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Three-dimensional polarization marked multiple-QR code encryption by optimizing a single vectorial beam
Optics Communications 352 (2015) 25–32
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Three-dimensional polarization marked multiple-QR code encryption by optimizing a single vectorial beam Chao Lin a,n, Xueju Shen a, Binbin Hua a, Zhisong Wang b a b
Department of Opto-electronic Engineering, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, PR China Ordnance Test Center of China, District Taobei, Baicheng 137001, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 25 February 2015 Received in revised form 14 April 2015 Accepted 25 April 2015 Available online 30 April 2015
We demonstrate the feasibility of three dimensional (3D) polarization multiplexing by optimizing a single vectorial beam using a multiple-signal window multiple-plane (MSW-MP) phase retrieval algorithm. Original messages represented with multiple quick response (QR) codes are first partitioned into a series of subblocks. Then, each subblock is marked with a specific polarization state and randomly distributed in 3D space with both longitudinal and transversal adjustable freedoms. A generalized 3D polarization mapping protocol is established to generate a 3D polarization key. Finally, multiple-QR code is encrypted into one phase only mask and one polarization only mask based on the modified Gerchberg– Saxton (GS) algorithm. We take the polarization mask as the cyphertext and the phase only mask as additional dimension of key. Only when both the phase key and 3D polarization key are correct, original messages can be recovered. We verify our proposal with both simulation and experiment evidences. & 2015 Elsevier B.V. All rights reserved.
Keywords: Polarization encryption Vectorial beam Phase retrieval algorithm
1. Introduction Securing information with optical techniques has become an attractive alternative in the biggest ever information explosive modern society. By virtue of the multiple degree of freedom that lightwave provides, original message can be hidden in a more security manner. After the successful report of Javidi et al. in the optical encryption technique [1], a vigorous development on numerous kinds of optical security system can be observed [2,3]. However, inasmuch as optical system is linear and canonical, it would be not complicated to analyze it and then hack it with methods such as phase retrieval algorithm [4,5]. In the light of this situation, security enhancement methods are proposed to eliminate the security deficiency such as optically-induced based nonlinear encryption [6], asymmetric cryptosystems [7,8] and so on. Another promising extension is known as multiplexing alternative, which may have potentiality in enduring the existed and intended attacks. Several optical parameters can be designed as the multiplexing key. Multiple-image encryption by wavelength multiplexing has been proposed to enlarge the system capacity [9]. Spread-space spread-spectrum technique is also developed to encrypt complex images [10]. Phase retrieval algorithm has been further launched to perform multiple-image security in which the wavelength and Fresnel diffraction position parameters can be n
Corresponding author. E-mail address: [email protected] (C. Lin).
http://dx.doi.org/10.1016/j.optcom.2015.04.068 0030-4018/& 2015 Elsevier B.V. All rights reserved.
combined as the multiplexing keys [11]. Polarized light is utilized to multiplex data within a photorefractive crystal [12]. However, additional hardware is mandatory within certain systems, for example, multiplexing systems using multiple-wavelength illumination require multiple light source which may increase the system complexity and cost. Furthermore, mechanical or manual movements such as rotation multiplexing [13], angular multiplexing [14] etc. are unavoidable in some multiplexing techniques. This will lower the systems' response speed and accuracy. In practical application, we expect for one-step multiple-image encryption system with least extra operations [15]. Another problem is that the dimensions of multiplexing keys are restricted within one-dimensional (1D) or two-dimensional (2D) space, limiting the attack resistibility of cryptosystem. Hence, we expect for a onestep 3D optical multiple-image encryption technique with ultrasecurity level [16]. As one reconfigurable parameter of light, polarization may be competent to fulfill this task. However, previously reported cryptosystems using polarization freedom of light such as geometrical phase encryption [17], double random polarization encoding [18], and polarization security based on Mueller matrix [19] facilitates only 2D polarization key. One pioneering work involving 3D polarization encryption necessitates superposition of one radially polarized beam and one azimuthally polarized beam to generate arbitrary 3D polarization orientation in the focal volume [20]. Other than their approach, we generate the 3D polarization key by optimizing a single vectorial beam using a modified GS phase retrieval algorithm without additional mechanical adjustment to
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achieve optical multiplexing. The proposed system is easy to implement with a vector beam generator, leading to a simple optical structure and high efficiency. Since the multiplexing technique can significantly enlarge the system capacity of cryptosystem, one accompanying problem known as the cross talk is hard to be eliminated when demultiplexing. Hence, there is a lack of original quality due to not only the speckle noise but also the cross talk when decryption using optical hardware. In order to deal with this problem, some techniques have been proposed to improve the decryption quality [21,22]. However, the complete removal of noise is still difficult to achieve. As a promising and widely accessible tool, the quick response (QR) code shows potentiality in the noise free recovery of original information. The merging of optical encryption methods and QR code has drawn much attention since its first proposal [23]. The QR code can be designed as a container before the standard optical encrypting procedure and it offers the main advantage of being tolerant of pollutant speckle noise and cross talk noise. A lot of experimental results have verified the feasibility of QR code in noise free data recovery using the joint transform correlator (JTC) scheme [24,25]. Some other techniques have also been activated and become energetic with the help of QR code. For example, the security system based on incoherent superposition of two diffraction wave fields shows advantages of high security level and robustness against noise attack [26]. A single intensity recording optical cryptosystem based on phase retrieval and QR code is claimed to be invulnerable to various attacks and suitable for harsh transmission conditions [27]. In our previous work, a cryptosystem with four-dimensional keys also employs the QR code which can provide ultra security level and noise free data recovery [28]. In view of these, the QR code is integrated into our one step 3D polarization multiplexing system to overcome the deficiency of cross talk and achieve noise free data retrieval. Hereinafter, we accomplish this novel 3D polarization multiplex system design using a modified MSW-MP GS phase retrieval algorithm. The illumination lightwave can be engineered in both phase and polarization freedoms in a common-path interferometric vector generator [29]. It is also worth noting that the proposed system can make full use of the multi-dimensional capability of optical method.
