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Optics and Lasers in Engineering 46 (2008) 243–251

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Multiplexing in optical encryption by using an aperture system and arotating sandwich random phase diffuser in the Fourier plane

Madan Singha, Arvind Kumarb,�, Kehar Singhb

aInstruments Design, Development, and Facilities Center, Staff Road, Ambala, Haryana 133001, IndiabDepartment of Physics, Indian Institute of Technology, Delhi, New Delhi 110 016, India

Received 7 June 2007; received in revised form 30 September 2007; accepted 1 October 2007

Available online 28 November 2007

Abstract

In the present paper, we describe multiplexing in optical encryption of two-dimensional images, by using apertures and rotation of one

of the constituent phase diffusers of a sandwich phase diffuser in the Fourier plane. The sandwich phase diffuser is made with two

random constituent phase-diffusing surfaces sandwiched together. The apertures of different sizes and shapes are made with the help of

‘paint brush’ software. Simulation results are presented showing the effects of size, shape, and orientation of the apertures on the

decrypted images obtained via multiplexing techniques. In addition to the results of using aperture systems in encryption and decryption,

the results of rotation of one of the constituent phase diffusers in decryption are analyzed and used in multiplexing. Due to the use of

aperture systems and the rotation of the constituent phase diffuser, the multiplexing capability of the system in encryption is enhanced

along with the enhanced security due to using a sandwich diffuser. To evaluate the reliability of the technique, mean square error between

the decrypted and the original image has been calculated.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Optical encryption; Sandwich random phase diffuser; Apertures; Photorefractive crystal; Multiplexing; Phase conjugation

1. Introduction

In recent years, there has been an increasing interest inthe use of optical techniques for information securityapplications. The optical parameters such as phase,polarization, and wavelength are used to hide theinformation, making it possible to encode data moresecurely. In addition to this, the characteristics of fastcomputing and parallelism of optics make it very useful forreal-time applications. It has been established that opticalencryption techniques provide a more complex environ-ment, and are more resistant to attacks compared withdigital electronic systems. In this process of development,the double random phase encoding technique has beeninvestigated in the past, enabling one to encrypt a primaryimage into stationary white noise [1,2]. The encoding isdone by use of two statistically independent random phasecodes in the input and Fourier planes, with their phases

e front matter r 2007 Elsevier Ltd. All rights reserved.

tlaseng.2007.10.001

ing author.

ess: arvindk_542005@yahoo.co.in (A. Kumar).

uniformly distributed in the interval [0, 2p]. The perfor-mance of the system has been studied in the presence ofdifferent types of input noise and distortions such asscratches, fingerprint marks, and bending of the phasemask [3]. The result shows that the image can be wellencrypted using a random phase mask with a limitednumber of pixels. Also, the fault-tolerance properties of thedouble random phase encoding geometry have beenstudied [4].The encrypted image is also recorded in a barium

titanate crystal holographically, using double-randomFourier transform as well as fractional Fourier transformgeometries [5,6]. It has been reported that the decryptedinformation obtained from fully phase-based encryption ismuch more robust to additive noise than that obtainedfrom the amplitude-based encryption [7]. A phase-image-based content-addressable holographic data storage withsecurity using random phase in the Fresnel domain hasbeen described [8].Securing data in high-capacity storage systems is one of the

challenging tasks in order to meet the user’s requirements.

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There has been a continuous effort on the multiplexingfor data storage, and data security [9,10]. Multiplexingtechniques have been used to store multiple images in asingle crystal without cross-talk by using angular, peristrophic(rotational), and wavelength multiplexing [11–13]. Anothermultiplexing technique involves use of deterministic orthogo-nal phase codes in the reference beam [14]. This arrangementallows retrieving multiple images with high diffractionefficiency without adjustment problems [15,16].

The effects of lateral displacement on the performance ofthe encryption and decryption system [17], and the effectsof three-dimensional shifting selectivity of volume holo-gram based on random phase encoding with ground glasshave been investigated [18]. The shifting selectivity, being akey in phase encoding, can be used for holographicmultiplexing and encryption. Recording of multiplexedencrypted images based on the successive shifting of arandom pure-phase mask has been described [19]. Multi-plexing in image encryption has also been done by using anaperture-modulated optical system [20].

Recently, a possibility of known-plaintext attack on anoptical encryption scheme based on double random phasekey has been investigated [21]. With this algorithm, anopponent can access both random phase keys by phase-retrieval techniques. In view of the above, there is a needfor more sophisticated and complicated techniques (longerkey size) to be applied in the security systems. A sandwichspecklegram may be used in optical data security archi-tectures to make the system more secure.

