Abstract

We report a novel optical encryption strategy that utilizes highly scattered wavefront of light field to encrypt the plaintext and exploits a scattering medium as the unique physical key. For information decryption, an imaging technique based on the speckle-correlation scattering matrix is adopted to directly extract the wavefront information from speckles, i.e., the ciphertext. The decryption relies on the transmission matrix of the scattering medium which serves as the unique key. In particular, different parts of a scattering medium have absolutely different TMs. Thus, even if attackers get the cryptosystem and repeat the measurement process, they cannot recover the key without knowing the exact part of the medium we used. The security of this scheme is further guaranteed by the advantage that data cannot be leaked without a large percentage (>60%) of the key eavesdropped. In addition, its feasibility and advantage are demonstrated experimentally.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optical encryption has been widely adopted in the field of information security. Distinguished from digital encryption that depends on digital signal processing by computers [1], information encryption using optics and photonics features the properties of parallelism, high-speed and high-security benefiting from many complex degrees of freedom of light and the ability of multiplexing [2]. Recently, several optical encryption architectures have been developed, such as the double random phase encoding [3,4], ptychography [5], the digital holographic encryption [68], and asymmetric methods based on information truncation [9,10]. Further, the compressive sensing (CS) theory has also been combined with the optical encryption techniques [1113], reducing the size of ciphertext and enabling efficient information exchange. Encryption based on computational ghost imaging [14,15] with single-pixel detectors that is compatible with CS can support unusual spectral bands, improving encryption operations. Moreover, arbitrary manipulation of light intensity, phase and polarization at the nano- or micro-scale facilitates miniaturized optical cryptography and anti-counterfeiting [16]. Besides, quantum imaging can benefit optical encryption systems by using few photons [17], and thus an attacker cannot emulate the key to decrypt the information. More strategies are being exploited to promote modern optical security and encryption technologies.

Light undergoes multiple scattering when passing through scattering media. The wavefront of light field would be seriously scrambled to generate optical intensity speckles, and only part of the optical speckles can be recorded actually. Although these speckle patterns are different from the incident patterns, there is still much information related to the incident field in the speckles. This information can be extracted and utilized for optical sensing [18] and optical communication [19]. In addition, multiple scattering can also be exploited for three-dimensional imaging [20] and holographic display with enhanced viewing angle and image size [21]. Remarkably, the mesoscopic physics of coherent transport through a disordered medium has been used to allocate and authenticate identifiers, as a physical one-way function for cryptographic practice [22].

Here, we propose to utilize the highly scattered wavefront of light field for optical encryption and exploit the scattering medium as the unique physical key for information decryption. In this scheme, part of the recorded optical intensity speckles forms the ciphertext. To decrypt the hidden information, we adopt an algorithm based on the speckle-correlation scattering matrix (SSM) [23] to directly retrieve the wavefront information from the speckle pattern. Such a decryption algorithm requires a unique key, i.e., the transmission matrix (TM) of the scattering medium. In particular, different scattering media or even different parts of a scattering medium have absolutely different TMs. That means even though attackers steal the medium and repeat the measurement process, they cannot recover the unique key without knowing the exact part of the medium we used for optical encryption. To validate the proposed method, we used a digital micromirror device (DMD) to generate optical fields that encode plaintext images and measure the unique key. The encoded light field is encrypted by part of a scattering medium and decrypted using the SSM algorithm with the physical key. It is found that the image can be recovered with merely correct key and data cannot be leaked without a large percentage (>60%) of the key eavesdropped. Further, the experiments of quick response (QR) code recognition are performed to quantitatively evaluate the security and the reliability. Results show that QR codes cannot be identified when less than 80% of the key was eavesdropped, implying the high security of our encryption method. Thus, our encryption strategy would provide new perspectives for optical encrypted communication, authentication, and anti-counterfeiting.

2. Principle

Figure 1 illustrates the principle of scattering-assisted optical encryption. The plaintext is encoded into the wavefront of light field, which undergoes multiple scattering after passing through a scattering medium. The information is encrypted in the highly scattered light field and only random intensity speckles can be observed after the encryption, which forms the ciphertext. Assume that the plaintext image is composed of N pixels. Mathematically, light field containing the plaintext can be regarded as a superposition of orthogonal field basis k1, k2, …, kN and thus the incident field (x, an N×1 vector) is expressed as: $x = \sum\nolimits_{p = 0}^N {{\alpha _p}} {k_p}$, where α1, α2, …, αN are the coefficients. The incident field is scattered by the scattering media that can be described by a TM (an M×N matrix) in mathematics [24,25]. Thus, the relationship between the resultant field (y, an M×1 vector) and the incident field follows a linear equation, y = Tx, where T represents the TM. Further, the output field can be written as $y = \sum\nolimits_{p = 0}^N {{\alpha _p}} {t_p}$, where tp is the p-th column of TM. Actually, only the intensity (y*y) can be directly observed, which is presented as the ciphertext. To decrypt the information from the speckle pattern, an algorithm based on the SSM is utilized to recover the incident field. The SSM (Z) reads [23]

