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Current Optics and Photonics 2019; 3(5): 390-400

Published online October 25, 2019 https://doi.org/10.3807/COPP.2019.3.5.390

Copyright © Optical Society of Korea.

Efficient Compression Schemes for Double Random Phase-encoded Data for Image Authentication

Samaneh Gholami1, Keyvan Jaferzadeh2, Seokjoo Shin1, and Inkyu Moon2,*

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1Department of Computer Engineering, Chosun University, Gwangju 61452, Korea, 2Department of Robotics Engineering, DGIST, Daegu 42988, Korea

Corresponding author: inkyu.moon@dgist.ac.kr

Received: March 28, 2019; Revised: June 21, 2019; Accepted: June 27, 2019

Abstract

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Encrypted images obtained through double random phase-encoding (DRPE) occupy considerable storage space. We propose efficient compression schemes to reduce the size of the encrypted data. In the proposed schemes, two state-of-art compression methods of JPEG and JP2K are applied to the quantized encrypted phase images obtained by combining the DRPE algorithm with the virtual photon counting imaging technique. We compute the nonlinear cross-correlation between the registered reference images and the compressed input images to verify the performance of the compression of double random phase-encoded images. We show quantitatively through experiments that considerable compression of the encrypted image data can be achieved while security and authentication factors are completely preserved.

Keywords: Optical security and encryption, Double random phase encoding, Image cryptography, Pattern recognition

I. INTRODUCTION

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The amount of data, especially images, being transferred and stored is growing dramatically, necessitating the design of effective methods to solve the problem of digital image authentication, particularly for important digital images whose security must be preserved. Image authentication is the application of image science to determine if a particular image is an accurate representation of the original data based on a defined criterion. Optical information security technology has been studied and developed for various practical applications for protecting secret data during storage and transmission. One of the optical methods that has been applied to image authentication is double random phase-encoding (DRPE) [1-14]. Since the introduction of the DRPE method, a survey of this method has been considered in many studies. In Ref. [13] Liu mentioned the DRPE spread-space spread-spectrum watermarking (DRPE SS-SS) technique is robust to scaling, and to JPEG compression distortion. Also, it is robust to spatial cropping and both low and high pass filtering. According to Ref. [15], analyzing the resistance of the encryption scheme under some of the commonly known attacks reported in the literature can demonstrate the validity of our proposed method. Although conventional DRPE is robust against brute force attack, it is still fragile to a few specific attacks. It has been determined that DRPE is vulnerable to impulse attacks [16, 17]. To overcome this issue integrating photon-counting and DRPE has been introduced [18-24]. Photon-counting imaging (PCI) technique generates distributions with far fewer photons than conventional imaging, which may permit bandwidth reduction since it generates sparse encrypted data. In addition, the output image from the system does not resemble its input image and cannot be visually distinguished from its counterpart, which can safeguard DRPE-PCI from unauthorized attacks and improve its security to the desired level [20, 21].

At a basic level, DRPE transforms an input image into phase and amplitude objects. The storage space or transmission time required for these objects makes the DRPE method unsuitable for practical applications. Therefore, developing efficient compression schemes is essential for speeding up transmission time and decreasing storage size of DRPE results. For compression methods, the Joint Photography Experts Group (JPEG) has proposed many successful standards. The JPEG proposed many popular compression techniques for imaging applications. These techniques are used in applications ranging from the internet to digital photography and show good performance for the storage of many images in storage media elements [25-35].

In this paper, we propose efficient compression schemes to reduce the size of the encrypted image data from the fusion of the DRPE algorithm, the virtual PCI technique, and two main compression algorithms. The compression method is applied to the sparse encrypted data of the PCI technique. The proposed method has several advantages. First, the complex images yielded by the proposed authentication procedures cannot be visually recognized because they contain photon-limited encrypted data, obtained by combining the DRPE and PCI methods. Second, by applying the proposed compression methods, the size of the encrypted images is reduced significantly without affecting authentication results. Finally, the photon-limited input phase image can be authenticated using a nonlinear cross-correlation metric.

II. BACKGROUND

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Before describing the proposed approach, we first briefly review the basic techniques that we have used for efficient compression of DRPE data for image authentication.

2.1. Double Random Phase Encoding (DRPE)

DRPE allows the encoding of a primary image into complex stationary white noise using two random phase masks [1]. The random phase masks for the spatial and frequency domains, φ1(x, y) and φ2(μ, ν), respectively, are statistically independent and uniformly distributed over [0, 2π]. The encryption process of the DRPE algorithm is described by the following equation [1]:

where ℑ and ℑ−1 represent a Fourier transform and inverse Fourier transform, respectively. The decryption process for DRPE is the reverse of the encryption process shown in Eq. (1).

2.2. Photon Counting Imaging

Photon Counting Imaging (PCI) is a special class of optical imaging techniques that was designed for low-light conditions or night vision imaging systems. PCI can also be computationally simulated by changing a limited number of photons based on the expected number of incident photons in the entire scene. In the virtual PCI scheme, the probability of counting photons (pj) at an arbitrary pixel (xj) in an image can be modeled as a Poisson distribution, as follows:

where λj is the Poisson parameter that is computed by λj = Npfj, Np is the expected number of incident photons, and fj is the normalized irradiance at pixel (xj) such that , with M being the total number of pixels in the image. In the proposed compression scheme, PCI is virtually applied to the amplitude portion of the encrypted complex amplitude image fc(x, y) obtained from DRPE [19, 20].

2.3. Compression Method

As mentioned earlier, the output of the DRPE technique is very large. Thus, efficient compression techniques are crucial for storage and transmission purposes. Because the JPEG and JP2K compression techniques have superior performance compared to existing standards [27-29], these two techniques are explained briefly in this section.

2.3.1. JPEG

JPEG is a well-known standardized image compression technique. It has been widely used for several purposes, including reduction of the size of image files, storage of full-color information, and automatic error recovery [25]. This technique is the most popular compression technique and supports lossy coding. Lossy compression reduces the original image size by removing non-vital information. In the baseline mode, the image is divided into 8 × 8 blocks and each block is transformed using the discrete cosine transform (DCT). The DCT is typically applied to reduce spatial redundancy to achieve good compression performance. The transformed blocks are quantized using a uniform scalar quantization, zig-zag scanned, and eventually, entropy coded using Huffman coding. The quantization step size for each of the 64 DCT coefficients is specified in a quantization table, which remains the same for all blocks [25].

2.3.2. JPEG 2000 (JP2K)

JP2K is based on a discrete wavelet transform (DWT), scalar quantization, context modeling, arithmetic coding, and post-compression rate allocation. Preprocessing steps include tile component partitioning, DC shifting, and component transformation. During preprocessing, each slice of the original image block is partitioned into one or more disjoint rectangular regions called tiles. In terms of coding, these tile components are independent. DC shifting converts the input unsigned sample values of the image tile components into signed sample values with zero point symmetry. Thus, the relationships between the image tile components are decreased through component transformation. JP2K uses a DWT for transformation as its core coding technology. A DWT can support the transmission of multi-resolution images by using an image multi-resolution representation and decrease the correlation between pixels in the full frame to reduce the blocking effect in the codec process. After the entire image is transformed, the resulting coefficients are quantized and different levels of image quality are acquired based on the minimal precision required. The quantizer assigns different quantization levels for different sub-bands by using a scalar quantization method with a dead zone. The final step of encoding is called entropy encoding. The entropy encoder divides the wavelet sub-band into code blocks. DWT coefficients are then organized into binary bit planes. The entropy encoder uses context modeling and bit-plane arithmetic coding to encode the binary bit planes [26-33].