In this paper, we describe the multiplexing in opticalencryption of two-dimensional images using an aperturesystem; and using a rotating constituent diffuser of asandwich diffuser in the Fourier plane. An aperture systemhaving apertures of different shapes and sizes is made withthe help of ‘‘paint brush’’ software. The encrypted imagemay be holographically recorded in a photorefractiveBaTiO3 crystal. Generating a phase-conjugated imagethrough the phase conjugation technique leads to decryp-tion. Due to double diffraction, a single sandwich diffuseroffers large key size in the security systems. In addition toenhancing the security, one of the diffusers constituting asandwich diffuser is used in multiplexing by rotating itaround the optical axis. It will facilitate the multiplexing inencryption along with enhanced security by a factor equalto the product of the number of apertures used, and thenumber of rotation steps used for the purpose. To evaluatethe reliability of the technique, the mean square errorbetween the decrypted and the original image has beencalculated. Simulation results are presented in support ofthe proposed idea.

2. Methodology

Fig. 1 shows the schematic of the 4-f system used formultiplexing in encryption, and the decryption process.The encryption of the input image is done in two steps.First, the object pattern f(x, y) is multiplied by a random

phase mask (RPM) Ro(x, y) at the input plane. Thisproduct is then convolved with Rc(x, y) and an apertureplaced in contact with the sandwich diffuser made ofdiffusers Rfm(u, v) and Rsm(u, v). Here Rc(x, y) may bedefined as the impulse response of Rfm(u, v) and Rsm(u, v)combined. The Fourier transform of the modified inputimage, i.e. the product of f(x, y) and Ro(x, y), is passedthrough the sandwich diffuser. The resultant informationthen passes through corresponding aperture of an aperturesystem in the Fourier plane kept in contact with thesandwich diffuser. The random phase functions Ro(x, y),Rfm(u, v) and Rsm(u, v) are chosen to be statisticallyindependent. The modified encrypted image due to the firstinput image f1(x, y) is given by

C1ðx; yÞ ¼ FTfFT½f 1ðx; yÞRoðx; yÞ� ½Rf1ðu; vÞRs1ðu; vÞA1�g.

(1)

Similarly the encrypted image of the second input imagef2(x, y) with second sandwich diffuser and second apertureis given by

C2ðx; yÞ ¼ FTfFT½f 2ðx; yÞRoðx; yÞ� ½Rf2ðu; vÞRs2ðu; vÞA2�g.

(2)

The ‘n’ different input images can be recorded one byone, keeping the apertures at different locations in theFourier plane. The encrypted image of the nth input imagewith mth sandwich diffuser and mth apertures written as

Cnðx; yÞ ¼ FTfFT½f nðx; yÞRoðx; yÞ�

� ½Rfmðu; vÞRsmðu; vÞAm�g. ð3Þ

The resultant encrypted image of N input images and M

apertures may be expressed by

CN ðx; yÞ ¼XMm¼1

XN

n¼1

½FTfFT½f nðx; yÞRoðx; yÞ� ½Rfmðu; vÞRsmðu; vÞAm�g�:

(4)

After multiplexing, the constituent diffusers Rfm(u, v)and Rsm(u, v) in each recording may be separated, thusacting as 2M keys. Here the number of apertures also actsas key, thus creating a total of 3M keys. In our case ‘m’ and‘n’ are kept equal, thus number of keys are 3N.For decryption, it should be noted that the constituent

diffusers making a sandwich diffuser should be placed atthe same location and orientation that they occupiedduring the encryption and the proper conjugate should bemade. The decrypted image may be expressed as

f nðx; yÞ ¼ IFTfFT½CNðx; yÞ� ½Am Conj ½Rfmðu; vÞRsmðu; vÞ�g.

(5)

For m ¼ n, we get the nth decrypted image with the rightkey. For m 6¼n we get the nth decrypted image fn(x, y) withwrong keys i.e., no image is obtained and we get only thenoise. To get the decrypted images, the aperture system andthe two diffusers Rfm(u, v) and Rsm(u, v) constituting thesandwich diffuser have to be aligned and brought back tothe same position and orientation which they occupied

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Ψ n(x,y) f1(x,y) Ro(x,y)

fn(x,y)

f2(x,y)

L1 L2 Rfm Rsm An

f f f f

DIΨ n (x,y) L2 L1 AmR*sm R*

fm

f f f f

Fig. 1. Schematic diagram of (a) multiplexing in encryption, (b) decryption set-up: encryption set-up Ro(x, y), Rfm Rsm random phase masks; R*fm R*

sm

conjugates of random phase masks; L1, L2, lenses; Am, apertures; f1(x, y) f2(x, y), y fn(x, y), input images; Cn(x, y), multiplexed encrypted images; DI,

decrypted image.