2. Principle The encryption should be conducted using an iterative phase retrieval algorithm. And, a schematic optical setup for decryption is illustrated in Fig. 1. The vectorial beam generator acts as the core component of this cryptosystem, in which a holographic grating (HG) is
loaded on a spatial light modulator (SLM) with an amplitude transmittance t (x, y ) = 0.5 + γ (cos(2πf0 x + δ+(x, y )) + cos(2πf0 y + δ −(x, y ))) /4 , in which δ+ and δ − are additional phase distributions imposed on vertical and horizontal HGs, f0 and γ are the spatial frequency and modulation depth, respectively. The HG can be conceived as a superposition of two one-dimensional gratings oriented along x and y directions, respectively, each carrying its respective phase functions as δ −(x, y ) and δ+(x, y ). The configuration of this vectorial beam generator is a 4-f system composed of a pair of identical lens with the same focal length. For a linearly polarized light incident on the SLM, its first-order diffraction will produce four light beams. In the Fourier plane of the 4-f system, only two of the first orders located in the x and y axes are selected by two separate apertures and filtered by two quarter wave plates (QWP) in frequency plane. Then, the linearly polarized beams are converted by the QWPs into left- and right-hand circularly polarized beams. After recombined by the second Fourier lens in its rear focal plane, in which a Ronchi phase grating is placed by 45° with respect to x axis, this configuration enables the generation of vectorial beam with space-variant distribution of both polarization and phase. The Ronchi grating has a ∼40% diffraction efficiency for first orders and ability of suppression of all even orders. The period of HG is also adjusted to match with that of Ronchi grating as much as possible. Following these protocols, the output vectorial beam can be denoted as the superposition of left-hand and right-hand circular polarized components [29],
⎡1 ⎤ ⎡1⎤ E(x, y) = exp[jδ+(x, y)]⎢ ⎥ + exp[jδ−(x, y)]⎢ ⎥ ⎣−j ⎦ ⎣ j⎦ ⎡cosα(x, y)⎤ = exp[jβ(x, y)]⎢ ⎥, ⎣sinα(x, y) ⎦
(1)
in which α = (δ+ − δ −) /2, β = (δ+ + δ −) /2 and j denotes the imaginary unit. Eq. (1) describes a vectorial beam with phase and local linear polarization distributions. The phase terms δ+ and δ − are free parameters needed to be optimized to generate the desired 3D polarization and intensity patterns in the Fresnel volume domain. The two free phase-only beams are denoted as [30],
⎧ E ⎪ E+(x, y) = 0 exp[jδ+(x, y)] ⎪ 2 ⎨ . E0 ⎪ ( ) = [ δ ( )] E x , y exp j x , y − − ⎪ ⎩ 2
(2)
Within Eq. (2), E0 denotes a constant amplitude profile. The iterative phase retrieval algorithm starts with specifying a set of randomly distributed phases to the circular components of incident vectorial beam δ+ and δ − with uniform random numbers in (0, 2π ). Then, the Fresnel diffraction integral is calculated to yield the field distributions of circular components in the plane zi . Note
Fig. 1. Schematic decryption setup for the proposed cryptosystem.
C. Lin et al. / Optics Communications 352 (2015) 25–32
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that the Fresnel number can be F = a2/(λz ) > 1, in which a is the size of aperture, λ denotes the wavelength of illumination laser under the experimental condition. And, this corresponds to paraxial propagation of lightwave, the scalar Fresnel integral is accurate enough to describe the field as,
⎧O (n)(u, v) = Fres [E (n)(x, y)] ⎪ i+ zi + ⎨ , (n) (n) ⎪ ⎩Oi − (u, v) = Fres z i[E− (x, y)]
(3)
where the superscript (n) denotes the iterative number (integer n ¼1,2,3…), Fres denotes the Fresnel diffraction integral operator, zi is a series of axial distances between the output plane of vectorial beam generator (z0 = 0 at the plane of Ronchi grating) and the predefined planes where specific polarization and intensity patterns appears. Meanwhile, we partition each plaintext into M pieces of subblocks with the same size. After this partitioning, if we intend to multiplex N plaintexts, we can randomly select N pieces of subblocks from all the M × N subblocks and locate them in a specific Fresnel plane zi with separated transversal positions. Hence, within certain Fresnel plane zi , the N signal windows constrains on the diffracted field can be imposed. In this procedure, the number of Fresnel planes should be M and there also should be N pieces of subblocks placed in the same longitudinal axis. To avoid quality loss of decrypted images caused by superposition, each longitudinal axis must be mutually unoverlapped. The amplitudes of diffracted vectorial components are replaced by the desired ones which are the amplitudes of subblocks within regions of interest (ROI) in each Fresnel diffraction plane, this can be denoted as,
⎧O (n)(u, v) = FMSWAC [O (n)(u, v)] ⎪ i+ + i+ ⎨ (n) (n) ⎪ ⎩Oi − (u, v) = FMSWAC−[Oi − (u, v)].
Fig. 2. Principle of three-dimensional polarization mapping operation.
(4)
In Eq. (4), FMSWAC[•] denotes the Fresnel diffraction plane multiple-signal window amplitude constrains which can be described as,
⎧ (u, v) ∈ S ⎪ ΩPi(u , v ) , FMSWAC[Oi(n)(u, v)] = ⎨ (n) ⎪ ⎩|Oi (u, v)| , (u, v) ∉ S
(5)
where Pi(u, v ) denotes the desired outputs of amplitude patterns within the predefined signal windows, Ω denotes a ratio between summations of calculated and desired amplitude map, S is the multiple-signal window support regions [31]. The signal windows are defined as several specific transverse areas which contain the subblocks in the Fresnel diffraction planes as shown in Fig. 1. Other than the traditional GS phase retrieval algorithm and the previous calculation of phase structure to achieve desired diffraction pattern [32,33], which imposes amplitude only constrains on the pre-defined signal windows within several target planes, our modified one takes phase difference between orthogonal polarization components as another parameter to be restricted on a series of target (Fresnel) planes in order to obtain the desired spatial polarization distribution. In this sense, the modified one can be regarded as an extension to polarization equivalent to the scalar version of the previous proposal [32] which introduces ROI in the output plane. In essence, compared with the previous proposal which optimizes one phase only function based on the iterative Fourier transform algorithm, in our proposal, two phase only functions are both engaged in the iterative process. Due to the additional constrain on the phase difference between orthogonal polarization components, the modified one is less accurate in the image quality of reconstructed diffraction patterns than the previous one. However, the modified algorithm is efficient enough in our calculation for optical decryption algorithm which will be
shown in the following simulation and experiment results. Here, we assign each signal window on specific Fresnel plane with a predefined polarization state and name it as a “polarization marker”. Each marker is associated with a signal window within which a desired intensity pattern appears. As annotated within Fig. 1, three distinguishable polarization markers, such as horizontal linear polarized (HL-P), left circular polarized (LC-P) and right circular polarized (RC-P) are chosen when we intend to multiplex three plaintexts, namely, N = 3. Each signal window with specific intensity pattern belongs to a plaintext. However, it would be difficult for the attacker to decide which signal window corresponds to which plaintext without the key. Hence, a recombination of wrong selected subblocks will lead to a failure of data recovery. Only when all the right subblocks are incorporated within right positions of each plaintext, original messages can be retrieved. This 3D polarization marking process is executed based on a 3D polarization map as shown in Fig. 2. From Fig. 2, we can figure out that signal windows with the same polarization marker belong to a single plaintext. Note that this 3D mapping graphic is plotted when M = 16 and N = 3. Then, the constrain on the phase difference can be expressed as,
Pha[Oi(−n)(u, v)] =
Oi(+n)(u, v) |Oi(+n)(u, v)|
exp[jϕ(u, v)],
(u, v) ∈ S.
(6)
Within Eq. (6), Pha[•] denotes the extraction of phase, ϕ(u, v ) is the desired phase difference which determines the polarization state. Note that the phase component of Oi(+n)(u, v ) as a global phase factor is left unchanged. After imposing the constrains on both amplitude and phase profiles of diffracted field, a backward propagation to the z0 = 0 plane should be calculated as,
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⎧ E (n)(x, y) = Fres [O (n)(u, v)] ⎪ i+ −z i i + ⎨ . (n) (n) ⎪ ⎩ Ei − (x, y) = Fres−z i[Oi − (u, v)]
C. Lin et al. / Optics Communications 352 (2015) 25–32
that is,
(7)
At plane z0 = 0, a uniform amplitude constrain should be imposed,
(n) (n) ⎧ ⎪ E+ (x , y) = UAC[E i + (x, y)] ⎨ , (n) ⎪ (n) ⎩ E− (x, y) = UAC[Ei − (x, y)]
(8)
Fig. 3. (a)–(c) Original QR codes, (d) cyphertext, (e) 2D phase only key, (f)–(g) retrieved subblocks in z9 and z11 planes, (h)–(i) averaged and binary version of (f)–(g), (j)– (l) decrypted QR codes after recombination, (m)–(o) averaged and binary version of (j)–(l), (p)–(r) scan results of Fig. 3(m)–(o) respectively.