III. PROPOSED COMPRESSION SCHEMES

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Figure 1 presents the proposed compression procedure for DRPE-PCI image authentication. By following the algorithm in Fig. 1, the input image is encrypted and then transferred to the image authentication-verification part. In addition, the output of each step is demonstrated in the table that is linked to each related section, which shows how pixel values of the input image are affected during the execution of the proposed encryption process. In the proposed method, a quantization method based on the PCI technique is applied to the amplitude (labeled as a(x, y)) portion of the encrypted image, fc(x, y) obtained from DRPE. The virtual PCI technique changes the pixel values in a(x, y) to zero or very small values. The phase portion p(x, y) of DRPE contains a real value in the range [−π, π]. Thus, p(x, y) is converted into quantized values through a uniform quantization method similar to that used in [19]. The number of bits used for the uniform quantization process determines the quantized integer range. In this study, two-bit and four-bit quantization processes are considered. To construct a phase image, a binary mask of the photon limited amplitude portion can be directly multiplied by the quantized phase values. The entry for each binary mask is unity if the corresponding photon limited amplitude portion is a nonzero value; otherwise, the entry is zero. Finally, the JPEG and JP2K compression techniques are applied to the new phase image obtained by using the binary mask and uniform quantization.

Although the amplitude portions a(x, y) of the input image is not sent during the transmission, the new phase image can still be verified in the authentication step. It should be mentioned that authentication verification rejects false input images when their peak-to-correlation energy (PCE) is smaller than 0.1. The authentication system or receiver decompresses the compressed phase images for the performance evaluation of the proposed compression schemes. Because the decrypted images from the proposed procedure are not visually recognizable, it is necessary to adopt a comparison scheme to authenticate the retrieved images. In this study, nonlinear cross-correlation (NCC) is used to compare the reference image to the input image, which has a different photon-limited amplitude mask from that of the reference image (see Fig. 1) [19, 20].

Figure 1.The conceptual scheme of the proposed method. The method is composed of two sections: the DRPE-based encrypted image compression and image authentication verification.

Our proposed image authentication schemes efficiently compress the DRPE-encrypted images, store the compressed images in the authentication system, and utilize the decompressed images for private user image verification. It should be noted that it is likely a bad idea to directly store original images as a reference in a system for verifying personal user images because these images would be prime targets for attackers or malicious system administrators. Therefore, another advantage of the proposed approach is that, even if attackers or malicious administrators invade the system, they cannot obtain the original user images because our method utilizes efficiently compressed DRPE-encrypted images, rather than storing raw images (or original images) for user image verification.

IV. NUMERICAL SIMULATIONS

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The following simulations were performed on a PC with a 32-bit Windows 7 Enterprise OS, Intel(R) Core(TM) i5-2500K 3.30 GHz processor, 4 GB of RAM. The test images (256 × 256 pixels) shown in Figs. 2 and 3 are used to evaluate the proposed image authentication schemes. In the following experiments, two pair of images are used “Peppers”, “Cameraman” and “Baboon”, “Mona-Lisa”. Two input images are selected to be verified. For the true input image, “Peppers, “Baboon” are selected, and for the false input image, “Cameraman” and “Mona-Lisa” are considered. All simulations were implemented in MATLAB 2016. There is a full implementation of JP2K available in a low-level C API under a BSD 2-clause license (Version 2.1.0). We downloaded and used this source code with some minor changes based on our data types and the experiments we wished to perform.

Figure 2.Two test images used in our numerical experiments: (a) Peppers (reference image and true input image), (b) phase values after DRPE, (c) phase image obtained by the proposed method, (d) phase image after compression and decompression (JP2K technique; CR = 64). (e) Cameraman (false input image), (f) phase values after DRPE, (g) phase image obtained by the proposed method, (h) phase image after compression and decompression (JP2K technique; CR = 64).
Figure 3.Two test images used in our numerical experiments: (a) Baboon (reference image and true input image), (b) phase values after DRPE, (c) phase image obtained by the proposed method, (d) phase image after compression and decompression (JP2K technique; CR = 64). (e) Mona-Lisa (false input image), (f) phase values after DRPE, (g) phase image obtained by the proposed method, (h) phase image after compression and decompression (JP2K technique; CR = 64).

In the following simulation, the lossy compression of JPEG and JP2K are tested on phase images from the DRPE-PCI scheme with various Np and quantization bit sizes (nk = 2 and nk = 4 bits). We attempt to obtain the highest possible compression ratio without losing authentication efficiency. The compression ratio (CR) in this paper is defined as

Figures 2(b) and 3(b) show the phase portions (p(x, y)) of the encrypted Peppers image (Fig. 2(a)) and Baboon image (Fig. 3(a)) from DRPE, respectively. The phase image of Peppers and Baboon, as it has been explained previously, are shown in Figs. 2(c) and 3(c), respectively. Figures 2(d) and 3(d) show the phase image after applying compression and decompression using JP2K. Based on the properties of PCI, it is difficult to reconstruct a reference image after applying the PCI algorithm. Therefore, PCE is used for authentication between the reference image and input image, with its value calculated as follows:

where M and N are the image sizes along x and y axes, respectively, and ncc(x, y) is

where the parameter k defines the strength of the applied nonlinearity and determines the performance features of the processor.

Figures 4(a), 4(b), and 4(c) plot the PCE of non-compressed images and compressed phase images using the JPEG and JP2K methods, respectively. It has been demonstrated that PCE increases with an increase in the expected number of photons for the true class, particularly when Np > 105. As expected, PCE values are near unity when the parameter k is equal to 0.1. It can be seen in Figs. 4(d), 4(e), and 4(f) that PCE is less than 0.1 in false input images, even when increasing the total number of photons. It can be readily seen in Fig. 4 that PCE values have nearly the same trends in non-compressed and compressed images. In this case, the quantization bit size for the phase value is set to 2 bits. In addition, Fig. 5 demonstrates the results of Baboon (true input image) and Mona-Lisa (false input image) image in non-compressed images and compressed phase images using the JPEG and JP2K methods similarly to Fig. 4.

According to Figs. 6(a), 6(b) and Figs. 7(a), 7(b) (the results of 4-bit quantization), when increasing the total number of photons (Np > = 105), the PCEs of the compressed phase images using the JPEG and JP2K methods increase similar to Figs. 4(b), 4(c) and Figs. 5(b), 5(c), respectively. Additionally, one can see from Figs. 6(c), 6(d) and Figs. 7(c), 7(d) that both JPEG and JP2K yield similar PCE results in cases with a false input image. Furthermore, PCE in JP2K is marginally larger than the same value in JPEG in the case of true class input. It specifies that JP2K have less information lost comparing with the JPEG method.