M. Singh et al. / Optics and Lasers in Engineering 46 (2008) 243–251 245

during the recording, and the proper conjugate of thesandwich diffuser has to be made.

For the optical implementation of present technique, aphotorefractive crystal may be used to record the encryptedimages. All the encrypted images can be stored in a singlerecording medium such as a photorefractive BaTiO3

crystal. We can record multiple images using angularmultiplexing in the same crystal. Changing the inputobject and the corresponding aperture position betweenthe successive recordings facilitates multiplexing ofthe encrypted images. An intensity detector, i.e. a CCD,can capture the decoded amplitude image that can bedisplayed onto a SLM for decryption process. Therecorded multiplexed encrypted image hologram isread with the conjugate of the reference beam to obtainthe decrypted images by phase conjugation. It alsocorrects other phase distortions such as defects of opticalcomponents.

The combination of other multiplexing techniques usedwith the aperture system increases the capacity of conven-tional multiplexing used for data storage. In addition tothis, multiplexing is done by rotating one of the diffusersconstituting the sandwich diffuser between the successiverecordings. For proper image decryption the value of nshould be equal to m.

The simulation study was carried out on a MATLABplatform. To evaluate the reliability of the proposedalgorithm, mean square error (MSE) was calculated byusing the MSE criterion:

MSE ¼ E1

N �M

XP�1x¼0

XQ�1y¼0

jjCnðx; yÞj � jf nðx; yÞjj2

" #, (6)

where P�Q is the size of the image in numbers of pixels,and E{ � }is the expectation value. Amplitude data, binaryimages, and gray scale images of sizes 256� 256 pixels eachwere chosen for the study.

3. Results and discussion

3.1. Effect of aperture size on the encryption and decryption

A binary and gray scale image of size 256� 256 pixels[Figs. 2(a) and 3(a)] has been chosen for the study. We havestudied the effect of changing the size of the circularapertures [Figs. 2(b–e) and 3(b–e)] in encryption anddecryption. For encryption, first the original image ismultiplied by the first random phase mask (RPM) Ro(x, y),and the product is Fourier transformed. This Fouriertransform is then multiplied by a sandwich RPM along

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Fig. 2. Simulation results of binary image for encryption and decryption

using a single aperture of different sizes: (I) input image; (a–e) apertures;

(f) encrypted image in case of full aperture; (g–j) encrypted image by using

apertures as shown in (b–e); (k) decrypted image in case of full aperture;

(l–o), decrypted images corresponding to the apertures as shown in (b–e).Fig. 3. Simulation results of gray scale image for encryption and

decryption using a single aperture of different sizes: (I) input image;

(a–e) apertures; (f) encrypted image in case of full aperture; (g–j) encrypted

image by using apertures as shown in (b–e); (k) decrypted image in case of

full aperture; (l–o) decrypted images corresponding to the apertures as

shown in (b–e).

M. Singh et al. / Optics and Lasers in Engineering 46 (2008) 243–251246

with an aperture system placed in contact with thesandwich diffuser at the Fourier plane, and inverse Fouriertransformed to get the encrypted image. The results

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Table 1

Effect of the size of apertures on the MSE value for binary and gray scale

images as shown in Figs. 2 and 3

SL. no. Size of the aperture MSE (binary

image)

MSE (gray

scale image)

1. Full aperture 4.2� 10�32 7.30� 10�27

2. 20% reduction 0.041 0.058

3. 60% reduction 0.083 0.174

4. 90% reduction 0.125 0.262

5. 95% reduction 0.223 0.291

Fig. 4. Simulation results for encryption and decryption using a single

aperture of different sizes: (a) input image; (b–f) apertures; (g–k) encrypted

images by using the apertures as in (b–f); (l–p) decrypted images

corresponding to the encrypted images as in (g–k).

