双随机位相编码技术—仿射密码的光学实现
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摘要
在回顾双随机位相编码技术的发展历程并总结已有双随机位相编码方案的基础上，本文对这项技术能够实现光学信息保密的密码学原理进行了新的探索，并对其安全性等问题做了较详细的分析讨论，同时就某些具体的应用提出了切实可行的方案。主要研究内容和结论如下：
提出双随机位相编码技术对光学图像的加密应属于密码学上的仿射密码，它实际上是仿射密码在光学上的一种实现；其信息保密功能源于充分利用了扩散和混淆技术，将明文与密文、密钥与密文之间的对应关系复杂化，从而达到置乱明文的目的：系统地分析了基于双随机位相编码技术的密码体制具备的五个要素以及该密码体制的理论安全性和实际安全性；根据光学成像公式，说明了基于光学4f系统和菲涅耳衍射域的双随机位相编码技术中，原始图像与加密图像之间的仿射映射关系；应用仿射密码模型和随机过程相关理论讨论了加密图像的统计特性，并通过数值模拟验证了加密图像可看作是高斯型白噪声随机过程；对基于双随机位相编码技术的密码体制在密码学上具有的特点进行了总结。
概述了二维离散多重分数傅里叶变换的光学图像加密技术，指出其对图像的加密原理依然是属于仿射密码范畴，并推导了基于标准加权类分数傅里叶变换的双随机位相编码过程的仿射映射表达式；对基于光波传播的二次位相系统
The development of the double random phase encryption technique has been reviewed in this doctoral dissertation. Based on the summary of the existing schemes of double random phase encryption, a new research for the cryptology explanation of its ability to realize maintaining secrecy of optical information has been implemented. Some detailed analysis and discussion have been made for the problems such as security of this technique. Operable schemes have been proposed for some practical applications. The main contents and results have been summarized as follows:
It is put forward that the encryption mechanism of optical images by the double random phase encryption technique can be categorized to the affine cipher on the cryptology and this technique can be regarded as an optical realization of the affine cipher. The secrecy comes from making best of diffusion and confusion techniques. The relationships between the plaintext and the ciphertext, the plaintext and the key have been complicated for the purpose of disordering the plaintext. Five main factors of the cryptosystem based on the double random phase encryption have been analyzed systematically as well as the theoretical security and practical security of that cryptosystem. According to the equation of imaging, the affine map relationship between the original image and encrypted image has been illustrated in the technique based on the optical 4f system and Fresnel diffraction domain. The statistical property of the encrypted image has been discussed by utilizing the model of affine cipher and the related theory of stochastic process. It has been verified by numerical simulations that the encrypted image may be regarded as stochastic white Gaussian noise. The characteristics on cryptology of the cryptosystem based on the double random phase encryption have been summarized.
提出双随机位相编码技术对光学图像的加密应属于密码学上的仿射密码，它实际上是仿射密码在光学上的一种实现；其信息保密功能源于充分利用了扩散和混淆技术，将明文与密文、密钥与密文之间的对应关系复杂化，从而达到置乱明文的目的：系统地分析了基于双随机位相编码技术的密码体制具备的五个要素以及该密码体制的理论安全性和实际安全性；根据光学成像公式，说明了基于光学4f系统和菲涅耳衍射域的双随机位相编码技术中，原始图像与加密图像之间的仿射映射关系；应用仿射密码模型和随机过程相关理论讨论了加密图像的统计特性，并通过数值模拟验证了加密图像可看作是高斯型白噪声随机过程；对基于双随机位相编码技术的密码体制在密码学上具有的特点进行了总结。
概述了二维离散多重分数傅里叶变换的光学图像加密技术，指出其对图像的加密原理依然是属于仿射密码范畴，并推导了基于标准加权类分数傅里叶变换的双随机位相编码过程的仿射映射表达式；对基于光波传播的二次位相系统
The development of the double random phase encryption technique has been reviewed in this doctoral dissertation. Based on the summary of the existing schemes of double random phase encryption, a new research for the cryptology explanation of its ability to realize maintaining secrecy of optical information has been implemented. Some detailed analysis and discussion have been made for the problems such as security of this technique. Operable schemes have been proposed for some practical applications. The main contents and results have been summarized as follows:
It is put forward that the encryption mechanism of optical images by the double random phase encryption technique can be categorized to the affine cipher on the cryptology and this technique can be regarded as an optical realization of the affine cipher. The secrecy comes from making best of diffusion and confusion techniques. The relationships between the plaintext and the ciphertext, the plaintext and the key have been complicated for the purpose of disordering the plaintext. Five main factors of the cryptosystem based on the double random phase encryption have been analyzed systematically as well as the theoretical security and practical security of that cryptosystem. According to the equation of imaging, the affine map relationship between the original image and encrypted image has been illustrated in the technique based on the optical 4f system and Fresnel diffraction domain. The statistical property of the encrypted image has been discussed by utilizing the model of affine cipher and the related theory of stochastic process. It has been verified by numerical simulations that the encrypted image may be regarded as stochastic white Gaussian noise. The characteristics on cryptology of the cryptosystem based on the double random phase encryption have been summarized.
引文
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11. B. Javidi, A. Sergent, G. S. Zhang, L. Guibert. Fault tolerance properties of a double phase encoding encryption technique, Opt. Eng. 1997, 36(4): 992-998
12. L. G.. Neto, Y. Sheng. Optical implementation of image encryption using random phase encoding. Opt. Eng. 1996, 35(9): 2459-2463
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14. J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim. Optical image encryption based on XOR operations. Opt. Eng. 1999, 38(1): 47-54
15. F. Goudail, B. Javidi, P. Refregier. Influence of a perturbation in a double phase-encoding system. J. Opt. Soc. Am. A. 1998, 15 (10): 2629-2637
16. B. Wang, C. C. Sun, W. C. Su, E. T. Chiou. Shift-tolerance property of an optical double-random phase-encoding encryption system. Appl. Opt. 2000, 39 (26): 4788-4793
17. B. Wang, C. C. Sun. Enhancement of signal-to-noise ratio of a double random phase encoding encryption system. Opt. Eng. 2001, 40(8):1502-1506
18. B. Wang, J. Y. Chang, W. C. Su, C. C. Sun. Optical security using a random binary phase code in volume holograms. Opt. Eng. 2001, 43(9): 2048-2052
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