-order diffraction h(x, y) of the output intensity distribution by CCD and finally inversely scramble the parts of the h(x, y) to get the original image h0 (x, y) ¼ IPS1{h(x, y)}. Fig. 4 shows the encryption and decryption processes.
Fig. 7. The encrypted images with adding zero-mean Gaussian white noise of variance 0.3 and 0.5, respectively: (a) pixel-scrambling technology, (c) the method in this paper, (b) and (d) the corresponding decrypted images of (a) and (c).
3. Computer simulation results and discussion In this section, we apply the method discussed in Section 2 to construct CGH as the encrypted image. The sizes of the original image and the scrambling subsection in the input plane are 64 64 pixels and 4 4 pixels, respectively. M1 ¼ (64/4) (64/4) ¼ 256, and the size of pixel scrambling in Fourier plane is 4 4 pixels, M2 ¼ (64/ 4) (64/4) ¼ 256. The binary Fourier transform CGH has 512 512 pixels, and each cell is 8 8 pixels. In the CGH encoding process, the quantization levels of amplitude and phase are nine and eight, respectively. All of them can be generated by computer. Fig. 5(a) is the original image and Fig. 5(b) is the image after pixel scrambling in the input plane. Before Fourier transformation, the image is multiplied by a phase function exp[ij(x, y)] in which j(x, y) has random value between 0 and 2p in order to smooth the Fourier frequency. Fig. 5(c) shows the encrypted image. Figs. 5(d) and (e) are decrypted images without the first step inverse pixel scrambling and the second step inverse pixel scrambling, respectively. Fig. 5(f) is the correct decrypted image with the correct inverse pixels scrambling. In Fig. 5, we can draw a conclusion that the security of this method is rather higher. If the impostors copy the
encryption image without the corresponding parameters M1 and M2, they cannot get any information of the original image. The robustness of the method is also examined. We compare this method with the image encryption method, which is only based on pixel-scrambling technology. In the first example of distortions illustrated in Figs. 6(a) and (c), the images encrypted by pixel-scrambling technology and our method, respectively, are covered by a zero-value square, where the area values vary from 30% to 50% of the encrypted image. The corresponding decrypted images are shown in Figs. 6(b) and (d), respectively. From these figures, we can see that the image based on our method will be retrieved even if half of the encrypted image pixels have been lost. In another example illustrated in Figs. 7(a) and (c), the additive zero-mean Gaussian noise of variance 0.3 and 0.5, respectively, are added to the encrypted images based on two methods, Figs. 7(b) and (d) are the corresponding images revealed from the encrypted images, respectively. Compared with the pixel-scrambling technology, our method has higher degree of robustness to distortions and noise.
ARTICLE IN PRESS Y.-Y. Wang et al. / Optics and Lasers in Engineering 45 (2007) 761–765
4. Conclusions We have proposed an image encryption method based on pixel-scrambling technology and binary Fourier transform CGH. The binary encrypted image has the structure that is simplest to be fabricated, and its robustness to distortions and noise is increasing. The decryption process can be carried out optically by using spatial light modulator with the function of modulating amplitude. Computer simulations are performed to verify the validity of the proposed method. This method has significant potential for verification, anti-counterfeiting application and encryption security. Acknowledgments The authors acknowledge the support by the Natural Science Foundations of Shandong Province, China, Grant No. Y2004G01. References [1] Refregier P, Javidi B. Optical image encryption based on input plane and Fourier plane random encoding. Opt Lett 1995;20(7):767–9.
765
[2] Wang RK, Chatwin C. Random phase encoding for optical security. Opt Eng 1996;35(9):2464–9. [3] Li Y, Kreske K, Rosen J. Security and encryption optical systems based on a correlator with significant output images. Appl Opt 2000;39(29):5295–301. [4] Chang HT. Image encryption using separable amplitude-based virtual image and iteratively retrieved phase information. Opt Eng 2001;40(10):2165–71. [5] Situ G, Zhang J. Image hiding with computer-generated phase codes for optical authentication. Opt Commun 2005;245:55–65. [6] Peng X, Yu L, Cai L. Double lock for image encryption with virtual optical wavelength. Opt Express 2002;10(1):41–5. [7] Peng X, Cui Z, Tan T. Information encryption with virtual-optics imaging system. Opt Commun 2002;212(4–6):235–45. [8] Hennelly B, Sheridan JT. Optical image encryption by random shifting in fractional Fourier domains. Opt Lett 2003(28):269–71. [9] Zhao J, Lu H, Song X, Li J, Ma Y. Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique. Opt Commun 2005;249:493–9. [10] Meng X-F, Cai L-Z, Yang X-L, Shen X-X, Dong G-Y. Information security system by iterative multiple-phase retrieval and pixel random permutation. Appl Opt 2006(45):3289–97. [11] Brown BR, Lohmann AW. Complex spatial filtering with binary masks. Appl Opt 1966;5(6):967–9. [12] Lohmann AW, Paris DP. Binary Fraunhofer holograms, generated by computer. Appl Opt 1967;6(10):1739–48. [13] Dallas WJ. Magnitude-coupled phase quantization. Appl Opt 1974;13(10):2274–9.