M. Singh et al. / Optics and Lasers in Engineering 46 (2008) 243–251 247

showing the effect of changing the size, shape andorientation/position of the apertures on the decryptedimage have been presented. Apertures of different sizes asshown in Figs. 2(b–e) and 3(b–e) are kept in contact withthe sandwich diffuser at the Fourier plane and therecording is done for the binary and gray scale object.The encrypted images obtained are shown in Figs. 2(f–j)and 3(f–j) in case of binary image and gray scale image,respectively. Figs. 2(f) and 3(f) are the encrypted imagesobtained with full open aperture with binary and gray scaleimages, respectively. Figs. 2(g–j) and 3(g–j) are theencrypted images recorded with the apertures as shown inFigs. 2(b–e) and 3(b–e), respectively.

For decryption, the encrypted images are Fouriertransformed and multiplied by the conjugate of thesandwiched RPM and the aperture system at the Fourierplane. Further Fourier transform generates the decryptedimages. For perfect decryption, the sandwich diffuser andthe aperture system should be placed at the same positionand orientation which they occupied during the encryption.The resultant decrypted images are shown in Figs. 2(k–o)and 3(k–o). From Figs. 2, 3 and Table 1, it is very muchevident that the decrease in the aperture size results in adecrease of the resolution of the decrypted images. So acompromise has to be made between the size of theaperture used and the resolution of the image required.

3.2. Effect of increasing the number and size of the apertures

A binary image of size 256� 256 pixels [Fig. 4(a)] hasbeen chosen for the study. We have studied the effect ofincreasing the number and size of circular apertures inperforming encryption and decryption. Following theprocedure described in the previous section, the encryptedimages obtained with various apertures [Figs. 4(b–f)] areshown in Figs. 4(g–k), respectively. The recovered imageswith the corresponding apertures are shown in Figs. 4(l–p).The mean square errors obtained are shown in Table 2.From Fig. 4 and Table 2, it is clear that an increase in thenumber of apertures or the aperture size results in animprovement in the resolution of the decrypted images. Soa compromise has to be made between the number ofapertures to be used and the resolution of the recoveredimages. However, using a number of apertures facilitatesthe enhancement of capabilities of the recording system. In

the section below, we describe the use of an aperture systemfor multiplexing in encryption.

3.3. Multiplexing in encryption using circular apertures

In the first case, images in the form of letters A, B, C andD are taken as objects [Figs. 5(a–d)]. For multiplexing in

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encryption, we record the images of these four objects oneby one by keeping the circular apertures at differentlocations as shown in Figs. 5(e–h), respectively. The

Table 2

Effect of numbers and size of the apertures on the MSE value for binary

images as shown in Fig. 4

SL. no. Number of apertures MSE (binary image)

1. 1 0.105

2. 2 0.102

3. 4 0.097

Size of apertures

4. 4 times the size of apertures in Fig. 4(d) 0.084

5. 8 times the size of apertures in Fig. 4(d) 0.071

Fig. 5. Simulation results for encryption and decryption using a circular ap

(i) encrypted images; (j–m) decrypted images; (n) set of four apertures; (o) de

any aperture.

multiplexed encrypted image is shown in Fig. 5(i). Thedecrypted images recovered from the multiplexed en-crypted image [Fig. 5(i)] are shown in Figs. 5(j–m), withthe apertures being kept at the previous positions. TheMSEs between the decrypted image and the primary imageare 0.028, 0.0339, 0.025, and 0.030, respectively. Fig. 5(o)is the decrypted image obtained on using all four aperturessimultaneously as shown in Fig. 5(n) during the decryption.The image recovered without any aperture is shownin Fig. 5(p). The results show that the use of an aperturesystem for encryption suffers due to decrease in signal-to-noise ratio as the other decrypted images with wrong keysare present while getting the decrypted image with correctkey. However, using a number of apertures facilitates theenhancement of capabilities of the recording system.

erture at different positions: (a–d) input images; (e–h) aperture systems;

crypted image with a set of four apertures; (p) decrypted image without

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3.4. Multiplexing in encryption using square apertures

In this case, images in the form of transparent letters A,B, C and D are taken as objects [Figs. 6(a–d)]. Followingthe procedure described in Section 3.1, for multiplexing, werecord the images of these objects one by one by keeping apair of small square apertures at different locations asshown in Figs. 6(e–h), respectively. The multiplexedencrypted image is shown in Fig. 6(i) and decrypted imagesobtained from it are shown in Figs. 6(j–m). The meansquare errors calculated are 0.033, 0.038, 0.031, and 0.036.The combined decrypted images [Figs. 6(o) and (p)] areobtained with a set of four apertures and without anyaperture, respectively. In Figs. 6(j–m), we observe fringe

Fig. 6. Simulation results for encryption and decryption using a pair of sm

aperture systems; (i) encrypted images; (j–m) decrypted images; (n) set of four

image without any aperture.

structures on the decrypted images. It is due to use of anaperture system containing a pair of apertures.

