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Inkyu Moon: Provided feasible methods and algorithms to authenticate color images by using multispectral photon counting imaging and double random phase encoding techniques. He analyzed the authentication results and the demosaicing approach with better performance. He applied nonlinear correlation metrics to illustrate that the reference color image can be efficiently verified with the sparse DRPE data. He collaborated with the other authors to analyze the experimental results and prepare this manuscript.

Yeon H. Lee: Participated in the discussions about the feasibility of solution methods for the problems that appeared during collaborative research on the proposed method. He has also collaborated with the other authors to analyze the experimental results and prepare this manuscript.

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

In this paper, we propose a new method for color image-based authentication that combines multispectral photon-counting imaging (MPCI) and double random phase encoding (DRPE) schemes. The sparsely distributed information from MPCI and the stationary white noise signal from DRPE make intruder attacks difficult. In this authentication method, the original multispectral RGB color image is down-sampled into a Bayer image. The three types of color samples (red, green and blue color) in the Bayer image are encrypted with DRPE and the amplitude part of the resulting image is photon counted. The corresponding phase information that has nonzero amplitude after photon counting is then kept for decryption. Experimental results show that the retrieved images from the proposed method do not visually resemble their original counterparts. Nevertheless, the original color image can be efficiently verified with statistical nonlinear correlations. Our experimental results also show that different interpolation algorithms applied to Bayer images result in different verification effects for multispectral RGB color images.

Double random phase encoding (DRPE) and its applications have been extensively studied for image encryption, information hiding and watermarking [

In this study, we show that the integration of MPCI and DRPE can be used for the authentication of multispectral images. In this procedure, the three color samples (pixels of red, green, and blue color [

This paper is organized as follows: in Section 2, we describe double random phase encryption. In Section 3, the concept of multispectral photon-counting imaging techniques is explained. In Section 4, we present the procedure for the combination of MPCI and DRPE. Section 5 includes the experimental results. We conclude the paper with Section 6.

Optical and digital information security systems [^{−1} denote a two-dimensional Fourier transform and an inverse Fourier transform, respectively. For decryption, the procedure is reversed. The DRPE schematic in the Fourier domain is given in

Photon-counting imaging, a special class of optical imaging techniques, has been successfully applied in fields such as 3D imaging and 2D/3D object recognition in photon-limited situations [_{w}_{w}_{w}_{B,w}_{p}_{p}_{B,w}_{B}_{ph}_{w}

Though DRPE on its own is vulnerable to chosen-plaintext and chosen-cyphertext attacks [

The input multispectral color image _{B}_{B}_{B}_{B}_{B}_{B}

In this paper, all of the results are obtained from numerical simulation using virtual optics on Matlab (R2010a) that is executed on a 32-bits window 7 OS computer which includes an Intel Core i5-2500k processor of 3.3 GHz and the RAM is 4 GB. The quantization level is 256 for the original and output image. Also, all of the processing data are digitally recorded on computer without optical configurations. Since the decrypted images from the proposed procedure are not visually recognizable with a limited number of photons, it is necessary to adopt some comparison scheme to authenticate the retrieved image. In this paper, nonlinear cross-correlation [_{D}_{F}_{i},y_{j}

In ^{4} is the watershed for the number of photons to achieve a better nonlinear correlation plane with sharp peak. It is verified in the following simulation that the information authentication for true class image can also be realized for Bayer image when the number of photons is equal to 10^{4}.

In this simulation, three standard multispectral RGB color images taken from Kodak true color image data sets were used and are shown in

The down-sampled Bayer images were encrypted with DRPE and then the three color samples of amplitude image in the Bayer image encrypted by DRPE were photon-counted individually to obtain the sparse encrypted image. In order to evaluate the proposed authentication method's performance, the sparse encrypted image was decrypted in Bayer format and corresponding decrypted multispectral color image was obtained from Malvar's demosaicing approach [^{4} (3.8% of total image pixels). Note from

^{3} and 10^{4} for true-class Bayer and demoasiced image, respectively. In this paper, all the maximum nonlinear cross-correlation values are an average of 50 numerical simulations and are normalized as a whole.

