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2009Photonics, ICOP 2009-International Conference on Optics and Photonics, Oct.CSIO,Chandigarh, India, 30 Oct.-1 Nov.2009

ENCRYPTION AND DECRYPTION USING A PHASE MASK SET CONSISTING OF A RANDOM PHASE MASK AND A SINUSOIDAL PHASE GRATING IN THE FOURIER PLANE

Madan Singha, Arvind Kumar* and Kehar Singh Instruments Design, Development, and Facilities Center, Staff Road, Ambala, Haryana, - 133001, (INDIA) Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110 016, (INDIA) *Email: - [email protected]

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Abstract: In the present paper, we demonstrate encryption and decryption of images using a phase mask set consisting of a random phase mask (RPM) and a sinusoidal phase grating (SPG) in the Fourier plane of a double random phase encoding system (DRPE). It makes the system more secure as compared to using a simple RPM at the Fourier transform plane, due to larger key size. After encryption, if the grating is removed, the system becomes resistant to impulse attack. Experimentally, the display and eraser of the grating at the Fourier transform plane can be realized by using a Spatial Light Modulator (SLM) working in phase mode. Simulation results are presented in support of the proposed idea. The robustness of the technique has been analyzed by calculating mean-square-error (MSE) between the decrypted and the original image. 1. INTRODUCTION The present information age and its overreliance on computer networks has created enormous possibilities of both frauds and compromising of digital assets. The whole new breed of attacks due to international terrorism, new vicious viruses, and stealing of company secrets from internet data bases, have given birth to new brand of billion-dollar esecurity business world wide. Various techniques [1] have been proposed to encrypt and decrypt the images/data. Optical encryption system that uses phase conjugate in a photorefractive crystal has been described by Unnikrishanan et al. [2]. Nomura et al. [3] have described a method to design an input phase mask for DRPE optical encryption. By using the designed input phase mask, the bit error rate has been improved. Barrera et al. [4] have investigated a method for image encryption by multiple-step random phase encoding with an undercover multiplexing operation. Singh and Kumar [5] have investigated a highly secure encryption and decryption system using a sandwich diffuser made with two normal speckle patterns and placed in the Fourier plane. Such a sandwich diffuser offers enhanced security of the system due to double diffraction in the FT plane. Fractional Fourier transform (FrFT) geometry has been used extensively [6-15] for secure encryption and decryption of the images. Barrera et al. [16] have investigated a holographic memory system in which an encrypted image is obtained by multiple image recording using varying lateral shift of a random phase mask. They have also investigated an optical architecture [17] in which multiple image encryption has been done by using different pupil aperture shapes in the optical system, together with multiple holographic storage, thereby increasing the security of image encryption without degradation of its noise robustness. Multiplexing in optical encryption of twodimensional images, by using various apertures and rotation of one of the constituent phase diffusers of a sandwich phase diffuser in the Fourier plane have been investigated by Singh et al. [18]. In order to further enhance the security of the system, Hennelly and Sheridan [19] have proposed a system to encrypt and decrypt a 2-D image using a random shifting, or jigsaw algorithm. Nishchal et al. [20] proposed a method to encrypt and decrypt a 2-D image that uses jigsaw transform and localized FRT. The jigsaw transform is applied to the original image to be encrypted and the image is then divided into independent non-overlapping segments. Sinha and Singh [21] have investigated a technique to encrypt and decrypt the image by breaking it into bit planes. In this process, each bit plane undergoes a jigsaw transform and is then encrypted using fractional Fourier transform. In view of the importance of the subject, researches on encryption continue unabated. Situ et al. [22] have proposed a cryptanalysis of optical security systems with significant output images. Frauel et al. [23] have investigated the resistance of the DRP encryption against various attacks. Recently, a possibility of known-plaintext attack on an optical encryption scheme based on DRP key has been investigated compelling the scientific community to investigate encryption systems to make them more secure [24]. In the present paper, we have presented simulation