$${Z_{pq}} = \frac{1}{{{\sum _p}{\sum _q}}}\left[ {\left\langle {t_p^\ast {t_{_q}}{y^\ast }y} \right\rangle \textrm{ - }\left\langle {t_p^\ast {t_q}} \right\rangle \left\langle {{y^\ast }y} \right\rangle } \right]$$
where $\left\langle {} \right\rangle $ indicates a space average, ${\sum _p} = \left\langle {{{|{{t_p}} |}^2}} \right\rangle $, and the symbol * represents the complex conjugate of the corresponding variable. The TM of a highly scattering medium can be considered as a Gaussian random matrix, and thus Eq. (1) can be written as
$${Z_{pq}} = {\alpha _p}\alpha _q^\ast{+} \frac{1}{{{\sum _p}{\sum _q}}}\left\langle {t_p^\ast {y^\ast }} \right\rangle \left\langle {{t_q}y} \right\rangle$$
where ${\alpha _p} = \frac{1}{{{\sum _p}}}\left\langle {t_p^\ast y} \right\rangle $. Assuming that the columns of TM are orthogonal to each other, which can be attributed to the uncorrelation between the input and output fields due to high scattering, the general orthogonality relation $\frac{1}{{{\sum _p}{\sum _q}}}\left\langle {t_p^\ast {t_q}} \right\rangle = {\delta _{pq}}$ and $\frac{1}{{{\sum _p}}}\left\langle {{t_p}y} \right\rangle = 0$ hold. Under the condition that the $\gamma \textrm{ = }{M / N}$ ratio is much larger than 1, the matrix can be simplified as ${Z_{pq}} = {\alpha _p}\alpha _q^\ast $, and its eigenvector forms the retrieved incident field. Thus, the plaintext information encoded in the incident field can be obtained from the random speckle pattern.

 

Fig. 1. Principle of optical encryption exploiting multiple scattering media. (a) Encryption process. The plaintext image is encoded into the phase of light filed. Scattering media encrypt the field in random optical speckle pattern that is ciphertext. (b) Decryption process. Using the SSM algorithm, the information can be recovered from the speckle pattern with a physical key, that is, the TM of the scattering medium.

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In the decryption algorithm, TM plays a critical role in retrieving the initial field, and it serves as the key in the optical encryption. Thus, the TM of the scattering medium requires to be obtained by experiment in advance. Notably, different scattering media or even different parts of a scattering medium have absolutely different TMs, suggesting that the TM used for decryption serves as a unique key. Such a unique key ensures a high security for our optical encryption method.

3. Experimental methodology

To validate the feasibility of our method, we utilized a DMD to perform the optical encryption and TM measurement. The experimental setup is illustrated in Fig. 2. A He-Ne laser (Coherent, 31-2140-000) with a wavelength of 632.8 nm was used as the light source. The laser beam was expanded with a magnification of 20 to fully illuminate the surface of the DMD (Vialux, V-9501). A 4-f system with the DMD and a pinhole filter enables us to generate the optical field where the image is encoded. The pinhole placed in the Fourier plane selects only the first-diffraction-order beam and performs low-pass filtering. To encrypt an image, an optical diffuser (DG10–220, Thorlabs, Inc.) was inserted behind the imaging plane of the 4-f system to serve as a scattering medium. The optical field was scattered by the medium and thus encrypted into the random optical speckles. A CMOS camera (PL-D752MU, PixeLINK) recorded the intensity speckle pattern, which was place at a position where the speckles have a comparable size with the camera pixels. Based on the recorded speckle pattern, the SSM algorithm can decrypt the hidden image with a particular key. The key, actually the TM of scattering medium, is obtained by the parallel wavefront optimization method [26] and a calibration algorithm proposed in Ref. [19]. During the experimental process, a polarizer can be placed in front of the camera to increase the speckle contrast. Actually, no matter what kind of the output polarization state is, the input field can be recovered via the SSM method when the TM is measured in the same condition.

 

Fig. 2. Experimental setup. L: lens; M: mirror; P: pinhole; SM: scattering medium; CMOS: complementary metal-oxide-semiconductor camera.

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Generating the optical field and acquiring the complex-valued TM rely on simultaneous modulation of light’s amplitude and phase using the DMD. DMD is actually a binary amplitude spatial light modulator, and thus binary holograms are required to modulate the complex amplitude. Here we adopted the superpixel method [27,28] to design the required holograms that encode the field. In this method, the square regions of nearby DMD pixels (4×4 pixels within 1080×1080 pixels in our case) were grouped into various superpixels to define a complex field in the imaging plane. Practically, a sequence of ON and OFF states to the micromirrors of the DMD according to the distribution of the binary holograms. The high fidelity of this method allows accurate optical field-based encryption and acquisition of the key.