C. Lin et al. / Optics Communications 352 (2015) 25–32
in which UAC[•] denotes the uniform amplitude constrain. Eqs. (2)–(8) are implemented once from plane z0 to plane z1 and backward. The updated two phase factors are then used as inputs for calculation from z0 to zi until i reaches the maximum value M . Thereafter, the next iteration is calculated for n = n + 1 until all the preset iterations are finished. Finally, the extracted two phase-only masks are utilized to derive a phase-only mask which serves as one encryption key (the other one is the 3D polarization mapping key) and a polarization-only mask which serves as the cyphertext based on Eq. (1). Since the decryption process can be accomplished using a vector wave generator, a simple but stable optical structure based on the 4-f system can be utilized as shown in Fig. 1. However, the overall efficiency of this configuration is low because of the energy loss in the spatial filter. In this regard, the other types of vector wave generator can also be utilized in our scheme. For example, the two dimensional polarization encoding system using two parallel aligned LCSLMs [34–36] can generate arbitrary elliptical polarization states. The arbitrary complex fields generator may also be useful in the 3D polarization multiplexing cryptosystem because it can provide the independent control of amplitude, phase and polarization freedoms [37].
3. Results 3.1. Simulations We first present some simulation evidences which are obtained under the platform of MATLAB 7.01. It is worth noting that the QR code is quite essential for the input of this cryptosystem because that the edge of QR code would not render any clues for recombination during decryption. QR code is detected as a 2-dimensional digital image by an image sensor and analyzed by a
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programmed processor. The useful feature QR codes exhibit is a level of error correction which depends on the storage capacity. Thanks to these levels of correction contained in the generating algorithm, information can be noise-free retrieved despite of the pollution. For M = 16 and N = 3, the QR codes with 256 × 256 pixels are illustrated in Fig. 3(a)–(c) in which three messages “Mechanical Engineering College”, “QR Code Block Security” and “3D polarization multiplexing” are encoded. The Fresnel distance range z is set to be [15.0–21.3 mm], and the iterative number n is set to be 100 which is enough to output the desired intensity and polarization patterns. Following these protocols, the cyphertext which is a linearly polarization only mask is shown in Fig. 3(d). The phase only key is shown in Fig. 3(e). The decryption process should be performed with optical method. Since the polarization marked subblocks are randomly located in Fresnel volume based on the 3D polarization map, one can trace back the flow of every subblock based on the inverse 3D polarization map and retrieve the plaintexts. The decrypted subblocks are shown in Fig. 3(f)– (g) when the 2D random phase key are correct in Fresnel distance z9 and z11, for instance. The post-processed subblocks are shown in Fig. 3(h)–(i) after averaging and binaryzation. The final retrieved QR codes are shown in Fig. 3(j)–(l) after incorporating all subblocks in its original positions. Due to the error correction property of QR code, we then can expect for a noise-free recovery. Using the application installed on our smart phone, the original message can be read out without noise after scanning Fig. 3(m)–(o). The scan results are respectively shown in Fig. 3(p)–(r) which validates the feasibility of our proposal. We then evaluate the sensitivity and fault tolerance on different keys during decryption. Note that the three QR codes are equivalent in essence, the first one (Fig. 3(a)) is chosen as example. We first conduct the decryption using a totally wrong 2D phase key, as illustrated in Fig. 4(a), a noisy image emerges. The wrong incorporated images provided that the polarization marker key is
Fig. 4. Wrong decrypted QR codes. (a) 2D phase key is wrong, (b)–(c) polarization mapping key is wrong, (d)–(e) subblocks when Fresnel distance key is wrong in z9 or z11 plane, and (f) synthetic image when all of the Fresnel distance keys are wrong.
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incorrect are shown in Fig. 4(b)–(c), leading to a failure on reading. The retrieved subblocks when Fresnel distance keys are incorrect within 0.25 mm are shown in Fig. 4(d)–(e) within z9 and z11 planes. The recombined QR code is shown in Fig. 4(f). We can figure out that the structure of QR code has been destroyed and a successful reading is impossible. Besides the QR code encryption, the proposed protocol is also suitable for any kind of input image theoretically. Here, we introduce two binary “number and letter” patterns as the plaintexts as shown in Fig. 5(a)–(b). Supposing that the Fresnel diffraction distance z′ is set to be [100.0–166.0 mm], and M = 9, N = 2. Following the same encryption and decryption protocols, the cyphertext is shown in Fig. 5(c) and the phase only key is illustrated in Fig. 5(d). The intensity images are shown in Fig. 5(e)– (f) provided that the left circular polarizer are placed before the camera in z3′ and z9′ planes and Fig. 5(g)–(h) for right circular polarizer in z4′ and z8′ planes, respectively. We can figure out that the sharpest and brightest pattern only appears in right longitudinal and transversal position when decryption keys are correct. When the 3D polarization mapping key is known and the polarization state of each sub-pattern is identified, we can incorporate each
Fig. 6. Experimental setup of the proposed 3D polarization multiplexing decryption system.
Fig. 5. (a)–(b) Original binary “number and letter” patterns, (c) cyphertext, (d) 2D phase only key, (e)–(h) retrieved subblocks on different Fresnel planes (see the text for details), and (i)–(j) decrypted patterns after recombination.
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Fig. 7. Experimental results of optical decryption. (a)–(b) original images, (c)–(d) and (e)–(f) captured images at specific distances when inserting left or right circular polarizers respectively.
sub-pattern into right position of each plaintext and achieve a successful decryption. The recombined images are shown in Fig. 5 (i)–(j) when all the decryption keys are correct. 3.2. Experiment At last, preliminary experiment results are presented to further verify our proposal. The effectiveness of developed MSW-MP algorithm is the main concern when conducting optical decryption. We utilize a reflective type Lcos SLM with pixel size of 12.3 mm to verify it. The Fresnel distance range z′ is also set to be [100.0– 166.0 mm] to perform an easy image registration. The photosensitive plane size of CCD camera is 576 × 768 with a pixel size of 10 mm. The experimental setup is illustrated in Fig. 6. The illumination source is a He–Ne laser with the wavelength of 633 nm. One computer is utilized to control both the SLM and the CCD camera independently. The micro quarter wave plates are adhered to a piece of silver paper with two open apertures on x and y axis respectively. The circular polarizer and the Ronchi grating are both integrated within the slots of the CCD iris diaphragm. Here, we demonstrate the possibility of our proposal to act as a code book based on the 3D polarization mapping for M = 9 and N = 2. The two plaintexts are shown in Fig. 7(a)–(b). The nine numbers and letters are selected to be elements in a code book. However, the personal key, such as a password is a specific combination of these characters. And it can be obtained based on the fixed 2D phase key and specially designed 3D polarization mapping key. The captured intensity images are shown in Fig. 7(c)– (d) provided that the left circular polarizer are inserted before the camera in z9′ and z3′ planes and Fig. 7(e)–(f) for right circular polarizer in z8′ and z4′ planes. Using the known 3D polarization mapping key, we retrieved the password “7E5FDA”. This example shows a potential application of our proposal in password security field.
