Multiple image encryption using an aperture ...

Optics Communications 261 (2006) 29–33 www.elsevier.com/locate/optcom

Multiple image encryption using an aperture-modulated optical system John Fredy Barrera a, Rodrigo Henao a, Myrian Tebaldi Roberto Torroba b, Ne´stor Bolognini c

b,*

,

a ´ ptica y Fotońica, Instituto de Fı´sica, Universidad de Antioquia, A. A. 1226, Medellıń, Colombia Grupo de O ´ pticas (CONICET-CIC), UID OPTIMO, Facultad de Ingenierıá, Universidad Nacional de La Plata, Centro de Investigaciones O P.O. Box 124, La Plata (1900), Argentina c ´ pticas (CONICET-CIC), UID OPTIMO, Facultad de Ingenierıá and Facultad de Ciencias Exactas, Centro de Investigaciones O Universidad Nacional de La Plata, La Plata, Argentina

b

Received 26 August 2005; received in revised form 9 November 2005; accepted 24 November 2005

Abstract A multiple image cryptosystem based on different apertures in an optical set-up under a holographic arrangement is proposed. The system is a security architecture that uses different pupil aperture mask in the encoding lens to encrypt different images. Based on this approach multiple encryption is achieved by changing the pupil aperture arrangement of the optical system among exposures. In addition to the classical speckle phase mask, the geometrical parameters characterizing the apertures are introduced to increase the system security. Even when an illegal user steals the speckle phase mask, the system cannot be broken into without the correct pupil geometrical parameters. The experimental set-up is based on a volume photorefractive BSO crystal as storing device. Information retrieval is done via a phase conjugation operation. We also have to stress that the multiple storage under this scheme, is only possible with the help of the aperture mask. Simulation and experimental results are further introduced to verify the proposed method. 2005 Elsevier B.V. All rights reserved. PACS: 42.30.d; 42.65.Hw; 42.40.i Keywords: Encryption; Photorefractive materials; Volume memories

1. Introduction Volume-holographic storage has received increasing attention owing to its potential high storage capacity and fast access rate. Many multiplexing techniques have been developed to perform high-density holographic storage [1–3]. One of the simplest phase multiplexing techniques consists in utilizing ground glasses in the reference beam to perform random phase multiplexing. In Ref. [4] the use of an aperture pupil that changes between exposures in a speckle arrangement is theoretically analyzed. This approach was successfully employed to perform optical

*

Corresponding author. Tel.: +54 221 4840280; fax: +54 221 4712771. E-mail address: [email protected] (M. Tebaldi).

0030-4018/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.11.055

image processing and several metrological applications (for instance, to store multiple in-plane displacements) [5,6]. The characteristics of the random phase multiplexing are used not only for holographic storage but also for optical encryption to prevent unauthorized users from obtaining the encrypted information [3,7–10]. Encryption in holographic storage can be accomplished in two ways. In the first approach, the reference beam is encoded. The user must have a phase key to encode the readout beam; otherwise nothing can be retrieved [3,9]. In the second approach the user can easily read-out the signal stored in the volume hologram; however, the encrypted information cannot be retrieved if a phase key is not used. Besides, good-fidelity phase-conjugated reading light [10,11] is required for diffraction of the phase conjugate of the stored signal.

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J.F. Barrera et al. / Optics Communications 261 (2006) 29–33

However, other possible keys can be employed to encrypt/ decrypt data, such as involving geometric or physical parameters. To explore the encryption possibilities beyond this point, we introduce in a double-random phase mask optical encryption arrangement another feature including an additional pupil aperture mask that is not only convenient but also is unique. Multiplexing techniques have been developed to perform multiple-image encryption, for instance angular multiplexing [12], wavelength multiplexing and multiplexing by random phase mask shifting. In this paper, we propose the mentioned novel approach based on the use of a pupil aperture mask that changes between exposures to implement multiple-image encryption. Considering the case of N different pupil apertures in the encoding lens, N different target images can be individually processed one for each aperture. The encrypted information can only be retrieved by using the original random phase mask and the additional pupil aperture mask. Position parameters are paired with N pupil apertures as a security enhancement prior to being introduced into the system. Consequently, aperture keys without precise distance or geometrical parameters cannot be used to access the system. Therefore, in this paper we propose, what is to our knowledge a new scheme for security systems, a technique based on a different apertures encoding scheme, which can be used to retrieve different target images from the encrypted record without changing the random phase mask, the angle between write-in beams or the wavelength. 2. Description of the method The multiple encryption arrangement is schematized in Fig. 1. In the recording process the signal beams are