4. Results and discussions

As a proof of concept demonstration, we encrypted a plaintext image into the highly scattered light field and tested the decryption with correct and incorrect keys. The DMD was used to generate the optical field that encodes a panda image [36×36 pixels, Fig. 3(a)]. The scattering medium enabled to encrypt the image in the random optical speckles, as shown in Fig. 3(b). For the testing purpose, we first measured the TM of a certain part of the scattering medium and used it as the correct key. Then, we shifted the medium a little bit laterally, measured the corresponding TM, and regarded it as the incorrected key. Using the correct and incorrect keys, we decrypted the ciphertext with the SSM algorithm. The results are presented in Figs. 3(c) and 3(d). As expected, the image that resembles the original one can be recovered with the correct key. In contrast, the wrong key yields another speckle pattern containing no information about the original object. It is demonstrated that, even if attackers get the medium and repeat the measurement process, they cannot recover the unique key without knowing the exact part of the medium and exact positions of all the components we used for optical encryption.

 

Fig. 3. Experimental results of optically encrypting a panda image. (a) The target image. (b) The ciphertext. (c, d) Decrypted images with the correct key and incorrect key. (e) Correlations between the recovered images and the target ones as a function of γ.

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In the experiments, we find that the similarity between the recovered image and the initial image is related to the ratio γ, which is decided by the camera sampling pixels (M) and pixels of the image (N). To quantitatively evaluate the influence of γ, we set different camera sampling pixels and calculated the correlation between them. The correlation is defined as $cor = {{{X^T}Y} / {{{||X ||}_2}{{||Y ||}_2}}}$, where X and Y are the original and recovered fields and ${||\cdot ||_2}$ indicates the Euclidean norm. Figure 3(e) shows the corresponding measured results. It is found that the recovered image becomes clear along with the increasing γ. Apart from the binary image information, we also tested our method in the encryption of grayscale image, for example, a helical phase front. The corresponding result is shown in Fig. 4, which demonstrates its feasibility for encrypting complicated image information. To obtain a good quality of recovered image and appropriate TM size, we choose γ = 237 for the optical encryption and decryption in the experiments.

 

Fig. 4. Experimental result for optical encryption of grayscale image.

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To quantitatively evaluate the security of our proposed method, we assumed that a potential attacker who knows the reconstruction mechanism eavesdropped a fraction of the key and attempted to decrypt the information from the speckle pattern. For this purpose, we performed QR code recognition experiments based on the recovered images obtained with various percentages of the key. In practice, a QR code containing the information of letters “USTC”, the abbreviation of our university, was tested. Figure 5(a) shows a sequence of the recovered images of QR codes under different percentages of key eavesdropped. The image begins to reveal until the eavesdropped key reaches ∼60% (an average value from different image tests) of the correct one, which is much better than the previous reports (∼10% [14]). Further, the recovered QR codes were identified by a smartphone, and the results are shown in Fig. 5(b). It is found that the QR codes cannot be identified when less than ∼80% of the key was eavesdropped, making encryption scheme much difficult to attack.

 

Fig. 5. Experimental results of QR code recognition. (a) Reconstructed images with various percentages of the key. (b) Results of identifying the QR codes containing the words “USTC”.

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In our current experiments, an optical diffuser is used as the scattering medium whose TM is not a fully random matrix. A highly scattering medium with a completely random TM, such as a zinc oxide layer or multiple diffusers, would be better for the optical encryption. Note that, our technique might suffer from the known plaintext attacks (KPA) [29]. For example, machine learning could be used to retrieve intensity images from speckles. Similarly, machine learning-based KPA might retrieve the plaintext images [29]. However, these images are commonly intensity ones and simple. In contrast, our technique encodes the plaintext image into the wavefront (phase) of light, which is very sensitive to the scattering compared with the intensity ones. Thus, it is more difficult to retrieve the phase information from intensity speckles. Exploiting scattered wavefront of light field for optical encryption seems straightforward, but it offers an effective and low-cost cryptosystem with high security. The high security of such a scheme is considered to be guaranteed by its two properties. First, the physical key is unique because different media or different parts of a scattering medium have absolutely different TMs, which required to be measured by experiments. As a consequence, even if an attacker steals the medium and gets the cryptosystem, he cannot obtain the key without knowing the exact part of the medium that we used for encryption. Second, the unauthorized attacker is difficult to decrypt critical data because a large percentage of the key needs to be eavesdropped even though the attacker knows the reconstruction mechanism. To further enhance the security, the nonlinear wavefront shaping techniques [30] might be introduced into the scattering-based optical encryption.