4. Conclusions In conclusion, we make full use of the vectorial beam with both random polarization and phase distributions to achieve optical data multiplexing. Based on the developed MSW-MP phase retrieval algorithm, original images can be encrypted into a single
vectorial beam. As a result, for the first time, the one-step 3D polarization multiplexing security system is established. The implementation of this cryptosystem requires no more extra hardware compared with existed techniques, such as, double random phase encoding, leading to a simple optical structure and high security level. In the future, how to increase the multiplex capacity and reduce cross talk may be our main concern.
References [1] B. Javidi, Securing information with optical technologies, Phys. Today 50 (1997) 27–32. [2] A. Alfalou, C. Brosseau, Optical image compression and encryption methods, Adv. Opt. Photonics 1 (2009) 589–636. [3] W. Chen, B. Javidi, X. Chen, Advances in optical security systems, Adv. Opt. Photonics 6 (2014) 120–155. [4] Y. Frauel, A. Castro, T.J. Naughton, B. Javidi, Resistance of the double random phase encryption against various attacks, Opt. Express 15 (2007) 10253–10265. [5] X. Peng, P. Zhang, H.Z. Wei, B. Yu, Known-plaintext attack on optical encryption based on double random phase keys, Opt. Lett. 31 (2006) 1044–1046. [6] B. Chen, H. Wang, Optically-induced-potential-based image encryption, Opt. Express 19 (2011) 22619–22627. [7] W. Qin, X. Peng, Asymmetric cryptosystem based on phase-truncated Fourier transforms, Opt. Lett. 35 (2010) 118–120. [8] C. Lin, X. Shen, Z. Wang, C. Zhao, Optical asymmetric cryptography based on elliptical polarized light linear truncation and a numerical reconstruction technique, Appl. Opt. 53 (2014) 3920–3928. [9] G. Situ, J. Zhang, Multiple-image encryption by wavelength multiplexing, Opt. Lett. 30 (2005) 1306–1308. [10] B. Hennelly, T. Naughton, J. McDonald, J. Sheridan, G. Unnikrishnan, D. Kelly, B. Javidi, Spread-space spread-spectrum technique for secure multiplexing, Opt. Lett. 32 (2007) 1060–1062. [11] H. Hwang, H. Chang, W. Lei, Multiple-image encryption and multiplexing using a modified Gerchberg–Saxton algorithm and phase modulation in Fresnel-transform domain, Opt. Lett. 34 (2009) 3917–3919. [12] J. Barrera, R. Henao, M. Tebaldi, R. Torroba, N. Bolognini, Multiplexing encrypted data by using polarized light, Opt. Commun. 260 (2006) 109–112. [13] E. Rueda, C. Rios, J. Barrera, R. Henao, R. Torroba, Experimental multiplexing approach via code key rotations under a joint transform correlator scheme, Opt. Commun. 284 (2011) 2500–2504. [14] C. Lin, X. Shen, Multiple images encryption based on Fourier transform hologram, Opt. Commun. 285 (2012) 1023–1028. [15] J. Barrera, R. Torroba, One step multiplexing optical encryption, Opt. Commun. 283 (2010) 1268–1272. [16] W. Chen, X. Chen, Optical image encryption based on multiple-region plaintext and phase retrieval in three-dimensional space, Opt. Lasers Eng. 51 (2013) 128–133. [17] G. Biener, A. Niv, V. Kleiner, E. Hasman, Geometrical phase image encryption obtained with space-variant subwavelength gratings, Opt. Lett. 30 (2005) 1096–1098. [18] O. Matoba, B. Javidi, Secure holographic memory by double-random
32
C. Lin et al. / Optics Communications 352 (2015) 25–32
polarization encryption, Appl. Opt. 43 (2004) 2915–2919. [19] A. Alfalou, C. Brosseau, Dual encryption scheme of images using polarized light, Opt. Lett. 35 (2010) 2185–2187. [20] X. Li, T.-H. Lan, C.-H. Tien, M. Gu, Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam, Nat. Commun. 3 (2012) 998. [21] R. Henao, E. Rueda, J.F. Barrera, R. Torroba, Noise-free recovery of opto-digital encrypted and multiplexed images, Opt. Lett. 35 (2010) 333–335. [22] X.F. Meng, L.Z. Cai, M.Z. He, G.Y. Dong, X.X. Shen, Cross-talk-free double-image encryption and watermarking with amplitude–phase separate modulations, J. Opt. 7 (2005) 624–631. [23] J.F. Barrera, R.A. Mira, R. Torroba, Optical encryption and QR codes: secure and noise-free information retrieval, Opt. Express 21 (2013) 5373–5378. [24] J.F. Barrera, R.A. Mira, R. Torroba, Experimental QR code optical encryption: noise-free data recovering, Opt. Lett. 39 (2014) 3074–3077. [25] J.F. Barrera, R.A. Vélez, R. Torroba, Experimental scrambling and noise reduction applied to the optical encryption of QR codes, Opt. Express 22 (2014) 20268–20277. [26] Y. Qin, Q. Gong, Optical information encryption based on incoherent superposition with the help of the QR code, Opt. Commun. 310 (2014) 69–75. [27] Z.P. Wang, S. Zhang, H.Z. Liu, Y. Qin, Single-intensity-recording optical encryption technique based on phase retrieval algorithm and QR code, Opt. Commun. 332 (2014) 36–41. [28] C. Lin, X. Shen, B. Li, Four-dimensional key design in amplitude, phase, polarization and distance for optical encryption based on polarization digital
holography and QR code, Opt. Express 22 (2014) 20727–20739. [29] H. Chen, J. Hao, B. Zhang, J. Xu, J. Ding, H. Wang, Generation of vector beam with space-variant distribution of both polarization and phase, Opt. Lett. 36 (2011) 3179–3181. [30] J. Hao, Z. Yu, H. Chen, Z. Chen, H. Wang, J. Ding, Light field shaping by tailoring both phase and polarization, Appl. Opt. 53 (2014) 785–791. [31] C. Ying, H. Pang, C. Fan, W. Zhou, New method for the design of a phase-only computer hologram for multiplane reconstruction, Opt. Eng. 50 (2011) 055802. [32] F. Wyrowski, Diffractive optical elements: iterative calculation of quantized, blazed phase structures, J. Opt. Soc. Am. A 7 (1990) 961–969. [33] M. Montes-Usategui, J. Campos, I. Juvells, Computation of arbitrarily constrained synthetic discriminant functions, Appl. Opt. 34 (1995) 3904–3914. [34] J.A. Davis, D.E. McNamara, D.M. Cottrell, T. Sonehara, Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator, Appl. Opt. 39 (2000) 1549–1554. [35] R.L. Eriksen, P.C. Mogensen, J. Gluckstad, Elliptical polarisation encoding in two dimensions using phase-only spatial light modulators, Opt. Commun. 187 (2001) 325–336. [36] J.L. Martínez, I. Moreno, F. Mateos, Hiding binary optical data with orthogonal circular polarizations, Opt. Eng. 47 (2008) 030504. [37] W. Han, Y. Yang, W. Cheng, Q. Zhan, Vectorial optical field generator for the creation of arbitrarily complex fields, Opt. Express 21 (2013) 20692–20706.