3.5. Effect on decrypted images of rotation of one of the

constituent phase diffusers

The binary image of letter IITD and gray scale image ofLEENA of size 256� 256 have been chosen for study. Oneof the constituent random-phase diffusers Rsm is rotatedaround the optical axis at the time of recording thedecrypted images in order to determine the rotationsensitivity of the image decryption. The decrypted imagesobtained are shown in Figs. 7(a–f) for 0.001, 0.251, 0.501,1.001, 1.501 and 2.001 rotations, respectively. The mean

all-size square apertures at different positions: (a–d) input images; (e–h)

apertures; (o) decrypted image with a set of four apertures; (p) decrypted

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Fig. 7. Decrypted images for a binary object with angular rotation of the

constituent diffuser Rsm and keeping it at various positions: (a) at 01

(original position); (b) at 0.251; (c) at 0.501; (d) at 1.001; (e) at 1.501; and

(f) at 21.

Fig. 8. Decrypted images for a gray scale object with angular rotation of the co

position); (b) at 0.201; (c) at 0.401; (d) at 0.801.

Fig. 9. Encryption and decryption of images for angular rotation of a const

recorded by keeping the constituent diffuser Rsm at 01, 41, 81 and 121 positio

(diffuser R2 at 01, 41, 81 and 121 positions).

M. Singh et al. / Optics and Lasers in Engineering 46 (2008) 243–251250

square errors are 6.308� 10�33, 0.007, 0.026, 0.034, 0.036,and 0.037 for 01 (original position), 0.251, 0.501, 1.001,1.501 and 2.001 rotations of the constituent diffuser. Thedecrypted images in case of gray scale image are recordedas shown in Figs. 8(a–d) for 0.001, 0.201, 0.401, and 0.801,respectively, the mean square errors being 3.470� 10�027,0.345, 6.230 and 7.300, respectively. From Figs. 7 and 8 it isclear that in case of gray scale image the required angularrotation to get complete decrypted image is less than incase of binary image. This is due to the fact that the binaryimage contains mainly zero-order diffracted component,which falls on the rotating diffuser’s center, where thechange due to rotation is less as compared to that at theouter parts of the diffuser.

3.6. Multiplexing by rotating one of the constituent phase

diffusers

For multiplexing, we take the images in the form oftransparent letters A, B, C and D [Figs. 9(a–d)]. We record

nstituent diffuser Rsm and keeping it at various positions: (a) at 01 (original

ituent diffuser Rsm: (a–d) input images; (e) multiplexed encrypted image

ns, respectively; (f–i) decrypted images recovered by using the right keys

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the encrypted images of these objects one by one byrotating the constituent diffuser Rsm and keeping it at 01,41, 81, and 121 positions. The resultant encrypted image isshown in Fig. 9(e). The decrypted images obtained by useof right keys are shown in Figs. 9(f–i). The mean squarederrors are 0.144, 0.156, 0.167, and 0.157. The results ofFig. 9 show that the use of rotation for multiplexing inencryption is an appealing idea with acceptable resolutionbecause of using the full aperture for recordings.

4. Conclusion

We describe the multiplexing in optical encryption oftwo-dimensional images by using an aperture system alongwith a sandwich diffuser in the Fourier plane. The resultsof multiplexing by rotation of one of the constituentdiffuses of the sandwich random phase diffuser are alsopresented. It is found that any other multiplexing techniqueused with an aperture system increases the performance ofthe technique, but at the cost of resolution of the images.This is due to the fact that other decrypted images withwrong keys are present while retrieving the decryptedimage with a correct key. However, in some cases it may bevery useful to increase the multiplexing capability if themultiplexing is limited due to the physical and opticalparameters of the recording devices. The results of usingrotation for multiplexing in encryption and decryptionshow that it is an appealing idea, with acceptable resolutiondue to use of a full aperture for recordings.

Simulation results are presented in support of theproposed idea. To evaluate the reliability of the technique,mean square error between the decrypted and originalimage has been calculated. The use of aperture systemalong with rotation of sandwich diffuser enhances thecapability of multiplexing depending upon the numbers ofapertures and the number of rotation steps used. Combi-nations of these two techniques, i.e. use of the aperturesystem and the use of rotation of the constituent diffuser,may increase manifold the multiplexing capability of theencryption and decryption. This also results in enhancedcapability for multiplexing in data storage in addition tothe angle, shift, and other conventional multiplexingtechniques being used.

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