Our decryption process with the SSM algorithm can be regarded as a computational complex field imaging using the measured TM. In contrast, existing imaging techniques through scattering media using speckle correlations [3133] cannot recover the wave front information of light field. Thus, our encryption method would be immune to these scattering imaging techniques. Furthermore, compared with the common optical encryption schemes, such as double random phase encoding and ghost imaging-based encryption, our scheme exploits a physical key that are inexpensive to fabricate, prohibitively difficult to duplicate and intrinsically tamper-resistant. In real applications, the key must still be distributed to both parties in a secure way, a curtail step in which a hacker might obtain access to the key. A solution to this problem is quantum key distribution that involves additional steps.

5. Summary

In summary, we have proposed and demonstrated an optical encryption scheme by exploiting a scattering medium as the unique physical key. Such an optical scheme encrypts the plaintext into the highly scattered wavefront of light field and relies on the unique key to decrypt the information with an SSM-based algorithm. In particular, the physical key is very sensitive to the area of the scattering medium, suggesting no possibility to recover the key without known the exact part of the medium we used for optical encryption. Experimentally, we verified the feasibility of this scheme by a proof-of-concept experiment. Furthermore, a QR code recognition experiment was performed to demonstrated its advantage of high security. We expect this novel optical encryption strategy to benefit practical applications, such as optical encrypted communication, authentication, and anti-counterfeiting.

Funding

National Natural Science Foundation of China (61535011, 11974333, 11704369); National Key Research and Development Program of China (2017YFA0304800).

Disclosures

The authors declare no conflicts of interest.

References

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3. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995). [CrossRef]  

4. A. Velez Zea, J. F. Barrera Ramirez, and R. Torroba, “Optimized random phase encryption,” Opt. Lett. 43(15), 3558–3561 (2018). [CrossRef]  

5. Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013). [CrossRef]  

6. B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000). [CrossRef]  

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9. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010). [CrossRef]  

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11. B. Deepan, C. Quan, Y. Wang, and C. J. Tay, “Multiple-image encryption by space multiplexing based on compressive sensing and the double-random phase-encoding technique,” Appl. Opt. 53(20), 4539–4547 (2014). [CrossRef]  

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13. Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18(14), 15094–15103 (2010). [CrossRef]  

14. P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35(14), 2391–2393 (2010). [CrossRef]  

15. W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103(22), 221106 (2013). [CrossRef]  

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19. L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019). [CrossRef]  

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21. H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photonics 11(3), 186–192 (2017). [CrossRef]  

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24. S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010). [CrossRef]  

25. P. Yu, Q. Zhao, X. Hu, Y. Li, and L. Gong, “Tailoring arbitrary polarization states of light through scattering media,” Appl. Phys. Lett. 113(12), 121102 (2018). [CrossRef]  