The simulation results, presented in

^{4}, the image verification can be achieved between referennce and decrypted Bayer images because the maximum correlation values between the true and false images start to be especially distinct. However, the number of photons have to be at least 10^{5} so as to succesfully realize information authentication for multispectral demosaiced images. This may be explained that the demasicing technique can not exactly recover the missing color component in Bayer image. In ^{4} and 10^{5} are the watershed number of photons for Bayer and multispectral demosaiced images in terms of correct authentication. Here, we recommend that it is better to make the photon number more than 10^{4} for Bayer image authentication in the real situation since the energy of correlation peak in

Since the multispectral RGB color image obtained from the decrypted Bayer image is related to demosaicing (interpolation) algorithms, different demosaicing approaches will change RGB quality and interact with the nonlinear cross-correlation values. In ^{5}, the advantage is especially striking. In this study, we adopted Malvar's method as the demosaicing scheme to convert Bayer images into multispectral RGB color images. Malvar's demosaicing algorithm is a gradient-corrected linear interploation technique that can convert a Bayer-format image into a true-color (RGB) image for each pixel format by estimating the missing pixel values on the Bayer image with the help of interpolated current pixel values and the calculated gradient information. The combination of gradient values and linear interploation in Malvar's method can improve the image quality as compared to other interpolation algorithms [

The proposed procedure that integrate MPCI and DRPE can be robust even when the encrypted image has been occluded. When some parts of the encrypted image obtained from the procedure have been changed or removed, the image can still be authenticated with a nonlinear cross-correlation technique. ^{5} between reference color (Lena color image) image and the decrypted true-class color (Lena color image) image that is derived from the encrypted image, but where some portion of the pixels have been occluded and changed.Even when about 80% of the original pixel values in the encrypted images are occluded, the input images can still be authenticated, since the corresponding correlation values are larger than those from false-class images, as shown in

It is clear that an ideal image encryption scheme should be sensitive to its key, meaning that when a small number of key values are changed, the decrypted image should be totally different from an image decrypted using the correct key. The nonlinear cross-correlation values between the reference Bayer image and the decrypted Bayer image with the key values partially changed are calculated to be around 0.039 with the number of photons equal 10^{5} and parameter k = 0.3, even when the proportion of changed key values is varied from 1% to 100%. In this numerical simulation, the location of the partically changed pixel in the key is random and the values are set to be zero. These results (very small maximum nonlinear cross-correlation values) indicate that the image can not be verified with an incorrect phase key, even though the incorrect and correct phase keys share many common values. This result guarantees the security of the proposed method against brute-force attacks.

In this paper, we have proposed a combination of multispectral photon-counting imaging (MPCI) and double random phase encoding (DRPE) for multispectral image authentication. Experimental results showed that the decrypted images from the proposed combination cannot be visually recognized with a limited number of photons and thus can provide an additional layer of security. Nevertheless, the primary image can be authenticated with the decrypted image using nonlinear cross-correlation metrics based on either a Bayer or a RGB color image. The procedure can also achieve better bandwidth reduction since the encrypted image is sparsely distributed. In addition, the proposed system can be robust even with partial encryption and under brute-force attacks. When the encrypted images are partially occluded or changed, correct authentication results can be achieved. However, if even a few values are altered in the correct phase-decryption key, image verification will fail. Experimental results also reveal that Malvar's demosaicing algorithm can obtain better authentication results than other methods based on multispectral RGB color images.

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (NRF-2013R1A2A2A05005687). We thank Inbarasan Muniraj for his help with experiments.

The authors declare no conflict of interest.

Schematic diagram of the DRPE system (

The schematic diagram of MPCI.

Flow diagram of the proposed color image authentication method.

Illustration of down-sampling, image splitting and integration. (

PCE values with various

Reference multispectral images and the correspoding down-sampled Bayer images. (

(^{4}).

(

Non-authorized (false class) multispectral images and the correspoding down-sampled Bayer images (

(

(^{3}, 10^{4} and 10^{5} respectively; (^{3}, 10^{4} and 10^{5} respectively; (^{4}, 10^{5} and 10^{6} respectively; (^{4}, 10^{5} and 10^{6} respectively. (k = 0.3).

Maximum nonlinear cross-correlation values with different demosaicing techniques using Lena color image. [Error bars represent ±1 standard deviation of the 50 times measurement, (k = 0.3).

(^{5}).