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Three-dimensional polarization marked multiple-QR code encryption by optimizing a single vectorial beam Chao Lin a,n, Xueju Shen a, Binbin Hua a, Zhisong Wang b a b
Department of Opto-electronic Engineering, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, PR China Ordnance Test Center of China, District Taobei, Baicheng 137001, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 25 February 2015 Received in revised form 14 April 2015 Accepted 25 April 2015 Available online 30 April 2015
We demonstrate the feasibility of three dimensional (3D) polarization multiplexing by optimizing a single vectorial beam using a multiple-signal window multiple-plane (MSW-MP) phase retrieval algorithm. Original messages represented with multiple quick response (QR) codes are first partitioned into a series of subblocks. Then, each subblock is marked with a specific polarization state and randomly distributed in 3D space with both longitudinal and transversal adjustable freedoms. A generalized 3D polarization mapping protocol is established to generate a 3D polarization key. Finally, multiple-QR code is encrypted into one phase only mask and one polarization only mask based on the modified Gerchberg– Saxton (GS) algorithm. We take the polarization mask as the cyphertext and the phase only mask as additional dimension of key. Only when both the phase key and 3D polarization key are correct, original messages can be recovered. We verify our proposal with both simulation and experiment evidences. & 2015 Elsevier B.V. All rights reserved.
Keywords: Polarization encryption Vectorial beam Phase retrieval algorithm
1. Introduction Securing information with optical techniques has become an attractive alternative in the biggest ever information explosive modern society. By virtue of the multiple degree of freedom that lightwave provides, original message can be hidden in a more security manner. After the successful report of Javidi et al. in the optical encryption technique [1], a vigorous development on numerous kinds of optical security system can be observed [2,3]. However, inasmuch as optical system is linear and canonical, it would be not complicated to analyze it and then hack it with methods such as phase retrieval algorithm [4,5]. In the light of this situation, security enhancement methods are proposed to eliminate the security deficiency such as optically-induced based nonlinear encryption [6], asymmetric cryptosystems [7,8] and so on. Another promising extension is known as multiplexing alternative, which may have potentiality in enduring the existed and intended attacks. Several optical parameters can be designed as the multiplexing key. Multiple-image encryption by wavelength multiplexing has been proposed to enlarge the system capacity [9]. Spread-space spread-spectrum technique is also developed to encrypt complex images [10]. Phase retrieval algorithm has been further launched to perform multiple-image security in which the wavelength and Fresnel diffraction position parameters can be n
Corresponding author. E-mail address: [email protected] (C. Lin).
http://dx.doi.org/10.1016/j.optcom.2015.04.068 0030-4018/& 2015 Elsevier B.V. All rights reserved.
combined as the multiplexing keys [11]. Polarized light is utilized to multiplex data within a photorefractive crystal [12]. However, additional hardware is mandatory within certain systems, for example, multiplexing systems using multiple-wavelength illumination require multiple light source which may increase the system complexity and cost. Furthermore, mechanical or manual movements such as rotation multiplexing [13], angular multiplexing [14] etc. are unavoidable in some multiplexing techniques. This will lower the systems' response speed and accuracy. In practical application, we expect for one-step multiple-image encryption system with least extra operations [15]. Another problem is that the dimensions of multiplexing keys are restricted within one-dimensional (1D) or two-dimensional (2D) space, limiting the attack resistibility of cryptosystem. Hence, we expect for a onestep 3D optical multiple-image encryption technique with ultrasecurity level [16]. As one reconfigurable parameter of light, polarization may be competent to fulfill this task. However, previously reported cryptosystems using polarization freedom of light such as geometrical phase encryption [17], double random polarization encoding [18], and polarization security based on Mueller matrix [19] facilitates only 2D polarization key. One pioneering work involving 3D polarization encryption necessitates superposition of one radially polarized beam and one azimuthally polarized beam to generate arbitrary 3D polarization orientation in the focal volume [20]. Other than their approach, we generate the 3D polarization key by optimizing a single vectorial beam using a modified GS phase retrieval algorithm without additional mechanical adjustment to
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achieve optical multiplexing. The proposed system is easy to implement with a vector beam generator, leading to a simple optical structure and high efficiency. Since the multiplexing technique can significantly enlarge the system capacity of cryptosystem, one accompanying problem known as the cross talk is hard to be eliminated when demultiplexing. Hence, there is a lack of original quality due to not only the speckle noise but also the cross talk when decryption using optical hardware. In order to deal with this problem, some techniques have been proposed to improve the decryption quality [21,22]. However, the complete removal of noise is still difficult to achieve. As a promising and widely accessible tool, the quick response (QR) code shows potentiality in the noise free recovery of original information. The merging of optical encryption methods and QR code has drawn much attention since its first proposal [23]. The QR code can be designed as a container before the standard optical encrypting procedure and it offers the main advantage of being tolerant of pollutant speckle noise and cross talk noise. A lot of experimental results have verified the feasibility of QR code in noise free data recovery using the joint transform correlator (JTC) scheme [24,25]. Some other techniques have also been activated and become energetic with the help of QR code. For example, the security system based on incoherent superposition of two diffraction wave fields shows advantages of high security level and robustness against noise attack [26]. A single intensity recording optical cryptosystem based on phase retrieval and QR code is claimed to be invulnerable to various attacks and suitable for harsh transmission conditions [27]. In our previous work, a cryptosystem with four-dimensional keys also employs the QR code which can provide ultra security level and noise free data recovery [28]. In view of these, the QR code is integrated into our one step 3D polarization multiplexing system to overcome the deficiency of cross talk and achieve noise free data retrieval. Hereinafter, we accomplish this novel 3D polarization multiplex system design using a modified MSW-MP GS phase retrieval algorithm. The illumination lightwave can be engineered in both phase and polarization freedoms in a common-path interferometric vector generator [29]. It is also worth noting that the proposed system can make full use of the multi-dimensional capability of optical method.