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References

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  1. M. J. Hossain, M. B. Hossain, and K. M. Morshed, “Reconfigurable encryption system: Encrypt digital data,” in 2012 15th International Conference on Computer and Information Technology (ICCIT), 2012), 429–435.
  2. B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
    [Crossref]
  3. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
    [Crossref]
  4. A. Velez Zea, J. F. Barrera Ramirez, and R. Torroba, “Optimized random phase encryption,” Opt. Lett. 43(15), 3558–3561 (2018).
    [Crossref]
  5. Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
    [Crossref]
  6. B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
    [Crossref]
  7. E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39(35), 6595–6601 (2000).
    [Crossref]
  8. N. Yang, Q. Gao, and Y. Shi, “Visual-cryptographic image hiding with holographic optical elements,” Opt. Express 26(24), 31995–32006 (2018).
    [Crossref]
  9. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010).
    [Crossref]
  10. S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51(10), 1446–1452 (2012).
    [Crossref]
  11. B. Deepan, C. Quan, Y. Wang, and C. J. Tay, “Multiple-image encryption by space multiplexing based on compressive sensing and the double-random phase-encoding technique,” Appl. Opt. 53(20), 4539–4547 (2014).
    [Crossref]
  12. N. Rawat, I.-C. Hwang, Y. Shi, and B.-G. Lee, “Optical image encryption via photon-counting imaging and compressive sensing based ptychography,” J. Opt. 17(6), 065704 (2015).
    [Crossref]
  13. Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18(14), 15094–15103 (2010).
    [Crossref]
  14. P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35(14), 2391–2393 (2010).
    [Crossref]
  15. W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103(22), 221106 (2013).
    [Crossref]
  16. Z. Li, W. Liu, H. Cheng, D.-Y. Choi, S. Chen, and J. Tian, “Arbitrary Manipulation of Light Intensity by Bilayer Aluminum Metasurfaces,” Adv. Opt. Mater. 7, 1900260 (2019).
    [Crossref]
  17. S. A. Goorden, M. Horstmann, A. P. Mosk, B. Škorić, and P. W. H. Pinkse, “Quantum-secure authentication of a physical unclonable key,” Optica 1(6), 421 (2014).
    [Crossref]
  18. N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
    [Crossref]
  19. L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019).
    [Crossref]
  20. N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “DiffuserCam: lensless single-exposure 3D imaging,” Optica 5(1), 1–9 (2018).
    [Crossref]
  21. H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photonics 11(3), 186–192 (2017).
    [Crossref]
  22. R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical One-Way Functions,” Science 297(5589), 2026–2030 (2002).
    [Crossref]
  23. K. Lee and Y. Park, “Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor,” Nat. Commun. 7(1), 13359 (2016).
    [Crossref]
  24. S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
    [Crossref]
  25. P. Yu, Q. Zhao, X. Hu, Y. Li, and L. Gong, “Tailoring arbitrary polarization states of light through scattering media,” Appl. Phys. Lett. 113(12), 121102 (2018).
    [Crossref]
  26. J. Yoon, K. Lee, J. Park, and Y. Park, “Measuring optical transmission matrices by wavefront shaping,” Opt. Express 23(8), 10158–10167 (2015).
    [Crossref]
  27. L. Gong, X.-Z. Qiu, Y.-X. Ren, H.-Q. Zhu, W.-W. Liu, J.-H. Zhou, M.-C. Zhong, X.-X. Chu, and Y.-M. Li, “Observation of the asymmetric Bessel beams with arbitrary orientation using a digital micromirror device,” Opt. Express 22(22), 26763–26776 (2014).
    [Crossref]
  28. S. A. Goorden, J. Bertolotti, and A. P. Mosk, “Superpixel-based spatial amplitude and phase modulation using a digital micromirror device,” Opt. Express 22(15), 17999–18009 (2014).
    [Crossref]
  29. L. Zhou, Y. Xiao, and W. Chen, “Machine-learning attacks on interference-based optical encryption: experimental demonstration,” Opt. Express 27(18), 26143–26154 (2019).
    [Crossref]
  30. O. Katz, E. Small, Y. Guan, and Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1(3), 170–174 (2014).
    [Crossref]
  31. O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
    [Crossref]
  32. J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
    [Crossref]
  33. M. Liao, D. Lu, W. He, G. Pedrini, W. Osten, and X. Peng, “Improving reconstruction of speckle correlation imaging by using a modified phase retrieval algorithm with the number of nonzero-pixels constraint,” Appl. Opt. 58(2), 473–478 (2019).
    [Crossref]

2019 (4)

Z. Li, W. Liu, H. Cheng, D.-Y. Choi, S. Chen, and J. Tian, “Arbitrary Manipulation of Light Intensity by Bilayer Aluminum Metasurfaces,” Adv. Opt. Mater. 7, 1900260 (2019).
[Crossref]

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019).
[Crossref]

L. Zhou, Y. Xiao, and W. Chen, “Machine-learning attacks on interference-based optical encryption: experimental demonstration,” Opt. Express 27(18), 26143–26154 (2019).
[Crossref]

M. Liao, D. Lu, W. He, G. Pedrini, W. Osten, and X. Peng, “Improving reconstruction of speckle correlation imaging by using a modified phase retrieval algorithm with the number of nonzero-pixels constraint,” Appl. Opt. 58(2), 473–478 (2019).
[Crossref]

2018 (4)

2017 (2)

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
[Crossref]

H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photonics 11(3), 186–192 (2017).
[Crossref]

2016 (2)

K. Lee and Y. Park, “Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor,” Nat. Commun. 7(1), 13359 (2016).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

2015 (2)

N. Rawat, I.-C. Hwang, Y. Shi, and B.-G. Lee, “Optical image encryption via photon-counting imaging and compressive sensing based ptychography,” J. Opt. 17(6), 065704 (2015).
[Crossref]

J. Yoon, K. Lee, J. Park, and Y. Park, “Measuring optical transmission matrices by wavefront shaping,” Opt. Express 23(8), 10158–10167 (2015).
[Crossref]

2014 (6)

2013 (2)

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103(22), 221106 (2013).
[Crossref]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
[Crossref]

2012 (2)

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51(10), 1446–1452 (2012).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

2010 (4)

2002 (1)

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical One-Way Functions,” Science 297(5589), 2026–2030 (2002).
[Crossref]

2000 (2)

1995 (1)

Alfalou, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Antipa, N.

Barrera, J. F.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Barrera Ramirez, J. F.

Bertolotti, J.

S. A. Goorden, J. Bertolotti, and A. P. Mosk, “Superpixel-based spatial amplitude and phase modulation using a digital micromirror device,” Opt. Express 22(15), 17999–18009 (2014).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Boccara, A.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Bostan, E.

Brosseau, C.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Bruce, G. D.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
[Crossref]

Carminati, R.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Carnicer, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Chen, S.

Z. Li, W. Liu, H. Cheng, D.-Y. Choi, S. Chen, and J. Tian, “Arbitrary Manipulation of Light Intensity by Bilayer Aluminum Metasurfaces,” Adv. Opt. Mater. 7, 1900260 (2019).
[Crossref]

Chen, W.