Figure 4.PCE with various k and Np values: (a) without compression for the true class (Peppers). (b) applying JPEG compression for the true class (Peppers), (c) applying JP2K compression for the true class (Peppers), (d) without compression for the false class (Cameraman), (e) applying JPEG compression for the false class (Cameraman), (f) applying JP2K compression for the false class (Cameraman, CR is approximately 64 for the case of NP > = 105 ; nk = 2).
Figure 5.PCE with various k and Np values: (a) without compression for the true class (Baboon). (b) applying JPEG compression for the true class (Baboon), (c) applying JP2K compression for the true class (Baboon), (d) without compression for the false class (Mona-Lisa), (e) applying JPEG compression for the false class (Mona-Lisa), (f) applying JP2K compression for the false class (Mona-Lisa, CR is approximately 64 for the case of NP > = 105 ; nk = 2).
Figure 6.PCE with various k and Np values: (a) applying JPEG compression for the true class (Peppers), (b) applying JP2K compression for the true class (Peppers), (c) applying JPEG compression for the false class (Cameraman), (d) applying JP2K compression for the false class (Cameraman, CR is approximately 64 for the case of Np > = 105 ; nk = 4).
Figure 7.PCE with various k and Np values: (a) applying JPEG compression for the true class (Baboon), (b) applying JP2K compression for the true class (Baboon), (c) applying JPEG compression for the false class (Mona-Lisa), (d) applying JP2K compression for the false class (Mona-Lisa, CR is approximately 64 for the case of Np > = 105 ; nk = 4).

Figures 8(a) and 8(b) show the PCE changes when applying JPEG and JP2K with various CR and Np values when nk = 2. It is observed that by increasing Np, PCE is also increased in both graphs. In addition, the authentication strategy rejects false input images because PCE is far below 0.1, as shown in Figs. 8(c) and 8(d). It is worth noting that throughout the experiments, the random phase values (keys) used for encryption of the input images are assumed to be equal to those used for the reference images. Otherwise, the PCE value falls dramatically. Figure 9 shows the PCE changes when applying JPEG and JP2K with various CR in Baboon and Mona-Lisa images. The results is similar to that shown in Fig. 8.

Figure 8.PCE with various CR and Np values: (a) applying JPEG compression for the true class (Peppers), (b) applying JP2K compression for the true class (Peppers), (c) applying JPEG compression for the false class (Cameraman), (d) applying JP2K compression for the false class (Cameraman, nk = 2, k is 0.1).
Figure 9.PCE with various CR and Np values: (a) applying JPEG compression for the true class (Baboon), (b) applying JP2K compression for the true class (Baboon), (c) applying JPEG compression for the false class (Mona-Lisa), (d) applying JP2K compression for the false class (Mona-Lisa, nk = 2, k is 0.1).

Additionally, we tested the true input image with a photon-limited amplitude mask equal to that of the reference image in two cases of non-compressed (Figs. 10(a) and 11(a)) and compressed ones (Figs. 10(b) and 11(b)). As has been expected, PCE values are around 1 when the parameter k value is equal to 0. The trend in all figures is similar and shows that applying compression does not degrade the phase image significantly.

Figure 10.PCE with various k and Np values: (a) without compression for the true class (Peppers), (b) applying JP2K compression for the true class. (Reference and true input images have the same photon-limited amplitude mask, CR is approximately 64 for the case of Np > = 105 ; nk = 2).
Figure 11.PCE with various k and Np values: (a) without compression for the true class (Baboon), (b) applying JP2K compression for the true class. (Reference and true input images have the same photon-limited amplitude mask, CR is approximately 64 for the case of Np > = 105 ; nk = 2).

We are also interested in measuring the size of phase images compared to original gray-scale images (without applying any image encryption or compression techniques) to determine the compression gain (we call it true compression gain or TCG) of the proposed technique. The true compression gain can be obtained by

Figure 12 shows PCE, CR, and TCG values for nk = 1, 2, and 4 in black, blue, and red lines, respectively. TCG values are indicated by the labels on the graph. The test image was Peppers. Various CR values were evaluated. The y-axis of the graph shows PCE changes and the x-axis represents various CR values (calculated using Eq.3). We can see that 4-bit quantization has the highest PCE values, but the lowest TCG values due to the usage of 4 bits.

Figure 12.PCE after applying JP2K compression for the true input image (Peppers) with Np = 6 × 106 and various CRs, nk = 1, 2, and 4.

It can be observed that by using the compression methods the PCE is marginally similar to the non-compressed scheme. Indeed, we can claim that JP2k marginally outperforms JPEG if PCE is the main concern. Also, it worth mentioning that the proposed authentication system not only resists against unauthorized attacks but also has had the influence of decreasing the size of the encrypted image by combining compression method and PCI.

V. CONCLUSION

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We aimed to provide a comparative evaluation and assessment of JPEG and JP2K compression algorithm performance on the quantized phase images from DRPE-PCI using various numbers of photons from the perspective of authentication efficiency. The proposed technique considers not only quantized phase values but also a binary mask of photon-counted amplitude values. This study demonstrated that as far as lossy compression is concerned, JP2K seems to perform reasonably well in terms of its ability to efficiently handle various CRs. The results for the JP2K method showed that phase images can be compressed several times while still allowing images to be verified using a nonlinear cross-correlation technique.