2. Principle The encryption should be conducted using an iterative phase retrieval algorithm. And, a schematic optical setup for decryption is illustrated in Fig. 1. The vectorial beam generator acts as the core component of this cryptosystem, in which a holographic grating (HG) is
loaded on a spatial light modulator (SLM) with an amplitude transmittance t (x, y ) = 0.5 + γ (cos(2πf0 x + δ+(x, y )) + cos(2πf0 y + δ −(x, y ))) /4 , in which δ+ and δ − are additional phase distributions imposed on vertical and horizontal HGs, f0 and γ are the spatial frequency and modulation depth, respectively. The HG can be conceived as a superposition of two one-dimensional gratings oriented along x and y directions, respectively, each carrying its respective phase functions as δ −(x, y ) and δ+(x, y ). The configuration of this vectorial beam generator is a 4-f system composed of a pair of identical lens with the same focal length. For a linearly polarized light incident on the SLM, its first-order diffraction will produce four light beams. In the Fourier plane of the 4-f system, only two of the first orders located in the x and y axes are selected by two separate apertures and filtered by two quarter wave plates (QWP) in frequency plane. Then, the linearly polarized beams are converted by the QWPs into left- and right-hand circularly polarized beams. After recombined by the second Fourier lens in its rear focal plane, in which a Ronchi phase grating is placed by 45° with respect to x axis, this configuration enables the generation of vectorial beam with space-variant distribution of both polarization and phase. The Ronchi grating has a ∼40% diffraction efficiency for first orders and ability of suppression of all even orders. The period of HG is also adjusted to match with that of Ronchi grating as much as possible. Following these protocols, the output vectorial beam can be denoted as the superposition of left-hand and right-hand circular polarized components [29],
⎡1 ⎤ ⎡1⎤ E(x, y) = exp[jδ+(x, y)]⎢ ⎥ + exp[jδ−(x, y)]⎢ ⎥ ⎣−j ⎦ ⎣ j⎦ ⎡cosα(x, y)⎤ = exp[jβ(x, y)]⎢ ⎥, ⎣sinα(x, y) ⎦
(1)
in which α = (δ+ − δ −) /2, β = (δ+ + δ −) /2 and j denotes the imaginary unit. Eq. (1) describes a vectorial beam with phase and local linear polarization distributions. The phase terms δ+ and δ − are free parameters needed to be optimized to generate the desired 3D polarization and intensity patterns in the Fresnel volume domain. The two free phase-only beams are denoted as [30],
⎧ E ⎪ E+(x, y) = 0 exp[jδ+(x, y)] ⎪ 2 ⎨ . E0 ⎪ ( ) = [ δ ( )] E x , y exp j x , y − − ⎪ ⎩ 2
(2)
Within Eq. (2), E0 denotes a constant amplitude profile. The iterative phase retrieval algorithm starts with specifying a set of randomly distributed phases to the circular components of incident vectorial beam δ+ and δ − with uniform random numbers in (0, 2π ). Then, the Fresnel diffraction integral is calculated to yield the field distributions of circular components in the plane zi . Note
Fig. 1. Schematic decryption setup for the proposed cryptosystem.
C. Lin et al. / Optics Communications 352 (2015) 25–32
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that the Fresnel number can be F = a2/(λz ) > 1, in which a is the size of aperture, λ denotes the wavelength of illumination laser under the experimental condition. And, this corresponds to paraxial propagation of lightwave, the scalar Fresnel integral is accurate enough to describe the field as,
⎧O (n)(u, v) = Fres [E (n)(x, y)] ⎪ i+ zi + ⎨ , (n) (n) ⎪ ⎩Oi − (u, v) = Fres z i[E− (x, y)]
(3)
where the superscript (n) denotes the iterative number (integer n ¼1,2,3…), Fres denotes the Fresnel diffraction integral operator, zi is a series of axial distances between the output plane of vectorial beam generator (z0 = 0 at the plane of Ronchi grating) and the predefined planes where specific polarization and intensity patterns appears. Meanwhile, we partition each plaintext into M pieces of subblocks with the same size. After this partitioning, if we intend to multiplex N plaintexts, we can randomly select N pieces of subblocks from all the M × N subblocks and locate them in a specific Fresnel plane zi with separated transversal positions. Hence, within certain Fresnel plane zi , the N signal windows constrains on the diffracted field can be imposed. In this procedure, the number of Fresnel planes should be M and there also should be N pieces of subblocks placed in the same longitudinal axis. To avoid quality loss of decrypted images caused by superposition, each longitudinal axis must be mutually unoverlapped. The amplitudes of diffracted vectorial components are replaced by the desired ones which are the amplitudes of subblocks within regions of interest (ROI) in each Fresnel diffraction plane, this can be denoted as,
⎧O (n)(u, v) = FMSWAC [O (n)(u, v)] ⎪ i+ + i+ ⎨ (n) (n) ⎪ ⎩Oi − (u, v) = FMSWAC−[Oi − (u, v)].
Fig. 2. Principle of three-dimensional polarization mapping operation.
(4)
In Eq. (4), FMSWAC[•] denotes the Fresnel diffraction plane multiple-signal window amplitude constrains which can be described as,
⎧ (u, v) ∈ S ⎪ ΩPi(u , v ) , FMSWAC[Oi(n)(u, v)] = ⎨ (n) ⎪ ⎩|Oi (u, v)| , (u, v) ∉ S
(5)
where Pi(u, v ) denotes the desired outputs of amplitude patterns within the predefined signal windows, Ω denotes a ratio between summations of calculated and desired amplitude map, S is the multiple-signal window support regions [31]. The signal windows are defined as several specific transverse areas which contain the subblocks in the Fresnel diffraction planes as shown in Fig. 1. Other than the traditional GS phase retrieval algorithm and the previous calculation of phase structure to achieve desired diffraction pattern [32,33], which imposes amplitude only constrains on the pre-defined signal windows within several target planes, our modified one takes phase difference between orthogonal polarization components as another parameter to be restricted on a series of target (Fresnel) planes in order to obtain the desired spatial polarization distribution. In this sense, the modified one can be regarded as an extension to polarization equivalent to the scalar version of the previous proposal [32] which introduces ROI in the output plane. In essence, compared with the previous proposal which optimizes one phase only function based on the iterative Fourier transform algorithm, in our proposal, two phase only functions are both engaged in the iterative process. Due to the additional constrain on the phase difference between orthogonal polarization components, the modified one is less accurate in the image quality of reconstructed diffraction patterns than the previous one. However, the modified algorithm is efficient enough in our calculation for optical decryption algorithm which will be
shown in the following simulation and experiment results. Here, we assign each signal window on specific Fresnel plane with a predefined polarization state and name it as a “polarization marker”. Each marker is associated with a signal window within which a desired intensity pattern appears. As annotated within Fig. 1, three distinguishable polarization markers, such as horizontal linear polarized (HL-P), left circular polarized (LC-P) and right circular polarized (RC-P) are chosen when we intend to multiplex three plaintexts, namely, N = 3. Each signal window with specific intensity pattern belongs to a plaintext. However, it would be difficult for the attacker to decide which signal window corresponds to which plaintext without the key. Hence, a recombination of wrong selected subblocks will lead to a failure of data recovery. Only when all the right subblocks are incorporated within right positions of each plaintext, original messages can be retrieved. This 3D polarization marking process is executed based on a 3D polarization map as shown in Fig. 2. From Fig. 2, we can figure out that signal windows with the same polarization marker belong to a single plaintext. Note that this 3D mapping graphic is plotted when M = 16 and N = 3. Then, the constrain on the phase difference can be expressed as,
Pha[Oi(−n)(u, v)] =
Oi(+n)(u, v) |Oi(+n)(u, v)|
exp[jϕ(u, v)],
(u, v) ∈ S.
(6)
Within Eq. (6), Pha[•] denotes the extraction of phase, ϕ(u, v ) is the desired phase difference which determines the polarization state. Note that the phase component of Oi(+n)(u, v ) as a global phase factor is left unchanged. After imposing the constrains on both amplitude and phase profiles of diffracted field, a backward propagation to the z0 = 0 plane should be calculated as,
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⎧ E (n)(x, y) = Fres [O (n)(u, v)] ⎪ i+ −z i i + ⎨ . (n) (n) ⎪ ⎩ Ei − (x, y) = Fres−z i[Oi − (u, v)]
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that is,
(7)
At plane z0 = 0, a uniform amplitude constrain should be imposed,
(n) (n) ⎧ ⎪ E+ (x , y) = UAC[E i + (x, y)] ⎨ , (n) ⎪ (n) ⎩ E− (x, y) = UAC[Ei − (x, y)]
(8)
Fig. 3. (a)–(c) Original QR codes, (d) cyphertext, (e) 2D phase only key, (f)–(g) retrieved subblocks in z9 and z11 planes, (h)–(i) averaged and binary version of (f)–(g), (j)– (l) decrypted QR codes after recombination, (m)–(o) averaged and binary version of (j)–(l), (p)–(r) scan results of Fig. 3(m)–(o) respectively.