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results of encryption and decryption of 2-D images by employing a phase mask set consisting of an RPM and a SPG, in the Fourier plane of a DRPE system. The successful retrieval of the correct image is possible only if both the RPM2 and the grating are placed at the original position they occupied during the encryption. The use of a phase mask set makes the system more secure as compared to using a simple RPM due to a larger key size. After the encryption if the grating is removed, the system becomes resistant to delta function attack. After the encryption, if we remove the SPG it becomes impossible to obtain the correct image. Simulation results are presented in support of the proposed idea. To evaluate the reliability of the technique, MSE between the decrypted and original image has been calculated. 2. THEORETICAL ANALYSIS A 4-f setup may be used for encryption and decryption process. Let (x,y) and (u,v) denote respectively the coordinates in the object and the Fourier transform plane. The real-valued function f(x,y) denotes the primary 2-D image to be encrypted, and function (x,y) denotes the encrypted image. The encryption of the input image f(x,y) is done in two steps. First, we multiply the input image f(x,y) with RPM1 denoted as R1(x,y) at the input plane. This product is then convolved with a phase mask set R(u,v) kept at the Fourier plane. This mask R(u,v) is made by combining a second RPM denoted as R2(u,v) with the SPG denoted as R3(u,v) generated by using the MATLAB® platform. The random phase functions R1(x,y), R2(u,v), and R3(u,v) are chosen to be statistically independent. The image modified by these random phase functions is given by (x,y)=FT{FT[f(x,y)*R1(x,y)]*[R2(u,v)* R3(u,v)]} (1) where FT denotes the Fourier transform operation. Let R2(x,y) and R3(x,y) denote the inverse Fourier transforms of R2(u,v) and R3(u,v) respectively. The functions R2(u,v) and R3(u,v) are chosen to be the phase functions and denoted as exp[i2(u,v)] and exp[i3(u,v)] respectively, with phases uniformly distributed in the interval [0, 2]. It may be noted that R2(x,y) and R3(x,y) are the impulse responses of the phase only transfer functions R2(u,v) and R3(u,v), and thus provide stationary white noise. For decryption, the encrypted image is Fourier transformed and multiplied by the conjugates of the R2(u,v) and R3(u,v). This product is then inverse Fourier transformed, thus giving the decrypted image. For optical implementation, the encrypted image has to be recorded in a holographic recording material such as a photorefractive crystal to generate the phase conjugate wave. As the detector at the recording plane is an intensity detector, the phase

introduced by R1(x,y) is nullified. The decrypted image fd(x,y) may be expressed as: fd(x,y)=IFT{FT[*(x,y)]*[R2(u,v)*R3(u,v)]} (2) After the encryption, we remove the phase grating. This act can be realized by using an SLM working in phase mode. This makes the system resistant to delta function attack. For decryption, we have to display the same SPG on the SLM because the decryption is not possible without the SPG. If the phase mask set R(u,v) made by using R2(u,v) and R3(u,v) is shifted in position, it is also impossible to retrieve the original data. For decryption, we have to bring both the RPM2 and RPM3 constituting a set phase mask in their original position occupied by them during the encryption. To evaluate the reliability of the proposed algorithm, MSE has been calculated by using the following criterion

2 1 N-1M-1 fd (x,y) - f ( x,y) N×M x=0 y=0

MSE =

(3)

where (N×M) is the size of the image in numbers of pixels. fd(x,y) and f(x,y) are respectively the decrypted image and the primary image. 3. SIMULATION RESULTS AND DISCUSSION The simulation study was carried out on a MATLAB® platform. A gray-, and a binary scale image of size 256×256 pixels have been chosen for study. One RPM at the input plane and combination of the RPM2 and SPG denoted as R2(u,v) and R3(u,v) respectively at the Fourier plane have been employed in the conventional DRPE algorithm. The first RPM1 is placed in close contact with the original image and the other combination of the RPM2 and grating denoted as R2(u,v) and R3(u,v) respectively are placed in the Fourier plane. The encryption and decryption have been performed by employing the single as well as cross gratings in the Fourier plane. 3.1 With Single Grating Case 1: The original primary (gray) image is Fourier [Fig.1(a)] multiplied by the RPM1 transformed, and then multiplied by the combination of the RPM2 and a single SPG, denoted as R3 (u,v) and R3(u,v) respectively. The sinusoidal grating is