References

Go to
  1. P. Refregier, and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett. 20, 767-769 (1995).
    CrossRef
  2. I. Moon, F. Yi, Y. H. Lee, and B. Javidi, "Avalanche and bit independence characteristics of double random phase encoding in the Fourier and Fresnel domains," J. Opt. Soc. Am. A 31, 1104-1111 (2014).
    CrossRef
  3. R. Tao, Y. Xin, and Y. Wang, "Double image encryption based on random phase encoding in the fractional Fourier domain," Opt. Express 15, 16067-16079 (2007).
    CrossRef
  4. Z. Liu, Y. Zhang, S. Li, W. Liu, W. Liu, Y. Wang, and S. Liu, "Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains," Opt. Lasers Technol. 47, 152-158 (2013).
    CrossRef
  5. G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett. 25, 887-889 (2000).
    CrossRef
  6. W. Chen, "Multiple-wavelength double random phase encoding with CCD-plane sparse-phase multiplexing for optical information verification," Appl. Opt. 54, 10711-10716 (2015).
    CrossRef
  7. L. Akter, I. Moon, and G. Kwon, "Double random phase encoding with a Poisson-multinomial distribution for efficient colorful image authentication," Multimedia Tools Appl 78, 14613-14632 (2019).
    CrossRef
  8. X. Wang, W. Chen, and X. Chen, "Optical information authentication using compressed double-random-phase-encoded images and quick-response codes," Opt. Express 23, 6239-6253 (2015).
    CrossRef
  9. Z. Leihong, Y. Xiao, Z. Dawei, and C. Jian, "Research on multiple-image encryption scheme based on Fourier transform and ghost imaging algorithm," Curr. Opt. Photon. 2, 315-323 (2018).
  10. J. Chen, N. Bao, L. Y. Zhang, and Z. Zhu, "Optical information authentication using optical encryption and sparsity constraint," Opt. Lasers Eng. 107, 352-363 (2018).
    CrossRef
  11. Z. Shao, Y. Shang, Q. Tong, H. Ding, X. Zhao, and X. Fu, "Multiple color image encryption and authentication based on phase retrieval and partial decryption in quaternion gyrator domain," Multimed. Tools Appl. 77, 25821-25840 (2018).
    CrossRef
  12. G. Luan, A. Li, D. Zhang, and D. Wang, "Asymmetric image encryption and authentication based on equal modulus decomposition in the Fresnel transform domain," IEEE Photon. J. 11, 6900207 (2019).
  13. S. Liu, B. M. Hennelly, C. Guo, and J. T. Sheridan, "Robustness of double random phase encoding spread-space spread-spectrum watermarking technique," Sig. Process. 109, 345-361 (2015).
    CrossRef
  14. S. Gholami, K. Jaferzadeh, S. Shin, and I. Moon, "An efficient image-based verification scheme by fusion of double random phase encoding and dynamic chaotic map," Multimed. Tools Appl. 78, 25001-25018 (2019).
    CrossRef
  15. A. V. Zea, J. F. Barrera, and R. Torroba, "Cryptographic salting for security enhancement of double random phase encryption schemes," J. Opt. 19, 105703 (2017).
    CrossRef
  16. X. Liu, J. Wu, W. He, M. Liao, C. Zhang, and X. Peng, "Vulnerability to ciphertext-only attack of optical encryption scheme based on double random phase encoding," Opt. Express 23, 18955-18968 (2015).
    CrossRef
  17. Y. Frauel, A. Castro, T. Naughton, and B. Javidi, "Resistance of the double random phase encryption against various attacks," Opt. Express 15, 10253-10265 (2007).
    CrossRef
  18. F. Yi, I. Moon, and Y. H. Lee, "A Multispectral photoncounting double random phase encoding scheme for image authentication," Sensors 14, 8877-8894 (2014).
    CrossRef
  19. I. Moon, F. Yi, M. Han, and J. Lee, "Efficient asymmetric image authentication schemes based on photon countingdouble random phase encoding and RSA algorithms," Appl. Opt. 55, 4328-4335 (2016).
    CrossRef
  20. E. Pérez-Cabré, M. Cho, and B. Javidi, "Information authentication using photon-counting double-random-phase encrypted images," Opt. Lett 36, 22-24 (2011).
    CrossRef
  21. E. Pérez-Cabré, H. C. Abril, M. S. Millán, and B. Javidi, "Photon-counting double-random-phase encoding for secure image verification and retrieval," J. Opt. 14, 094001 (2012).
    CrossRef
  22. F. Yi, Y. Jeoung, and I. Moon, "Three-dimensional image authentication scheme using sparse phase information in double random phase encoded integral imaging," Appl. Opt. 56, 4381-4387 (2017).
    CrossRef
  23. S. K. Rajput, D. Kumar, and N. K. Nishchal, "Photon counting imaging and phase mask multiplexing for multiple images authentication and digital hologram security," Appl. Opt 54, 1657-1666 (2015).
    CrossRef
  24. J. Lee, N. Sultana, F. Yi, and I. Moon, "Avalanche and bit independence properties of photon-counting double random phase encoding in gyrator domain," Curr. Opt. Photon. 2, 368-377 (2018).
  25. Y. Wiseman. Encyclopedia of Information Science and Technology, 3rd ed, Khosrow-Pour D. B. A. M. (IGI Global, PA 2015).
  26. P. Schelkens, A. Skodras, and T. Ebrahimi. The JPEG 2000 Suite (John Wiley & Sons, NY 2009).
  27. D. Santa-Cruz, T. Ebrahimi, J. Askelöf, M. Larsson, and C. Christopoulos, "JPEG 2000 still image coding versus other standards," Proc. SPIE 4115, 446-454 (2000).
  28. A. N. Skodras, C. A. Christopoulos, and T. Ebrahimi, "JPEG2000: the upcoming still image compression standard," Pattern Recogn. Lett. 22, 1337-1345 (2001).
    CrossRef
  29. D. Santa-Cruz, R. Grosbois, and T. Ebrahimi, "JPEG 2000 performance evaluation and assessment," Signal Process. Image Commun. 17, 113-130 (2002).
    CrossRef
  30. S. N. Sivanandam, A. Pasumpon, and P. Rani, "Lossy still image compression standards: JPEG and JPEG2000 - a survey," Int. J. Comput., Internet Manage. 17, 69-84 (2009).
  31. A. Skodras, C. Christopoulos, and T. Ebrahimi, "The JPEG 2000 still image compression standard," IEEE Signal Process. Mag. 18, 36-58 (2001).
    CrossRef
  32. G. K. Wallace, "The JPEG still picture compression standard," IEEE Trans. Consum. Electron. 38, xviii-xxxiv (1992).
  33. K. Jaferzadeh, S. Gholami, and I. Moon, "Lossless and lossy compression of quantitative phase images of red blood cells obtained by digital holographic imaging," Appl. Opt. 55, 10409-10416 (2016).
    CrossRef
  34. P. Li, and K. T. Lo, "A content-adaptive joint image compression and encryption scheme," IEEE Trans. Multimedia 20, 1960-1972 (2018).
    CrossRef
  35. V. Itier, P. Puteaux, and W. Puech, "Recompression of JPEG crypto-compressed images without a key," IEEE Trans. Circuits Syst. Video Technol.. to be published

Article

Article

Current Optics and Photonics 2019; 3(5): 390-400

Published online October 25, 2019 https://doi.org/10.3807/COPP.2019.3.5.390

Copyright © Optical Society of Korea.

Efficient Compression Schemes for Double Random Phase-encoded Data for Image Authentication

Samaneh Gholami1, Keyvan Jaferzadeh2, Seokjoo Shin1, and Inkyu Moon2,*

1Department of Computer Engineering, Chosun University, Gwangju 61452, Korea, 2Department of Robotics Engineering, DGIST, Daegu 42988, Korea

Correspondence to:inkyu.moon@dgist.ac.kr

Received: March 28, 2019; Revised: June 21, 2019; Accepted: June 27, 2019

Abstract

Encrypted images obtained through double random phase-encoding (DRPE) occupy considerable storage space. We propose efficient compression schemes to reduce the size of the encrypted data. In the proposed schemes, two state-of-art compression methods of JPEG and JP2K are applied to the quantized encrypted phase images obtained by combining the DRPE algorithm with the virtual photon counting imaging technique. We compute the nonlinear cross-correlation between the registered reference images and the compressed input images to verify the performance of the compression of double random phase-encoded images. We show quantitatively through experiments that considerable compression of the encrypted image data can be achieved while security and authentication factors are completely preserved.