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in which UAC[•] denotes the uniform amplitude constrain. Eqs. (2)–(8) are implemented once from plane z0 to plane z1 and backward. The updated two phase factors are then used as inputs for calculation from z0 to zi until i reaches the maximum value M . Thereafter, the next iteration is calculated for n = n + 1 until all the preset iterations are finished. Finally, the extracted two phase-only masks are utilized to derive a phase-only mask which serves as one encryption key (the other one is the 3D polarization mapping key) and a polarization-only mask which serves as the cyphertext based on Eq. (1). Since the decryption process can be accomplished using a vector wave generator, a simple but stable optical structure based on the 4-f system can be utilized as shown in Fig. 1. However, the overall efficiency of this configuration is low because of the energy loss in the spatial filter. In this regard, the other types of vector wave generator can also be utilized in our scheme. For example, the two dimensional polarization encoding system using two parallel aligned LCSLMs [34–36] can generate arbitrary elliptical polarization states. The arbitrary complex fields generator may also be useful in the 3D polarization multiplexing cryptosystem because it can provide the independent control of amplitude, phase and polarization freedoms [37].
3. Results 3.1. Simulations We first present some simulation evidences which are obtained under the platform of MATLAB 7.01. It is worth noting that the QR code is quite essential for the input of this cryptosystem because that the edge of QR code would not render any clues for recombination during decryption. QR code is detected as a 2-dimensional digital image by an image sensor and analyzed by a
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programmed processor. The useful feature QR codes exhibit is a level of error correction which depends on the storage capacity. Thanks to these levels of correction contained in the generating algorithm, information can be noise-free retrieved despite of the pollution. For M = 16 and N = 3, the QR codes with 256 × 256 pixels are illustrated in Fig. 3(a)–(c) in which three messages “Mechanical Engineering College”, “QR Code Block Security” and “3D polarization multiplexing” are encoded. The Fresnel distance range z is set to be [15.0–21.3 mm], and the iterative number n is set to be 100 which is enough to output the desired intensity and polarization patterns. Following these protocols, the cyphertext which is a linearly polarization only mask is shown in Fig. 3(d). The phase only key is shown in Fig. 3(e). The decryption process should be performed with optical method. Since the polarization marked subblocks are randomly located in Fresnel volume based on the 3D polarization map, one can trace back the flow of every subblock based on the inverse 3D polarization map and retrieve the plaintexts. The decrypted subblocks are shown in Fig. 3(f)– (g) when the 2D random phase key are correct in Fresnel distance z9 and z11, for instance. The post-processed subblocks are shown in Fig. 3(h)–(i) after averaging and binaryzation. The final retrieved QR codes are shown in Fig. 3(j)–(l) after incorporating all subblocks in its original positions. Due to the error correction property of QR code, we then can expect for a noise-free recovery. Using the application installed on our smart phone, the original message can be read out without noise after scanning Fig. 3(m)–(o). The scan results are respectively shown in Fig. 3(p)–(r) which validates the feasibility of our proposal. We then evaluate the sensitivity and fault tolerance on different keys during decryption. Note that the three QR codes are equivalent in essence, the first one (Fig. 3(a)) is chosen as example. We first conduct the decryption using a totally wrong 2D phase key, as illustrated in Fig. 4(a), a noisy image emerges. The wrong incorporated images provided that the polarization marker key is
Fig. 4. Wrong decrypted QR codes. (a) 2D phase key is wrong, (b)–(c) polarization mapping key is wrong, (d)–(e) subblocks when Fresnel distance key is wrong in z9 or z11 plane, and (f) synthetic image when all of the Fresnel distance keys are wrong.
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incorrect are shown in Fig. 4(b)–(c), leading to a failure on reading. The retrieved subblocks when Fresnel distance keys are incorrect within 0.25 mm are shown in Fig. 4(d)–(e) within z9 and z11 planes. The recombined QR code is shown in Fig. 4(f). We can figure out that the structure of QR code has been destroyed and a successful reading is impossible. Besides the QR code encryption, the proposed protocol is also suitable for any kind of input image theoretically. Here, we introduce two binary “number and letter” patterns as the plaintexts as shown in Fig. 5(a)–(b). Supposing that the Fresnel diffraction distance z′ is set to be [100.0–166.0 mm], and M = 9, N = 2. Following the same encryption and decryption protocols, the cyphertext is shown in Fig. 5(c) and the phase only key is illustrated in Fig. 5(d). The intensity images are shown in Fig. 5(e)– (f) provided that the left circular polarizer are placed before the camera in z3′ and z9′ planes and Fig. 5(g)–(h) for right circular polarizer in z4′ and z8′ planes, respectively. We can figure out that the sharpest and brightest pattern only appears in right longitudinal and transversal position when decryption keys are correct. When the 3D polarization mapping key is known and the polarization state of each sub-pattern is identified, we can incorporate each
Fig. 6. Experimental setup of the proposed 3D polarization multiplexing decryption system.
Fig. 5. (a)–(b) Original binary “number and letter” patterns, (c) cyphertext, (d) 2D phase only key, (e)–(h) retrieved subblocks on different Fresnel planes (see the text for details), and (i)–(j) decrypted patterns after recombination.
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Fig. 7. Experimental results of optical decryption. (a)–(b) original images, (c)–(d) and (e)–(f) captured images at specific distances when inserting left or right circular polarizers respectively.
sub-pattern into right position of each plaintext and achieve a successful decryption. The recombined images are shown in Fig. 5 (i)–(j) when all the decryption keys are correct. 3.2. Experiment At last, preliminary experiment results are presented to further verify our proposal. The effectiveness of developed MSW-MP algorithm is the main concern when conducting optical decryption. We utilize a reflective type Lcos SLM with pixel size of 12.3 mm to verify it. The Fresnel distance range z′ is also set to be [100.0– 166.0 mm] to perform an easy image registration. The photosensitive plane size of CCD camera is 576 × 768 with a pixel size of 10 mm. The experimental setup is illustrated in Fig. 6. The illumination source is a He–Ne laser with the wavelength of 633 nm. One computer is utilized to control both the SLM and the CCD camera independently. The micro quarter wave plates are adhered to a piece of silver paper with two open apertures on x and y axis respectively. The circular polarizer and the Ronchi grating are both integrated within the slots of the CCD iris diaphragm. Here, we demonstrate the possibility of our proposal to act as a code book based on the 3D polarization mapping for M = 9 and N = 2. The two plaintexts are shown in Fig. 7(a)–(b). The nine numbers and letters are selected to be elements in a code book. However, the personal key, such as a password is a specific combination of these characters. And it can be obtained based on the fixed 2D phase key and specially designed 3D polarization mapping key. The captured intensity images are shown in Fig. 7(c)– (d) provided that the left circular polarizer are inserted before the camera in z9′ and z3′ planes and Fig. 7(e)–(f) for right circular polarizer in z8′ and z4′ planes. Using the known 3D polarization mapping key, we retrieved the password “7E5FDA”. This example shows a potential application of our proposal in password security field.