Fig. 1. Experimental set-up. (CS: collimation system; BS1 and BS2: beam splitters, O: input object; R1 and R2: random phase masks; L1 and L2: lenses (distances s1 = 200 mm, s2 = 60 mm, s3 = 200 mm, s4 = 200 mm); P: pupil aperture mask; M1 and M2: mirrors; CCD1 and CCD2: CCD cameras; P plane: output plane; BSO: photorefractive crystal; A1, A2, A3, A4: optical beams).

encrypted by use of the double random-phase encoding technique [8,12] before they are incident on the photorefractive crystal. In every area in which Fourier transforms and frequency domain concepts are used, there exists potential for generalization and improvement by using the Fresnel domain. This is precisely what we also use in the present proposal. In our scheme, random phase masks (R1 and R2) are located in the input plane and in the Fresnel region of the lens L1, respectively. As it is well known, security increases by working in the Fresnel domain because this possibility adds an extra key to the whole process [13]. Nevertheless, in relation with the system capability to multiple encryption of our proposal, it should be pointed out that it is neither essential nor the main concern to work in the Fresnel domain. The image of the second random phase mask plane R2 is formed in the crystal volume through the lens L2. The basic architecture of the proposed system is composed of a pupil aperture mask attached to the lens L2 with the optical transmittance function denoted as P, an input plane O where the object is located and an output plane denoted as P. As usual in encryption procedures, the purpose of random phase mask R1 is to spread the respective object frequency content, therefore the use of both random phase masks transform the input image into a stationary white noise. In the crystal volume, the image bearing encrypted beam interferes with the reference beam so that the information is three dimensionally encrypted and fringe modulated. The angle between the reference and encrypted write-in beams is 16. Then, the average grating period is 4.3 lm at k = 532 nm. The use of a photorefractive material as an active medium allows obtaining the final successive decrypted image in real-time. In our set-up a BSO crystal cut normally to the h1 1 0 i crystallographic direction (transverse electro-optic configuration) and with dimensions 10 mm · 10 mm · 10 mm is utilized. This intensity distribution incident in the crystal volume generates a space charge field due to charge carrier redistribution. As a consequence of the linear electro-optical effect that the crystal exhibits, the resulting space charge field produces a refractive index perturbation which replicates and stores the encrypted information. Note that the application of an external electric field to the crystal (E0 = 7 kV) contributes to enhance the space charge field. Let us describe the experimental multiple encryption procedure. In doing so, each input to be encrypted is associated to a distinct pupil aperture, so that in the write-in step only that aperture is cleared. Therefore, each time a new input is presented, the aperture is changed in accordance. In this way, successive inputs are encrypted. To retrieve the stored data, a phase-conjugation readout scheme is used. The transmitted part of the reference beam is retroreflected by mirror M2, so that a beam is generated which is proportional to the conjugate of the image bearing beam. Note that the phase conjugate beam carries simultaneously the whole information associated with all the encrypted images. When the phase-conjugate waves of


the stored signals pass through the random phase mask again, the images are decrypted according to the appropriate clear aperture pupil mask in the encoding lens. In fact, the wavefront redistributes itself so that the phase conjugated wavefront corresponding to different pupil apertures in the recording step does not overlap in the pupil mask plane in the reconstruction step. Then, it is possible to reconstruct a determined image without cross talk. In summary, the ith image encrypted with the ith pupil is channelled in the phase conjugate process towards that part of the pupil plane where ith pupil aperture was positioned in the storage process. If the reading beam deviates from the original reading angle, the decryption signal degrades. The flow diagram of Fig. 2 shows the experimental results obtained with an aperture pupil mask positioned against lens L2, (a) original input objects, (b) pupil aperture mask employed to encrypt the input images (P1 is

