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In this paper, a new method of encrypting a color image based on θ modulation is proposed by using the tricolor principle and computer-generated hologram (CGH) technology. The encryption process includes the θ-modulated three primary color components and the coding of computer-generated hologram, which is implemented in a Fresnel diffraction and spatial filtering system. Firstly, the color image modulated by the first random phase key is divided into three encryption channels by red laser, green laser, blue laser, and tricolor filters. Each channel is introduced by a transmissive amplitude-type sinusoidal grating with different directions, which is used to separate the three primary color components in the spatial spectrum plane. Secondly, the modulation results of tricolor components are superimposed together to form a compound image, and the phase truncation of the superposition result is performed to achieve the asymmetric encryption. Finally, the amplitude of the compound image is modulated by the second random phase key and is encoded into a binary real-value gray-color CGH by Roman-type coding method. Therefore, the gray-color information of the original image is completely hidden in the encrypted CGH, which is more general and deceptive in the storage and transmission process. Decryption is an inverse process of the encryption. Firstly, the encrypted CGH is placed on the input plane of the spatial filtering and Fresnel diffraction system. Secondly, the demodulation of CGH phase key and the spatial filtering based on optical filter are performed. Finally, the color plaintext image is obtained by using the correct Fresnel diffraction. The simulation results show the validity and feasibility of the proposed method. In addition, the anti-noise attack and anti-shearing attack performance of this color image encryption method are investigated. Compared with results from the three presented methods reported in the literature, our investigated results demonstrate that this method has good robustness to noise attack and shearing attack, and has obvious advantages when the attack noise density is larger. Due to the characteristics of high security and anti-noise, we believe that this color image encryption method promises to have important applications in the information transmission and multi-user authentication.
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Keywords:
- color image encryption /
- computer generated holography /
- θ modulation /
- asymmetric encryption
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图 1 彩色图像的菲涅尔衍射和θ调制系统
Fig. 1. Fresnel diffraction and θ modulation system for color image.
图 3 彩色图像加密的计算全息编码流程图
Fig. 3. Flow chart of color image encryption by computer generated hologram.
图 4 (a)加密结果图; (b)加密计算全息图
Fig. 4. (a) The encrypted image; (b) the encrypted computer generated hologram.
图 7 密钥错误时的解密结果 (a)相位密钥
$p{_2}'$ 错误; (b)菲涅耳衍射距离错误(${z_0} = 0.35\;{\rm{m}}$ )Fig. 7. Decrypted results with wrong keys: (a) Wrong key
$p{_2}'$ ; (b) wrong key Fresnel diffraction distance with${z_0} = 0.35\;{\rm{m}}$ .
图 8 解密彩色图像三基色分量 (a)红色分量; (b)绿色分量; (c)蓝色分量; (a'), (b'), (c')原始图像三基色分量
Fig. 8. Tricolor components of color image: (a) Red component; (b) green component; (c) blue component; (a'), (b'), (c') red, green and blue components of original color image.
图 9 不同程度的剪切攻击和剪切攻击后的恢复图像
Fig. 9. Shear attack of different levels and image restoration after shear attack.
图 10 (a)—(d)分别加入密度0.1, 0.3, 0.5和1.0的椒盐噪声后的加密图像; (a')—(d')相应的解密结果图
Fig. 10. (a)－(d) Encrypted images with salt and pepper noises with density of 0.1, 0.3, 0.5 1.0; (a')－(d') corresponding decryption results.
表 1 剪切攻击处理
Table 1. Treatment of shear attack.
剪切攻击 1/32 1/16 1/8 1/4 评价标准 CC 0.858 0.803 0.765 0.668 IF 0.873 0.811 0.750 0.671 
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[1] Refregier P, Javidi B 1995 Opt. Lett. 20 767
Google Scholar
[2] Liu Z, Chen H, Blondel W, Shen Z, Liu S 2018 Opt. Lasers Eng. 105 1
[3] Chen L, Zhao D 2006 Opt. Express 14 8552
Google Scholar
[4] Borujeni S E 2013 J. Telecommun. Syst. 52 525
[5] Shi Y S, Li T, Wang Y L, Gao Q K, Zhang S G, Li H F 2013 Opt. Lett. 38 1425
Google Scholar
[6] Yang N, Gao Q K, Shi Y S 2018 Opt. Express 26 31995
Google Scholar
[7] Su Y, Tang C, Li B, Chen X, Xu W, Cai Y 2017 Appl. Opt. 56 498
Google Scholar
[8] Liu Z, Dai J, Sun X, Liu S 2010 Opt. Lasers Eng. 48 800
Google Scholar
[9] Abuturab M R 2012 Appl. Opt. 51 3006
Google Scholar
[10] Sui L S, Xin M T, Tian A L, Jin H 2013 Opt. Lasers Eng. 51 1297
Google Scholar
[11] 肖迪, 谢沂均 2013 物理学报 62 240508
Google Scholar
Xiao D, Xie Y J 2013 Acta Phys. Sin. 62 240508
Google Scholar
[12] 秦怡, 郑长波 2012 光子学报 41 326
Qin Y, Zheng C B 2012 Acta Phot. Sin. 41 326
[13] Yuan Q P, Yang X P, Gao L J, Zhai H C 2009 Optoelectron. Lett. 5 147
Google Scholar
[14] Faraoun K M 2014 Opt. Laser Technol. 64 145
Google Scholar
[15] Liu Z, Guo C, Tan J, Liu W, Wu J, Wu Q, Pan L, Liu S 2015 Opt. Lasers Eng. 68 87
Google Scholar
[16] 高丽娟, 杨晓苹, 李智磊, 王晓雷, 翟宏琛, 王明伟 2009 物理学报 58 1053
Google Scholar
Gao L J, Yang X P, Li Z L, Wang X L, Zhai H C, Wang M W 2009 Acta Phys. Sin. 58 1053
Google Scholar
[17] 高丽娟, 杨晓苹, 李智磊, 王晓雷, 翟宏琛, 王明伟 2009 物理学报 58 1662
Google Scholar
Yang X P, Gao L J, Wang X L, Zhai H C, Wang M W 2009 Acta Phys. Sin. 58 1662
Google Scholar
[18] Zhou N R, Wang Y X, Gong L H, He H, Wu J H 2011 Opt. Commun. 284 2789
Google Scholar
[19] Wang X, Zhao D 2012 Opt. Express 20 11994
Google Scholar
[20] 丁湘陵, 袁倩, 张乐冰 2014 激光技术 38 561
Google Scholar
Ding X L, Yuan Q, Zhang L B 2014 Laser Technol. 38 561
Google Scholar
[21] Xi S X, Wang X L, Song L P, Zhu Z Q, Yu N N, Wang H Y 2017 Opt. Express 25 8212
Google Scholar
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