4. Conclusions In conclusion, we make full use of the vectorial beam with both random polarization and phase distributions to achieve optical data multiplexing. Based on the developed MSW-MP phase retrieval algorithm, original images can be encrypted into a single
vectorial beam. As a result, for the first time, the one-step 3D polarization multiplexing security system is established. The implementation of this cryptosystem requires no more extra hardware compared with existed techniques, such as, double random phase encoding, leading to a simple optical structure and high security level. In the future, how to increase the multiplex capacity and reduce cross talk may be our main concern.
References [1] B. Javidi, Securing information with optical technologies, Phys. Today 50 (1997) 27–32. [2] A. Alfalou, C. Brosseau, Optical image compression and encryption methods, Adv. Opt. Photonics 1 (2009) 589–636. [3] W. Chen, B. Javidi, X. Chen, Advances in optical security systems, Adv. Opt. Photonics 6 (2014) 120–155. [4] Y. Frauel, A. Castro, T.J. Naughton, B. Javidi, Resistance of the double random phase encryption against various attacks, Opt. Express 15 (2007) 10253–10265. [5] X. Peng, P. Zhang, H.Z. Wei, B. Yu, Known-plaintext attack on optical encryption based on double random phase keys, Opt. Lett. 31 (2006) 1044–1046. [6] B. Chen, H. Wang, Optically-induced-potential-based image encryption, Opt. Express 19 (2011) 22619–22627. [7] W. Qin, X. Peng, Asymmetric cryptosystem based on phase-truncated Fourier transforms, Opt. Lett. 35 (2010) 118–120. [8] C. Lin, X. Shen, Z. Wang, C. Zhao, Optical asymmetric cryptography based on elliptical polarized light linear truncation and a numerical reconstruction technique, Appl. Opt. 53 (2014) 3920–3928. [9] G. Situ, J. Zhang, Multiple-image encryption by wavelength multiplexing, Opt. Lett. 30 (2005) 1306–1308. [10] B. Hennelly, T. Naughton, J. McDonald, J. Sheridan, G. Unnikrishnan, D. Kelly, B. Javidi, Spread-space spread-spectrum technique for secure multiplexing, Opt. Lett. 32 (2007) 1060–1062. [11] H. Hwang, H. Chang, W. Lei, Multiple-image encryption and multiplexing using a modified Gerchberg–Saxton algorithm and phase modulation in Fresnel-transform domain, Opt. Lett. 34 (2009) 3917–3919. [12] J. Barrera, R. Henao, M. Tebaldi, R. Torroba, N. Bolognini, Multiplexing encrypted data by using polarized light, Opt. Commun. 260 (2006) 109–112. [13] E. Rueda, C. Rios, J. Barrera, R. Henao, R. Torroba, Experimental multiplexing approach via code key rotations under a joint transform correlator scheme, Opt. Commun. 284 (2011) 2500–2504. [14] C. Lin, X. Shen, Multiple images encryption based on Fourier transform hologram, Opt. Commun. 285 (2012) 1023–1028. [15] J. Barrera, R. Torroba, One step multiplexing optical encryption, Opt. Commun. 283 (2010) 1268–1272. [16] W. Chen, X. Chen, Optical image encryption based on multiple-region plaintext and phase retrieval in three-dimensional space, Opt. Lasers Eng. 51 (2013) 128–133. [17] G. Biener, A. Niv, V. Kleiner, E. Hasman, Geometrical phase image encryption obtained with space-variant subwavelength gratings, Opt. Lett. 30 (2005) 1096–1098. [18] O. Matoba, B. Javidi, Secure holographic memory by double-random
32
C. Lin et al. / Optics Communications 352 (2015) 25–32
polarization encryption, Appl. Opt. 43 (2004) 2915–2919. [19] A. Alfalou, C. Brosseau, Dual encryption scheme of images using polarized light, Opt. Lett. 35 (2010) 2185–2187. [20] X. Li, T.-H. Lan, C.-H. Tien, M. Gu, Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam, Nat. Commun. 3 (2012) 998. [21] R. Henao, E. Rueda, J.F. Barrera, R. Torroba, Noise-free recovery of opto-digital encrypted and multiplexed images, Opt. Lett. 35 (2010) 333–335. [22] X.F. Meng, L.Z. Cai, M.Z. He, G.Y. Dong, X.X. Shen, Cross-talk-free double-image encryption and watermarking with amplitude–phase separate modulations, J. Opt. 7 (2005) 624–631. [23] J.F. Barrera, R.A. Mira, R. Torroba, Optical encryption and QR codes: secure and noise-free information retrieval, Opt. Express 21 (2013) 5373–5378. [24] J.F. Barrera, R.A. Mira, R. Torroba, Experimental QR code optical encryption: noise-free data recovering, Opt. Lett. 39 (2014) 3074–3077. [25] J.F. Barrera, R.A. Vélez, R. Torroba, Experimental scrambling and noise reduction applied to the optical encryption of QR codes, Opt. Express 22 (2014) 20268–20277. [26] Y. Qin, Q. Gong, Optical information encryption based on incoherent superposition with the help of the QR code, Opt. Commun. 310 (2014) 69–75. [27] Z.P. Wang, S. Zhang, H.Z. Liu, Y. Qin, Single-intensity-recording optical encryption technique based on phase retrieval algorithm and QR code, Opt. Commun. 332 (2014) 36–41. [28] C. Lin, X. Shen, B. Li, Four-dimensional key design in amplitude, phase, polarization and distance for optical encryption based on polarization digital
holography and QR code, Opt. Express 22 (2014) 20727–20739. [29] H. Chen, J. Hao, B. Zhang, J. Xu, J. Ding, H. Wang, Generation of vector beam with space-variant distribution of both polarization and phase, Opt. Lett. 36 (2011) 3179–3181. [30] J. Hao, Z. Yu, H. Chen, Z. Chen, H. Wang, J. Ding, Light field shaping by tailoring both phase and polarization, Appl. Opt. 53 (2014) 785–791. [31] C. Ying, H. Pang, C. Fan, W. Zhou, New method for the design of a phase-only computer hologram for multiplane reconstruction, Opt. Eng. 50 (2011) 055802. [32] F. Wyrowski, Diffractive optical elements: iterative calculation of quantized, blazed phase structures, J. Opt. Soc. Am. A 7 (1990) 961–969. [33] M. Montes-Usategui, J. Campos, I. Juvells, Computation of arbitrarily constrained synthetic discriminant functions, Appl. Opt. 34 (1995) 3904–3914. [34] J.A. Davis, D.E. McNamara, D.M. Cottrell, T. Sonehara, Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator, Appl. Opt. 39 (2000) 1549–1554. [35] R.L. Eriksen, P.C. Mogensen, J. Gluckstad, Elliptical polarisation encoding in two dimensions using phase-only spatial light modulators, Opt. Commun. 187 (2001) 325–336. [36] J.L. Martínez, I. Moreno, F. Mateos, Hiding binary optical data with orthogonal circular polarizations, Opt. Eng. 47 (2008) 030504. [37] W. Han, Y. Yang, W. Cheng, Q. Zhan, Vectorial optical field generator for the creation of arbitrarily complex fields, Opt. Express 21 (2013) 20692–20706.