Fig. 2. Encryption–decryption multiplexing flow diagram (a) O1 and O2: input images; (b) P1 and P2: aperture pupil utilized to encrypt O1 and O2, respectively; (c) E1 and E2: encrypted images; (d) P1, P2 and P3 pupil aperture masks utilized in the decryption step; (e) D1, D2 and D3: decrypted images obtained with pupils P1, P2 and P3, respectively; (f) D1 , D2 and D3 : simulated decrypted images obtained with pupils P1, P2 and P3, respectively).

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employed to encrypt O1 and P2 to encrypt O2, respectively) (c) E1 and E2 encrypted images stored in a BSO crystal which are obtained by introducing a beam splitter in order to capture the replica of the image formed in the crystal in a CCD2 camera (see Fig. 1), (d) pupil aperture mask (P1, P2 and P3) employed to decrypt the images (e) D1, D2 and D3 are the experimental decrypted images corresponding to the aperture channel P1, P2 and P3, respectively. These images are obtained by using CCD1. Note that P3 corresponds to the pupil composition of P1–P2. (f) D1 , D2 and D3 are the computer simulated decrypted images corresponding to the same apertures mentioned in e). During experiments, we open a single aperture for writing-in each input object image. Thus the encrypted images were stored in the crystal through multiplexing during writing. The experimental results of Fig. 2 are obtained by using the arrangement schematized in Fig. 1. In this case, the focal length of L1 and L2 is 100 mm and their clear aperture is 50 mm. The employed random phase mask is a standard pure phase glass diffuser (commercially available). The size of the aperture mask is 15 mm · 11 mm. Both apertures are identical. Registering intensities for each record were I1 = 195 lW/cm2, I2 = 60 lW/cm2 and I4 = 42 lW/cm2. Accordingly, the recording times for the multiplexing case were: s = 1 second for the first exposure and s/2 for the second. These exposures times follow a rule to achieve equal conjugation reflectivity in both cases. In order to demonstrate the capabilities of our proposal, in Fig. 3 a computer simulation employing a four-pupil arrangement is shown. The computer simulations were obtained by using the same parameters as those employed in the experimental results. The simulations are based on a

Fig. 3. The composite images show: (a) input images Oi (i = 1–4), (b) pupil aperture mask Pi (i = 1–5). Note that pupil Pi is utilized to encrypt image Oi (i = 1–4) and (c) decrypted image Di correspond to use in the decryption step pupil Pi (i = 1–5).

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Mathlab powered commercially available program. The input Oi (i = 1–4) (Fig. 3(a)) is encrypted by the aperture pupil Pi (i = 1–4). The pupil aperture mask Pi which is positioned against the lens L2, are schematized in Fig. 3 (b). In these cases, the size of each aperture Pi is 20 mm · 20 mm. In the decryption procedure, the decrypted image Di (i = 1–5) (Fig. 3 (c)) is obtained by using the aperture Pi. Decrypted image D5 is obtained by using the aperture P5. Note that only the images decrypted by using the same aperture pupil that was utilized in the encryption step are observed with high fidelity. In case that a pupil composition P1–P2–P3–P4 defined as pupil aperture P5 in the decryption step is used, all images will be simultaneously reconstructed because the composite aperture is equivalent to the original pupil of the optical system. However, the encrypted information is not recognized because all target images are overlapped. In this case, the phase conjugated wavefront which carries the information of all the encrypted images interacts with the composed pupil. Care should be taken for eventual cross-talk in the reconstructed images, influenced by the geometrical parameters of the apertures. The selection of the pupil apertures in order to avoid cross talk should be done so that non common parts exist between them. The additional security degree of our multiplexing method relies on dividing the original pupil as many times as the number of encrypted images needed to be stored. As it is well known, for a given optical system, the reduction of the pupil aperture reduces accordingly the available bandwidth of the system. Therefore, this multiplexing procedure affects the fidelity of the information to be decrypted, although this implies no reduction in the system security. This last exclusively depends on the precise knowledge of both size and position of each individual subdivision of the pupil aperture employed in the encryption procedure. Indeed, this knowledge precisely guarantees the proper input image reconstruction without any cross talk with the remaining stored images. Under our experimental conditions, the results show that the decrypted image fidelity is not highly affected by using the aperture multiplexing procedure. In case that a determined multiplexing operation requires a substantial increase in the number of aperture divisions to be employed as to dramatically reduce their size, the main consequence is that the fidelity could be severely affected. Even to a degree that the decrypted images could not be recognized. Under this technical issue, it should be necessary to adequate the parameters of the optical system (random phase mask roughness or pixel size in case of a SLM is employed, optical system numerical aperture, crystal size, etc.) in order to keep the desired fidelity and security requirements. Note that this operation must be understood as a redefinition of the system parameters but the security procedure itself remains without any change. It should be mentioned that the robustness of the method has been tested by encrypting rather complex input objects without significant degradation of the decrypted images.