Keywords: Optical security and encryption, Double random phase encoding, Image cryptography, Pattern recognition

I. INTRODUCTION

The amount of data, especially images, being transferred and stored is growing dramatically, necessitating the design of effective methods to solve the problem of digital image authentication, particularly for important digital images whose security must be preserved. Image authentication is the application of image science to determine if a particular image is an accurate representation of the original data based on a defined criterion. Optical information security technology has been studied and developed for various practical applications for protecting secret data during storage and transmission. One of the optical methods that has been applied to image authentication is double random phase-encoding (DRPE) [1-14]. Since the introduction of the DRPE method, a survey of this method has been considered in many studies. In Ref. [13] Liu mentioned the DRPE spread-space spread-spectrum watermarking (DRPE SS-SS) technique is robust to scaling, and to JPEG compression distortion. Also, it is robust to spatial cropping and both low and high pass filtering. According to Ref. [15], analyzing the resistance of the encryption scheme under some of the commonly known attacks reported in the literature can demonstrate the validity of our proposed method. Although conventional DRPE is robust against brute force attack, it is still fragile to a few specific attacks. It has been determined that DRPE is vulnerable to impulse attacks [16, 17]. To overcome this issue integrating photon-counting and DRPE has been introduced [18-24]. Photon-counting imaging (PCI) technique generates distributions with far fewer photons than conventional imaging, which may permit bandwidth reduction since it generates sparse encrypted data. In addition, the output image from the system does not resemble its input image and cannot be visually distinguished from its counterpart, which can safeguard DRPE-PCI from unauthorized attacks and improve its security to the desired level [20, 21].

At a basic level, DRPE transforms an input image into phase and amplitude objects. The storage space or transmission time required for these objects makes the DRPE method unsuitable for practical applications. Therefore, developing efficient compression schemes is essential for speeding up transmission time and decreasing storage size of DRPE results. For compression methods, the Joint Photography Experts Group (JPEG) has proposed many successful standards. The JPEG proposed many popular compression techniques for imaging applications. These techniques are used in applications ranging from the internet to digital photography and show good performance for the storage of many images in storage media elements [25-35].

In this paper, we propose efficient compression schemes to reduce the size of the encrypted image data from the fusion of the DRPE algorithm, the virtual PCI technique, and two main compression algorithms. The compression method is applied to the sparse encrypted data of the PCI technique. The proposed method has several advantages. First, the complex images yielded by the proposed authentication procedures cannot be visually recognized because they contain photon-limited encrypted data, obtained by combining the DRPE and PCI methods. Second, by applying the proposed compression methods, the size of the encrypted images is reduced significantly without affecting authentication results. Finally, the photon-limited input phase image can be authenticated using a nonlinear cross-correlation metric.

II. BACKGROUND

Before describing the proposed approach, we first briefly review the basic techniques that we have used for efficient compression of DRPE data for image authentication.

2.1. Double Random Phase Encoding (DRPE)

DRPE allows the encoding of a primary image into complex stationary white noise using two random phase masks [1]. The random phase masks for the spatial and frequency domains, φ1(x, y) and φ2(μ, ν), respectively, are statistically independent and uniformly distributed over [0, 2π]. The encryption process of the DRPE algorithm is described by the following equation [1]:

where ℑ and ℑ−1 represent a Fourier transform and inverse Fourier transform, respectively. The decryption process for DRPE is the reverse of the encryption process shown in Eq. (1).

2.2. Photon Counting Imaging

Photon Counting Imaging (PCI) is a special class of optical imaging techniques that was designed for low-light conditions or night vision imaging systems. PCI can also be computationally simulated by changing a limited number of photons based on the expected number of incident photons in the entire scene. In the virtual PCI scheme, the probability of counting photons (pj) at an arbitrary pixel (xj) in an image can be modeled as a Poisson distribution, as follows:

where λj is the Poisson parameter that is computed by λj = Npfj, Np is the expected number of incident photons, and fj is the normalized irradiance at pixel (xj) such that , with M being the total number of pixels in the image. In the proposed compression scheme, PCI is virtually applied to the amplitude portion of the encrypted complex amplitude image fc(x, y) obtained from DRPE [19, 20].

2.3. Compression Method

As mentioned earlier, the output of the DRPE technique is very large. Thus, efficient compression techniques are crucial for storage and transmission purposes. Because the JPEG and JP2K compression techniques have superior performance compared to existing standards [27-29], these two techniques are explained briefly in this section.

2.3.1. JPEG

JPEG is a well-known standardized image compression technique. It has been widely used for several purposes, including reduction of the size of image files, storage of full-color information, and automatic error recovery [25]. This technique is the most popular compression technique and supports lossy coding. Lossy compression reduces the original image size by removing non-vital information. In the baseline mode, the image is divided into 8 × 8 blocks and each block is transformed using the discrete cosine transform (DCT). The DCT is typically applied to reduce spatial redundancy to achieve good compression performance. The transformed blocks are quantized using a uniform scalar quantization, zig-zag scanned, and eventually, entropy coded using Huffman coding. The quantization step size for each of the 64 DCT coefficients is specified in a quantization table, which remains the same for all blocks [25].

2.3.2. JPEG 2000 (JP2K)

JP2K is based on a discrete wavelet transform (DWT), scalar quantization, context modeling, arithmetic coding, and post-compression rate allocation. Preprocessing steps include tile component partitioning, DC shifting, and component transformation. During preprocessing, each slice of the original image block is partitioned into one or more disjoint rectangular regions called tiles. In terms of coding, these tile components are independent. DC shifting converts the input unsigned sample values of the image tile components into signed sample values with zero point symmetry. Thus, the relationships between the image tile components are decreased through component transformation. JP2K uses a DWT for transformation as its core coding technology. A DWT can support the transmission of multi-resolution images by using an image multi-resolution representation and decrease the correlation between pixels in the full frame to reduce the blocking effect in the codec process. After the entire image is transformed, the resulting coefficients are quantized and different levels of image quality are acquired based on the minimal precision required. The quantizer assigns different quantization levels for different sub-bands by using a scalar quantization method with a dead zone. The final step of encoding is called entropy encoding. The entropy encoder divides the wavelet sub-band into code blocks. DWT coefficients are then organized into binary bit planes. The entropy encoder uses context modeling and bit-plane arithmetic coding to encode the binary bit planes [26-33].

III. PROPOSED COMPRESSION SCHEMES

Figure 1 presents the proposed compression procedure for DRPE-PCI image authentication. By following the algorithm in Fig. 1, the input image is encrypted and then transferred to the image authentication-verification part. In addition, the output of each step is demonstrated in the table that is linked to each related section, which shows how pixel values of the input image are affected during the execution of the proposed encryption process. In the proposed method, a quantization method based on the PCI technique is applied to the amplitude (labeled as a(x, y)) portion of the encrypted image, fc(x, y) obtained from DRPE. The virtual PCI technique changes the pixel values in a(x, y) to zero or very small values. The phase portion p(x, y) of DRPE contains a real value in the range [−π, π]. Thus, p(x, y) is converted into quantized values through a uniform quantization method similar to that used in [19]. The number of bits used for the uniform quantization process determines the quantized integer range. In this study, two-bit and four-bit quantization processes are considered. To construct a phase image, a binary mask of the photon limited amplitude portion can be directly multiplied by the quantized phase values. The entry for each binary mask is unity if the corresponding photon limited amplitude portion is a nonzero value; otherwise, the entry is zero. Finally, the JPEG and JP2K compression techniques are applied to the new phase image obtained by using the binary mask and uniform quantization.

Although the amplitude portions a(x, y) of the input image is not sent during the transmission, the new phase image can still be verified in the authentication step. It should be mentioned that authentication verification rejects false input images when their peak-to-correlation energy (PCE) is smaller than 0.1. The authentication system or receiver decompresses the compressed phase images for the performance evaluation of the proposed compression schemes. Because the decrypted images from the proposed procedure are not visually recognizable, it is necessary to adopt a comparison scheme to authenticate the retrieved images. In this study, nonlinear cross-correlation (NCC) is used to compare the reference image to the input image, which has a different photon-limited amplitude mask from that of the reference image (see Fig. 1) [19, 20].