L. Zhou, Y. Xiao, and W. Chen, “Machine-learning attacks on interference-based optical encryption: experimental demonstration,” Opt. Express 27(18), 26143–26154 (2019).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103(22), 221106 (2013).
[Crossref]

Chen, X.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103(22), 221106 (2013).
[Crossref]

Cheng, H.

Z. Li, W. Liu, H. Cheng, D.-Y. Choi, S. Chen, and J. Tian, “Arbitrary Manipulation of Light Intensity by Bilayer Aluminum Metasurfaces,” Adv. Opt. Mater. 7, 1900260 (2019).
[Crossref]

Choi, D.-Y.

Z. Li, W. Liu, H. Cheng, D.-Y. Choi, S. Chen, and J. Tian, “Arbitrary Manipulation of Light Intensity by Bilayer Aluminum Metasurfaces,” Adv. Opt. Mater. 7, 1900260 (2019).
[Crossref]

Chu, X.-X.

Clemente, P.

Deepan, B.

Dholakia, K.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
[Crossref]

Durán, V.

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Gao, Q.

Gershenfeld, N.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical One-Way Functions,” Science 297(5589), 2026–2030 (2002).
[Crossref]

Gigan, S.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Gong, L.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019).
[Crossref]

P. Yu, Q. Zhao, X. Hu, Y. Li, and L. Gong, “Tailoring arbitrary polarization states of light through scattering media,” Appl. Phys. Lett. 113(12), 121102 (2018).
[Crossref]

L. Gong, X.-Z. Qiu, Y.-X. Ren, H.-Q. Zhu, W.-W. Liu, J.-H. Zhou, M.-C. Zhong, X.-X. Chu, and Y.-M. Li, “Observation of the asymmetric Bessel beams with arbitrary orientation using a digital micromirror device,” Opt. Express 22(22), 26763–26776 (2014).
[Crossref]

Goorden, S. A.

Guan, Y.

Guo, C.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

He, W.

M. Liao, D. Lu, W. He, G. Pedrini, W. Osten, and X. Peng, “Improving reconstruction of speckle correlation imaging by using a modified phase retrieval algorithm with the number of nonzero-pixels constraint,” Appl. Opt. 58(2), 473–478 (2019).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Heckel, R.

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
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Horstmann, M.

Hossain, M. B.

M. J. Hossain, M. B. Hossain, and K. M. Morshed, “Reconfigurable encryption system: Encrypt digital data,” in 2012 15th International Conference on Computer and Information Technology (ICCIT), 2012), 429–435.

Hossain, M. J.

M. J. Hossain, M. B. Hossain, and K. M. Morshed, “Reconfigurable encryption system: Encrypt digital data,” in 2012 15th International Conference on Computer and Information Technology (ICCIT), 2012), 429–435.

Hu, X.

P. Yu, Q. Zhao, X. Hu, Y. Li, and L. Gong, “Tailoring arbitrary polarization states of light through scattering media,” Appl. Phys. Lett. 113(12), 121102 (2018).
[Crossref]

Hu, X.-Y.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019).
[Crossref]

Huang, K.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019).
[Crossref]

Hwang, I.-C.

N. Rawat, I.-C. Hwang, Y. Shi, and B.-G. Lee, “Optical image encryption via photon-counting imaging and compressive sensing based ptychography,” J. Opt. 17(6), 065704 (2015).
[Crossref]

Javidi, B.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
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Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18(14), 15094–15103 (2010).
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B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
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E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39(35), 6595–6601 (2000).
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P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
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Juvells, I.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Katz, O.

O. Katz, E. Small, Y. Guan, and Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1(3), 170–174 (2014).
[Crossref]

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
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Kuo, G.

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Lancis, J.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
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P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35(14), 2391–2393 (2010).
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Lee, B.-G.

N. Rawat, I.-C. Hwang, Y. Shi, and B.-G. Lee, “Optical image encryption via photon-counting imaging and compressive sensing based ptychography,” J. Opt. 17(6), 065704 (2015).
[Crossref]

Lee, K.

H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photonics 11(3), 186–192 (2017).
[Crossref]

K. Lee and Y. Park, “Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor,” Nat. Commun. 7(1), 13359 (2016).
[Crossref]

J. Yoon, K. Lee, J. Park, and Y. Park, “Measuring optical transmission matrices by wavefront shaping,” Opt. Express 23(8), 10158–10167 (2015).
[Crossref]

Lerosey, G.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Li, H.

Li, T.

Li, Y.