In a practical holographic storage system, the achievable density is limited by several parameters, including the dynamic range of the material, the signal-to-noise ratio (SNR) of the diffracted signal, and the maximum number of multiplexed holograms allowed by the multiplexing method used. Generally speaking, the dynamic range has a strong effect on the storage density that can be achieved. The encrypted information holographically recorded in a volume media is supported on a three-dimensional subjective speckle pattern. As demonstrated in Ref. [14], the phase conjugate reflectivity depends on the 3D nature of the speckle field stored in the photorefractive medium. The speckle size can be easily adjusted by modifying the imaging system parameters, which according to that Reference means to modify the pupil aperture diameter. Let us remember that in a subjective speckle the average speckle depth is given by hSZi k Æ (ZC/D)2 where ZC is the distance between the imaging lens and the crystal plane, k the wavelength and D the diameter of the aperture lens. Indeed, it was shown that the phase conjugation reflectivity increases as the pupil aperture size decreases. As it is well known, one of the problems for the double random phase encoding in a photorefractive material is to optimize the available energy flux. In particular, in our experimental results if the aperture dimensions decrease, the average speckle size that carries the encrypted information increases and then phase conjugate reflectivity increases as well. Therefore, the use of a pupil aperture does not necessarily imply to reduction in the phase conjugation reflectivity. Only when both the pupil aperture and the random phase mask are simultaneously used, the encoded information is revealed. Only when the exact encoding and decoding masks are used, exact reconstruction of the hidden information is obtained. This is of importance when the procedure of blind decryption is attempted. 3. Conclusions In this paper, we proposed a novel optical architecture for multiple image encryption, which uses pupil apertures in the optical system together with a multiple holographic storage. This method makes the full use of the additional degrees of freedom provided by the apertures as the additional encryption keys together with the geometrical features of these masks. This strategy increases the security of the image encryption without any degradation of its noise robustness. One of the advantages of this approach is the fact that, as it has a number of degrees of freedom, it is almost impossible to decode by unauthorized people and has at the same time a simplified optical implementation. It should be pointed out that in the proposed set-up the phase conjugate beam carries simultaneously the whole information associated with all the encrypted images. When the phase-conjugate waves of the stored signals pass through the second random phase mask again, images are decrypted according to the appropriate clear apertures in the encoding lens.


Computer simulations have been performed to verify its validity. Also, it demonstrates that the method proposed here has an excellent performance of noise robustness. These facts were corroborated when the method was optically implemented. Acknowledgements This research was performed under the auspicious of COLCIENCIAS (Colombia), CONICET PIP 2417 (Argentina), CICPBA (Argentina), ANPCYT PICT 12564 (Argentina) and Facultad Ingenierıá, Universidad Nacional de La Plata (Argentina). References [1] F.H. Mok, Opt. Lett. 18 (1993) 915.

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