Figure 1. The conceptual scheme of the proposed method. The method is composed of two sections: the DRPE-based encrypted image compression and image authentication verification.

Our proposed image authentication schemes efficiently compress the DRPE-encrypted images, store the compressed images in the authentication system, and utilize the decompressed images for private user image verification. It should be noted that it is likely a bad idea to directly store original images as a reference in a system for verifying personal user images because these images would be prime targets for attackers or malicious system administrators. Therefore, another advantage of the proposed approach is that, even if attackers or malicious administrators invade the system, they cannot obtain the original user images because our method utilizes efficiently compressed DRPE-encrypted images, rather than storing raw images (or original images) for user image verification.

IV. NUMERICAL SIMULATIONS

The following simulations were performed on a PC with a 32-bit Windows 7 Enterprise OS, Intel(R) Core(TM) i5-2500K 3.30 GHz processor, 4 GB of RAM. The test images (256 × 256 pixels) shown in Figs. 2 and 3 are used to evaluate the proposed image authentication schemes. In the following experiments, two pair of images are used “Peppers”, “Cameraman” and “Baboon”, “Mona-Lisa”. Two input images are selected to be verified. For the true input image, “Peppers, “Baboon” are selected, and for the false input image, “Cameraman” and “Mona-Lisa” are considered. All simulations were implemented in MATLAB 2016. There is a full implementation of JP2K available in a low-level C API under a BSD 2-clause license (Version 2.1.0). We downloaded and used this source code with some minor changes based on our data types and the experiments we wished to perform.

Figure 2. Two test images used in our numerical experiments: (a) Peppers (reference image and true input image), (b) phase values after DRPE, (c) phase image obtained by the proposed method, (d) phase image after compression and decompression (JP2K technique; CR = 64). (e) Cameraman (false input image), (f) phase values after DRPE, (g) phase image obtained by the proposed method, (h) phase image after compression and decompression (JP2K technique; CR = 64).
Figure 3. Two test images used in our numerical experiments: (a) Baboon (reference image and true input image), (b) phase values after DRPE, (c) phase image obtained by the proposed method, (d) phase image after compression and decompression (JP2K technique; CR = 64). (e) Mona-Lisa (false input image), (f) phase values after DRPE, (g) phase image obtained by the proposed method, (h) phase image after compression and decompression (JP2K technique; CR = 64).

In the following simulation, the lossy compression of JPEG and JP2K are tested on phase images from the DRPE-PCI scheme with various Np and quantization bit sizes (nk = 2 and nk = 4 bits). We attempt to obtain the highest possible compression ratio without losing authentication efficiency. The compression ratio (CR) in this paper is defined as

Figures 2(b) and 3(b) show the phase portions (p(x, y)) of the encrypted Peppers image (Fig. 2(a)) and Baboon image (Fig. 3(a)) from DRPE, respectively. The phase image of Peppers and Baboon, as it has been explained previously, are shown in Figs. 2(c) and 3(c), respectively. Figures 2(d) and 3(d) show the phase image after applying compression and decompression using JP2K. Based on the properties of PCI, it is difficult to reconstruct a reference image after applying the PCI algorithm. Therefore, PCE is used for authentication between the reference image and input image, with its value calculated as follows:

where M and N are the image sizes along x and y axes, respectively, and ncc(x, y) is

where the parameter k defines the strength of the applied nonlinearity and determines the performance features of the processor.

Figures 4(a), 4(b), and 4(c) plot the PCE of non-compressed images and compressed phase images using the JPEG and JP2K methods, respectively. It has been demonstrated that PCE increases with an increase in the expected number of photons for the true class, particularly when Np > 105. As expected, PCE values are near unity when the parameter k is equal to 0.1. It can be seen in Figs. 4(d), 4(e), and 4(f) that PCE is less than 0.1 in false input images, even when increasing the total number of photons. It can be readily seen in Fig. 4 that PCE values have nearly the same trends in non-compressed and compressed images. In this case, the quantization bit size for the phase value is set to 2 bits. In addition, Fig. 5 demonstrates the results of Baboon (true input image) and Mona-Lisa (false input image) image in non-compressed images and compressed phase images using the JPEG and JP2K methods similarly to Fig. 4.

According to Figs. 6(a), 6(b) and Figs. 7(a), 7(b) (the results of 4-bit quantization), when increasing the total number of photons (Np > = 105), the PCEs of the compressed phase images using the JPEG and JP2K methods increase similar to Figs. 4(b), 4(c) and Figs. 5(b), 5(c), respectively. Additionally, one can see from Figs. 6(c), 6(d) and Figs. 7(c), 7(d) that both JPEG and JP2K yield similar PCE results in cases with a false input image. Furthermore, PCE in JP2K is marginally larger than the same value in JPEG in the case of true class input. It specifies that JP2K have less information lost comparing with the JPEG method.

Figure 4. PCE with various k and Np values: (a) without compression for the true class (Peppers). (b) applying JPEG compression for the true class (Peppers), (c) applying JP2K compression for the true class (Peppers), (d) without compression for the false class (Cameraman), (e) applying JPEG compression for the false class (Cameraman), (f) applying JP2K compression for the false class (Cameraman, CR is approximately 64 for the case of NP > = 105 ; nk = 2).
Figure 5. PCE with various k and Np values: (a) without compression for the true class (Baboon). (b) applying JPEG compression for the true class (Baboon), (c) applying JP2K compression for the true class (Baboon), (d) without compression for the false class (Mona-Lisa), (e) applying JPEG compression for the false class (Mona-Lisa), (f) applying JP2K compression for the false class (Mona-Lisa, CR is approximately 64 for the case of NP > = 105 ; nk = 2).
Figure 6. PCE with various k and Np values: (a) applying JPEG compression for the true class (Peppers), (b) applying JP2K compression for the true class (Peppers), (c) applying JPEG compression for the false class (Cameraman), (d) applying JP2K compression for the false class (Cameraman, CR is approximately 64 for the case of Np > = 105 ; nk = 4).
Figure 7. PCE with various k and Np values: (a) applying JPEG compression for the true class (Baboon), (b) applying JP2K compression for the true class (Baboon), (c) applying JPEG compression for the false class (Mona-Lisa), (d) applying JP2K compression for the false class (Mona-Lisa, CR is approximately 64 for the case of Np > = 105 ; nk = 4).

Figures 8(a) and 8(b) show the PCE changes when applying JPEG and JP2K with various CR and Np values when nk = 2. It is observed that by increasing Np, PCE is also increased in both graphs. In addition, the authentication strategy rejects false input images because PCE is far below 0.1, as shown in Figs. 8(c) and 8(d). It is worth noting that throughout the experiments, the random phase values (keys) used for encryption of the input images are assumed to be equal to those used for the reference images. Otherwise, the PCE value falls dramatically. Figure 9 shows the PCE changes when applying JPEG and JP2K with various CR in Baboon and Mona-Lisa images. The results is similar to that shown in Fig. 8.