P. Yu, Q. Zhao, X. Hu, Y. Li, and L. Gong, “Tailoring arbitrary polarization states of light through scattering media,” Appl. Phys. Lett. 113(12), 121102 (2018).
[Crossref]

Li, Y.-M.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019).
[Crossref]

L. Gong, X.-Z. Qiu, Y.-X. Ren, H.-Q. Zhu, W.-W. Liu, J.-H. Zhou, M.-C. Zhong, X.-X. Chu, and Y.-M. Li, “Observation of the asymmetric Bessel beams with arbitrary orientation using a digital micromirror device,” Opt. Express 22(22), 26763–26776 (2014).
[Crossref]

Li, Z.

Z. Li, W. Liu, H. Cheng, D.-Y. Choi, S. Chen, and J. Tian, “Arbitrary Manipulation of Light Intensity by Bilayer Aluminum Metasurfaces,” Adv. Opt. Mater. 7, 1900260 (2019).
[Crossref]

Liao, M.

Liu, W.

Z. Li, W. Liu, H. Cheng, D.-Y. Choi, S. Chen, and J. Tian, “Arbitrary Manipulation of Light Intensity by Bilayer Aluminum Metasurfaces,” Adv. Opt. Mater. 7, 1900260 (2019).
[Crossref]

Liu, W.-W.

Lu, D.

Maker, G. T.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
[Crossref]

Malcolm, G.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
[Crossref]

Markman, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Matsumoto, T.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Mazilu, M.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
[Crossref]

Metzger, N. K.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
[Crossref]

Mildenhall, B.

Millán, M. S.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Miller, B.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
[Crossref]

Morshed, K. M.

M. J. Hossain, M. B. Hossain, and K. M. Morshed, “Reconfigurable encryption system: Encrypt digital data,” in 2012 15th International Conference on Computer and Information Technology (ICCIT), 2012), 429–435.

Mosk, A. P.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

S. A. Goorden, M. Horstmann, A. P. Mosk, B. Škorić, and P. W. H. Pinkse, “Quantum-secure authentication of a physical unclonable key,” Optica 1(6), 421 (2014).
[Crossref]

S. A. Goorden, J. Bertolotti, and A. P. Mosk, “Superpixel-based spatial amplitude and phase modulation using a digital micromirror device,” Opt. Express 22(15), 17999–18009 (2014).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Naruse, M.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Ng, R.

Nishchal, N. K.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51(10), 1446–1452 (2012).
[Crossref]

Nomura, T.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
[Crossref]

Osten, W.

Pappu, R.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical One-Way Functions,” Science 297(5589), 2026–2030 (2002).
[Crossref]

Park, J.

H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photonics 11(3), 186–192 (2017).
[Crossref]

J. Yoon, K. Lee, J. Park, and Y. Park, “Measuring optical transmission matrices by wavefront shaping,” Opt. Express 23(8), 10158–10167 (2015).
[Crossref]

Park, Y.

H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photonics 11(3), 186–192 (2017).
[Crossref]

K. Lee and Y. Park, “Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor,” Nat. Commun. 7(1), 13359 (2016).
[Crossref]

J. Yoon, K. Lee, J. Park, and Y. Park, “Measuring optical transmission matrices by wavefront shaping,” Opt. Express 23(8), 10158–10167 (2015).
[Crossref]

Pedrini, G.

Peng, X.

M. Liao, D. Lu, W. He, G. Pedrini, W. Osten, and X. Peng, “Improving reconstruction of speckle correlation imaging by using a modified phase retrieval algorithm with the number of nonzero-pixels constraint,” Appl. Opt. 58(2), 473–478 (2019).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010).
[Crossref]

Pérez-Cabré, E.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Pinkse, P. W. H.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

S. A. Goorden, M. Horstmann, A. P. Mosk, B. Škorić, and P. W. H. Pinkse, “Quantum-secure authentication of a physical unclonable key,” Optica 1(6), 421 (2014).
[Crossref]

Popoff, S.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Qin, W.

Qiu, X.-Z.

Quan, C.

Rajput, S. K.

Rawat, N.

N. Rawat, I.-C. Hwang, Y. Shi, and B.-G. Lee, “Optical image encryption via photon-counting imaging and compressive sensing based ptychography,” J. Opt. 17(6), 065704 (2015).
[Crossref]

Recht, B.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical One-Way Functions,” Science 297(5589), 2026–2030 (2002).
[Crossref]

Refregier, P.

Ren, Y.-X.

Rivenson, Y.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18(14), 15094–15103 (2010).
[Crossref]

Sheridan, J. T.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Shi, Y.

Silberberg, Y.

Situ, G.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Škoric, B.

Small, E.

Spesyvtsev, R.

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
[Crossref]

Stern, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18(14), 15094–15103 (2010).
[Crossref]

Tajahuerce, E.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35(14), 2391–2393 (2010).
[Crossref]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39(35), 6595–6601 (2000).
[Crossref]

Tay, C. J.

Taylor, J.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical One-Way Functions,” Science 297(5589), 2026–2030 (2002).
[Crossref]

Tian, J.