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(c) (d) (e) Fig. 1: Simulation results of gray scale image with one single grating: (a) Input image, (b) Single grating, (c) Encrypted image, (d) Decrypted image with correct key, (e) Decrypted image with wrong key (without grating). shown in Fig.1(b). This view is shown before changing it into the phase mode. The resultant is further inverse Fourier transformed to get the encrypted image [Fig.1(c)]. The random phase codes are generated on MATLAB®, the primary interval of phase taken as [0,2]. For decryption, the encrypted image is Fourier transformed and multiplied by the conjugate of the combination of the RPM R2(u,v) and the grating R3(u,v) used in the Fourier plane during encryption. The resultant image is further Fourier transformed to obtain the decrypted image. Since the detector can record only the intensity, further multiplication of the conjugate of R1(x,y) is not required. The recovered image with the correct key is shown in Fig.1(d). The decrypted image recovered with a wrong key (i.e. without a grating) is shown in Fig.1(e) . The MSE calculated between the decrypted image and the primary (gray scale) image with correct key is negligible (~10-31) and with wrong key the value is ~103. The use of additional RPM as a sinusoidal phase grating in combination with the RPM2 enhances the security of the system. Case 2: The same process is repeated for the binary image [Fig.2(a)] with 1-D grating as shown in Fig.2(b). This view was taken before changing it into the phase mode. The encrypted image is shown in Fig.2(c). The decrypted images recovered are shown

found to be negligible (~10-27) and with wrong key the value is 104. From the above-mentioned results, it is clear the use of 1-D grating in the Fourier plane with RPM2 is not more effective as we can see some structure in the decrypted images [Figs.2(e) and 3(e)] for both binary as well as gray scale image. 3.2 With Crossed Grating Case 3: To make the system more effective, we introduced a crossed grating in place of a simple grating. The previous process is repeated replacing a simple grating with the crossed grating as shown in [Fig.3(b)] and with the same primary gray scale

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(c) (d) (e) Fig. 3:. Simulation results of amplitude based gray scale image with cross grating: (a) Input image, (b) Cross grating, (c) Encrypted image, (d) Decrypted image with correct key, (e) Decrypted image with wrong key (without grating). image [Fig.3(a)]. The encrypted image is shown in Figs.3(c). The recovered image with the correct key is shown in Fig.3(d). Figs.3(e) is obtained with a wrong key (without grating). In case of binary image [Fig.4(a)] and with cross grating [Fig.4(b)] the encrypted image obtained is shown in Fig.4(c). The recovered image with the correct key is shown in Fig.4(d). Fig.4(e) is obtained with a wromg key i.e. without grating.

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(a) (c) (d) (e) Fig. 2: Simulation results of binary image with one single grating: (a) Input image, (b) Single grating, (c) Encrypted image, (d) Decrypted image with correct key, (e) Decrypted image with wrong key (without grating). in Figs.2(d) and 2(e) with the correct-, and wrong key (without grating) respectively. In this case also, the MSE between the decrypted image and the primary (binary) image with the correct key has been

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Fig. 4: .Simulation results of amplitude based binary image with cross grating: (a) Input image, (b) Cross grating , (c) Encrypted image, (d) Decrypted image with correct key, (e) Decrypted image with wrong key (without grating).