Figure 8. PCE with various CR and Np values: (a) applying JPEG compression for the true class (Peppers), (b) applying JP2K compression for the true class (Peppers), (c) applying JPEG compression for the false class (Cameraman), (d) applying JP2K compression for the false class (Cameraman, nk = 2, k is 0.1).
Figure 9. PCE with various CR and Np values: (a) applying JPEG compression for the true class (Baboon), (b) applying JP2K compression for the true class (Baboon), (c) applying JPEG compression for the false class (Mona-Lisa), (d) applying JP2K compression for the false class (Mona-Lisa, nk = 2, k is 0.1).

Additionally, we tested the true input image with a photon-limited amplitude mask equal to that of the reference image in two cases of non-compressed (Figs. 10(a) and 11(a)) and compressed ones (Figs. 10(b) and 11(b)). As has been expected, PCE values are around 1 when the parameter k value is equal to 0. The trend in all figures is similar and shows that applying compression does not degrade the phase image significantly.

Figure 10. PCE with various k and Np values: (a) without compression for the true class (Peppers), (b) applying JP2K compression for the true class. (Reference and true input images have the same photon-limited amplitude mask, CR is approximately 64 for the case of Np > = 105 ; nk = 2).
Figure 11. PCE with various k and Np values: (a) without compression for the true class (Baboon), (b) applying JP2K compression for the true class. (Reference and true input images have the same photon-limited amplitude mask, CR is approximately 64 for the case of Np > = 105 ; nk = 2).

We are also interested in measuring the size of phase images compared to original gray-scale images (without applying any image encryption or compression techniques) to determine the compression gain (we call it true compression gain or TCG) of the proposed technique. The true compression gain can be obtained by

Figure 12 shows PCE, CR, and TCG values for nk = 1, 2, and 4 in black, blue, and red lines, respectively. TCG values are indicated by the labels on the graph. The test image was Peppers. Various CR values were evaluated. The y-axis of the graph shows PCE changes and the x-axis represents various CR values (calculated using Eq.3). We can see that 4-bit quantization has the highest PCE values, but the lowest TCG values due to the usage of 4 bits.

Figure 12. PCE after applying JP2K compression for the true input image (Peppers) with Np = 6 × 106 and various CRs, nk = 1, 2, and 4.

It can be observed that by using the compression methods the PCE is marginally similar to the non-compressed scheme. Indeed, we can claim that JP2k marginally outperforms JPEG if PCE is the main concern. Also, it worth mentioning that the proposed authentication system not only resists against unauthorized attacks but also has had the influence of decreasing the size of the encrypted image by combining compression method and PCI.

V. CONCLUSION

We aimed to provide a comparative evaluation and assessment of JPEG and JP2K compression algorithm performance on the quantized phase images from DRPE-PCI using various numbers of photons from the perspective of authentication efficiency. The proposed technique considers not only quantized phase values but also a binary mask of photon-counted amplitude values. This study demonstrated that as far as lossy compression is concerned, JP2K seems to perform reasonably well in terms of its ability to efficiently handle various CRs. The results for the JP2K method showed that phase images can be compressed several times while still allowing images to be verified using a nonlinear cross-correlation technique.

Fig 1.

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Figure 1.The conceptual scheme of the proposed method. The method is composed of two sections: the DRPE-based encrypted image compression and image authentication verification.
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 2.

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Figure 2.Two test images used in our numerical experiments: (a) Peppers (reference image and true input image), (b) phase values after DRPE, (c) phase image obtained by the proposed method, (d) phase image after compression and decompression (JP2K technique; CR = 64). (e) Cameraman (false input image), (f) phase values after DRPE, (g) phase image obtained by the proposed method, (h) phase image after compression and decompression (JP2K technique; CR = 64).
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 3.

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Figure 3.Two test images used in our numerical experiments: (a) Baboon (reference image and true input image), (b) phase values after DRPE, (c) phase image obtained by the proposed method, (d) phase image after compression and decompression (JP2K technique; CR = 64). (e) Mona-Lisa (false input image), (f) phase values after DRPE, (g) phase image obtained by the proposed method, (h) phase image after compression and decompression (JP2K technique; CR = 64).
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 4.

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Figure 4.PCE with various k and Np values: (a) without compression for the true class (Peppers). (b) applying JPEG compression for the true class (Peppers), (c) applying JP2K compression for the true class (Peppers), (d) without compression for the false class (Cameraman), (e) applying JPEG compression for the false class (Cameraman), (f) applying JP2K compression for the false class (Cameraman, CR is approximately 64 for the case of NP > = 105 ; nk = 2).
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 5.

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Figure 5.PCE with various k and Np values: (a) without compression for the true class (Baboon). (b) applying JPEG compression for the true class (Baboon), (c) applying JP2K compression for the true class (Baboon), (d) without compression for the false class (Mona-Lisa), (e) applying JPEG compression for the false class (Mona-Lisa), (f) applying JP2K compression for the false class (Mona-Lisa, CR is approximately 64 for the case of NP > = 105 ; nk = 2).
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 6.

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Figure 6.PCE with various k and Np values: (a) applying JPEG compression for the true class (Peppers), (b) applying JP2K compression for the true class (Peppers), (c) applying JPEG compression for the false class (Cameraman), (d) applying JP2K compression for the false class (Cameraman, CR is approximately 64 for the case of Np > = 105 ; nk = 4).
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 7.

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Figure 7.PCE with various k and Np values: (a) applying JPEG compression for the true class (Baboon), (b) applying JP2K compression for the true class (Baboon), (c) applying JPEG compression for the false class (Mona-Lisa), (d) applying JP2K compression for the false class (Mona-Lisa, CR is approximately 64 for the case of Np > = 105 ; nk = 4).
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 8.

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Figure 8.PCE with various CR and Np values: (a) applying JPEG compression for the true class (Peppers), (b) applying JP2K compression for the true class (Peppers), (c) applying JPEG compression for the false class (Cameraman), (d) applying JP2K compression for the false class (Cameraman, nk = 2, k is 0.1).
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 9.

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Figure 9.PCE with various CR and Np values: (a) applying JPEG compression for the true class (Baboon), (b) applying JP2K compression for the true class (Baboon), (c) applying JPEG compression for the false class (Mona-Lisa), (d) applying JP2K compression for the false class (Mona-Lisa, nk = 2, k is 0.1).
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 10.

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Figure 10.PCE with various k and Np values: (a) without compression for the true class (Peppers), (b) applying JP2K compression for the true class. (Reference and true input images have the same photon-limited amplitude mask, CR is approximately 64 for the case of Np > = 105 ; nk = 2).
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 11.

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Figure 11.PCE with various k and Np values: (a) without compression for the true class (Baboon), (b) applying JP2K compression for the true class. (Reference and true input images have the same photon-limited amplitude mask, CR is approximately 64 for the case of Np > = 105 ; nk = 2).
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

Fig 12.