Z. Li, W. Liu, H. Cheng, D.-Y. Choi, S. Chen, and J. Tian, “Arbitrary Manipulation of Light Intensity by Bilayer Aluminum Metasurfaces,” Adv. Opt. Mater. 7, 1900260 (2019).
[Crossref]

Torres-Company, V.

Torroba, R.

A. Velez Zea, J. F. Barrera Ramirez, and R. Torroba, “Optimized random phase encryption,” Opt. Lett. 43(15), 3558–3561 (2018).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Velez Zea, A.

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Waller, L.

Wang, Y.

Xiao, Y.

Yamaguchi, M.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Yang, J.-M.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019).
[Crossref]

Yang, N.

Yoon, J.

Yu, H.

H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photonics 11(3), 186–192 (2017).
[Crossref]

Yu, P.

P. Yu, Q. Zhao, X. Hu, Y. Li, and L. Gong, “Tailoring arbitrary polarization states of light through scattering media,” Appl. Phys. Lett. 113(12), 121102 (2018).
[Crossref]

Zhang, H.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019).
[Crossref]

Zhang, S.

Zhao, Q.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019).
[Crossref]

P. Yu, Q. Zhao, X. Hu, Y. Li, and L. Gong, “Tailoring arbitrary polarization states of light through scattering media,” Appl. Phys. Lett. 113(12), 121102 (2018).
[Crossref]

Zhong, M.-C.

Zhou, J.-H.

Zhou, L.

Zhu, H.-Q.

Adv. Opt. Mater. (1)

Z. Li, W. Liu, H. Cheng, D.-Y. Choi, S. Chen, and J. Tian, “Arbitrary Manipulation of Light Intensity by Bilayer Aluminum Metasurfaces,” Adv. Opt. Mater. 7, 1900260 (2019).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (2)

P. Yu, Q. Zhao, X. Hu, Y. Li, and L. Gong, “Tailoring arbitrary polarization states of light through scattering media,” Appl. Phys. Lett. 113(12), 121102 (2018).
[Crossref]

W. Chen and X. Chen, “Ghost imaging for three-dimensional optical security,” Appl. Phys. Lett. 103(22), 221106 (2013).
[Crossref]

J. Opt. (2)

N. Rawat, I.-C. Hwang, Y. Shi, and B.-G. Lee, “Optical image encryption via photon-counting imaging and compressive sensing based ptychography,” J. Opt. 17(6), 065704 (2015).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Pérez-Cabré, M. S. Millán, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, “Roadmap on optical security,” J. Opt. 18(8), 083001 (2016).
[Crossref]

Light: Sci. Appl. (1)

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019).
[Crossref]

Nat. Commun. (2)

K. Lee and Y. Park, “Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor,” Nat. Commun. 7(1), 13359 (2016).
[Crossref]

N. K. Metzger, R. Spesyvtsev, G. D. Bruce, B. Miller, G. T. Maker, G. Malcolm, M. Mazilu, and K. Dholakia, “Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization,” Nat. Commun. 8(1), 15610 (2017).
[Crossref]

Nat. Photonics (2)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photonics 11(3), 186–192 (2017).
[Crossref]

Nature (1)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Opt. Express (6)

Opt. Lett. (6)

Optica (3)

Phys. Rev. Lett. (1)

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Science (1)

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical One-Way Functions,” Science 297(5589), 2026–2030 (2002).
[Crossref]

Other (1)

M. J. Hossain, M. B. Hossain, and K. M. Morshed, “Reconfigurable encryption system: Encrypt digital data,” in 2012 15th International Conference on Computer and Information Technology (ICCIT), 2012), 429–435.

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Figures (5)

Fig. 1.
Fig. 1. Principle of optical encryption exploiting multiple scattering media. (a) Encryption process. The plaintext image is encoded into the phase of light filed. Scattering media encrypt the field in random optical speckle pattern that is ciphertext. (b) Decryption process. Using the SSM algorithm, the information can be recovered from the speckle pattern with a physical key, that is, the TM of the scattering medium.
Fig. 2.
Fig. 2. Experimental setup. L: lens; M: mirror; P: pinhole; SM: scattering medium; CMOS: complementary metal-oxide-semiconductor camera.
Fig. 3.
Fig. 3. Experimental results of optically encrypting a panda image. (a) The target image. (b) The ciphertext. (c, d) Decrypted images with the correct key and incorrect key. (e) Correlations between the recovered images and the target ones as a function of γ.
Fig. 4.
Fig. 4. Experimental result for optical encryption of grayscale image.
Fig. 5.
Fig. 5. Experimental results of QR code recognition. (a) Reconstructed images with various percentages of the key. (b) Results of identifying the QR codes containing the words “USTC”.

Equations (2)

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Z p q = 1 p q [ t p t q y y  -  t p t q y y ]
Z p q = α p α q + 1 p q t p y t q y

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