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The MSE calculated between the decrypted image and the primary (binary) image with correct key is negligible (~10-27) and with wrong key the value is ~103 in case of binary image. Also in case of gray scale image, the MSE between the decrypted image and the primary image with the correct key has been found to be negligible (~10-31) and with wrong key the value is ~104. 5. CONCLUSION In the present paper, we have presented the simulation results of encryption and decryption of 2-D images by employing a phase mask sets consisting of RPM and a simple sinusoidal grating as well as a crossed grating, in the Fourier plane of a DRPE system. After the encryption, if the grating is erased, the system becomes resistant to delta function attack. Also the decryption becomes impossible without the grating. The successful retrieval of the correct image is possible only if both the RPM2 and the SPG are placed in the original position occupied be them during the encryption. The use of a phase mask set makes the system more secure as compared to using a simple RPM at the Fourier transform plane due to larger key size. Simulation results are presented in support of the proposed idea. To evaluate the reliability of the technique, MSE between the decrypted and original image has been calculated. REFERENCES [1] Javidi B, (Ed.). Optical and digital techniques for information security. Springer Verlag, 2004. [2] G. Unnikrishanan, J. Joseph, and K. Singh, "Optical encryption system that uses phase conjugate in a photorefractive crystal," Appl. Opt. 37, 8181 (1998). [3] T. Nomura, F. Nitanal, T. Numata, and B. Javidi, "Design of input phase mask for the space bandwidth of the optical encryption system,". Opt. Eng. 45, 017006 (2007). [4] J.F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, "Optical-encoding retrieval for optical security," Opt. Commun. 276, 231(2007). [5] M. Singh, Arvind Kumar,." Optical encryption and decryption using sandwich random phase diffuser in the Fourier plane," Opt. Eng. 46, 055201( 2007). [6] G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett. 25, 887(2002). [7] G. Unnikrishanan, and K. Singh, "Double random fractional Fourier domain encoding for optical security," Opt. Eng. 39, 853(2002):.

[8] Z-g Liu, and S. Liu, "Double image encryption based on iterative fractional Fourier Transform," Opt. Commun. 275, 324( 2007). [9] N. Singh, A. Sinha, "Optical image encryption using fractional Fourier transform and chaos, "Opt. Laser Eng. 46, 117 (2008). [10] R. Tao, Y. Xin, and Y. Wang, "Double image encryption based on random phase encoding in the fractional Fourier domain," Opt. Express 15, 16067 (2007). [11] Z. Liu, J. Dai, X. Sun, and S. Liu, "Triple image encryption scheme in fractional Fourier Transform domain," Opt. Commun. 282, 518 (2009). [12] D. Zhao, X. Li, and L. Chen, "Optical image encryption with redefined fractional Hartley transform," Opt Commun. 281, 5326 (2009). [13] S. Liu, Q. Mi, and B. Zhu, "Optical image encryption with multistage and multi channel fractional Fourier domain," Opt. Lett. 26, 1242 (2001). [14] N.K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption using cascaded extended fractional Fourier transform," Opt. Mem. Neural Net. 12, 139 (2003). [15] Madusudan Joshi, Chandrashakher, and K. Singh, "Color image encryption and decryption using fractional Fourier transform," Opt. Commun. 279, 35 (2007). [16] J.F.Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, "Multiplexing encryptiondecryption via lateral shifting of a random phase mask," Opt. Commun. 259, 532 (2006). [17] J.F.Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini,. "Multiple image encryption using an aperture-modulated optical system," Opt. Commun. 261, 29 (2006). [18] M. Singh, Arvind Kumar, and K. Singh, "Multiplexing in optical encryption by using an aperture system and a rotating sandwich random phase diffuser in the Fourier plane," Opt. Laser Eng. 46, 243 (2008). [19] B. Hennelly, and J. T. Sheridan, "Optical image encryption by random shifting in fractional Fourier domains," Opt. Lett. 28, 269 (2003). [20] N.K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh,." Optical encryption using a localized fractional Fourier transform," Opt. Eng. 42, 3566 (2003). [21] A. Sinha A, and K. Singh, "Image encryption by using fractional Fourier transforms and jigsaw transform in image bit plane," Opt. Eng. 44, 057000 (2005). [22] G. Situ, U. Gopinathan, D.S. Monaghan, T. Sheridan, "Cryptanalysis of optical security systems with significant output images," Appl. Opt. 46, 5257 (2007).

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[23] Y. Frauel, A. Castro, T.J. Naughton, and B. Javidi,." Resistance of the double random phase encryption against various attacks," Opt .Express 15, 10253 (2007). [24] X. Peng, P. Zhang, H. Wei, and G. Yu, "Knownplaintext attack on optical encryption based on double random phase keys," Opt. Lett. 31, 1044 (2006).

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