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Figure 12.PCE after applying JP2K compression for the true input image (Peppers) with Np = 6 × 106 and various CRs, nk = 1, 2, and 4.
Current Optics and Photonics 2019; 3: 390-400https://doi.org/10.3807/COPP.2019.3.5.390

References

  1. P. Refregier, and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett. 20, 767-769 (1995).
    CrossRef
  2. I. Moon, F. Yi, Y. H. Lee, and B. Javidi, "Avalanche and bit independence characteristics of double random phase encoding in the Fourier and Fresnel domains," J. Opt. Soc. Am. A 31, 1104-1111 (2014).
    CrossRef
  3. R. Tao, Y. Xin, and Y. Wang, "Double image encryption based on random phase encoding in the fractional Fourier domain," Opt. Express 15, 16067-16079 (2007).
    CrossRef
  4. Z. Liu, Y. Zhang, S. Li, W. Liu, W. Liu, Y. Wang, and S. Liu, "Double image encryption scheme by using random phase encoding and pixel exchanging in the gyrator transform domains," Opt. Lasers Technol. 47, 152-158 (2013).
    CrossRef
  5. G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett. 25, 887-889 (2000).
    CrossRef
  6. W. Chen, "Multiple-wavelength double random phase encoding with CCD-plane sparse-phase multiplexing for optical information verification," Appl. Opt. 54, 10711-10716 (2015).
    CrossRef
  7. L. Akter, I. Moon, and G. Kwon, "Double random phase encoding with a Poisson-multinomial distribution for efficient colorful image authentication," Multimedia Tools Appl 78, 14613-14632 (2019).
    CrossRef
  8. X. Wang, W. Chen, and X. Chen, "Optical information authentication using compressed double-random-phase-encoded images and quick-response codes," Opt. Express 23, 6239-6253 (2015).
    CrossRef
  9. Z. Leihong, Y. Xiao, Z. Dawei, and C. Jian, "Research on multiple-image encryption scheme based on Fourier transform and ghost imaging algorithm," Curr. Opt. Photon. 2, 315-323 (2018).
  10. J. Chen, N. Bao, L. Y. Zhang, and Z. Zhu, "Optical information authentication using optical encryption and sparsity constraint," Opt. Lasers Eng. 107, 352-363 (2018).
    CrossRef
  11. Z. Shao, Y. Shang, Q. Tong, H. Ding, X. Zhao, and X. Fu, "Multiple color image encryption and authentication based on phase retrieval and partial decryption in quaternion gyrator domain," Multimed. Tools Appl. 77, 25821-25840 (2018).
    CrossRef
  12. G. Luan, A. Li, D. Zhang, and D. Wang, "Asymmetric image encryption and authentication based on equal modulus decomposition in the Fresnel transform domain," IEEE Photon. J. 11, 6900207 (2019).
  13. S. Liu, B. M. Hennelly, C. Guo, and J. T. Sheridan, "Robustness of double random phase encoding spread-space spread-spectrum watermarking technique," Sig. Process. 109, 345-361 (2015).
    CrossRef
  14. S. Gholami, K. Jaferzadeh, S. Shin, and I. Moon, "An efficient image-based verification scheme by fusion of double random phase encoding and dynamic chaotic map," Multimed. Tools Appl. 78, 25001-25018 (2019).
    CrossRef
  15. A. V. Zea, J. F. Barrera, and R. Torroba, "Cryptographic salting for security enhancement of double random phase encryption schemes," J. Opt. 19, 105703 (2017).
    CrossRef
  16. X. Liu, J. Wu, W. He, M. Liao, C. Zhang, and X. Peng, "Vulnerability to ciphertext-only attack of optical encryption scheme based on double random phase encoding," Opt. Express 23, 18955-18968 (2015).
    CrossRef
  17. Y. Frauel, A. Castro, T. Naughton, and B. Javidi, "Resistance of the double random phase encryption against various attacks," Opt. Express 15, 10253-10265 (2007).
    CrossRef
  18. F. Yi, I. Moon, and Y. H. Lee, "A Multispectral photoncounting double random phase encoding scheme for image authentication," Sensors 14, 8877-8894 (2014).
    CrossRef
  19. I. Moon, F. Yi, M. Han, and J. Lee, "Efficient asymmetric image authentication schemes based on photon countingdouble random phase encoding and RSA algorithms," Appl. Opt. 55, 4328-4335 (2016).
    CrossRef
  20. E. Pérez-Cabré, M. Cho, and B. Javidi, "Information authentication using photon-counting double-random-phase encrypted images," Opt. Lett 36, 22-24 (2011).
    CrossRef
  21. E. Pérez-Cabré, H. C. Abril, M. S. Millán, and B. Javidi, "Photon-counting double-random-phase encoding for secure image verification and retrieval," J. Opt. 14, 094001 (2012).
    CrossRef
  22. F. Yi, Y. Jeoung, and I. Moon, "Three-dimensional image authentication scheme using sparse phase information in double random phase encoded integral imaging," Appl. Opt. 56, 4381-4387 (2017).
    CrossRef
  23. S. K. Rajput, D. Kumar, and N. K. Nishchal, "Photon counting imaging and phase mask multiplexing for multiple images authentication and digital hologram security," Appl. Opt 54, 1657-1666 (2015).
    CrossRef
  24. J. Lee, N. Sultana, F. Yi, and I. Moon, "Avalanche and bit independence properties of photon-counting double random phase encoding in gyrator domain," Curr. Opt. Photon. 2, 368-377 (2018).
  25. Y. Wiseman. Encyclopedia of Information Science and Technology, 3rd ed, Khosrow-Pour D. B. A. M. (IGI Global, PA 2015).
  26. P. Schelkens, A. Skodras, and T. Ebrahimi. The JPEG 2000 Suite (John Wiley & Sons, NY 2009).
  27. D. Santa-Cruz, T. Ebrahimi, J. Askelöf, M. Larsson, and C. Christopoulos, "JPEG 2000 still image coding versus other standards," Proc. SPIE 4115, 446-454 (2000).
  28. A. N. Skodras, C. A. Christopoulos, and T. Ebrahimi, "JPEG2000: the upcoming still image compression standard," Pattern Recogn. Lett. 22, 1337-1345 (2001).
    CrossRef
  29. D. Santa-Cruz, R. Grosbois, and T. Ebrahimi, "JPEG 2000 performance evaluation and assessment," Signal Process. Image Commun. 17, 113-130 (2002).
    CrossRef
  30. S. N. Sivanandam, A. Pasumpon, and P. Rani, "Lossy still image compression standards: JPEG and JPEG2000 - a survey," Int. J. Comput., Internet Manage. 17, 69-84 (2009).
  31. A. Skodras, C. Christopoulos, and T. Ebrahimi, "The JPEG 2000 still image compression standard," IEEE Signal Process. Mag. 18, 36-58 (2001).
    CrossRef
  32. G. K. Wallace, "The JPEG still picture compression standard," IEEE Trans. Consum. Electron. 38, xviii-xxxiv (1992).
  33. K. Jaferzadeh, S. Gholami, and I. Moon, "Lossless and lossy compression of quantitative phase images of red blood cells obtained by digital holographic imaging," Appl. Opt. 55, 10409-10416 (2016).
    CrossRef
  34. P. Li, and K. T. Lo, "A content-adaptive joint image compression and encryption scheme," IEEE Trans. Multimedia 20, 1960-1972 (2018).
    CrossRef
  35. V. Itier, P. Puteaux, and W. Puech, "Recompression of JPEG crypto-compressed images without a key," IEEE Trans. Circuits Syst. Video Technol.. to be published
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