基于分数阶Fourier变换的图像加密算法研究及实现
|
摘要
随着计算机网络和通信技术的发展,多媒体信息的应用越来越广泛,而由于数字信息容易被盗取和篡改,对数字信息的加密和保护成为了信息安全的重要课题。与此同时,分数阶Fourier变换是现阶段光学、信息学的研究热门,将分数阶Fourier变换应用到图像处理中也是一个重要的研究方向。论文重点研究了分数阶Fourier变换的基本理论和性质,和它在信号处理、图像分析和图像加密中的应用,并对现代图像加密技术中应用较为广泛的混沌加密技术做了研究,分别分析了混沌置乱加密技术和变换域加密技术的特点,并针对现有加密技术的不足,提出了结合混沌置乱和分数阶Fourier变换的多重图像加密算法。
本文对基于分数阶Fourier变换的单、多分量chirp信号检测、参数估计及分离,含噪LMF信号滤波进行了分析讨论,仿真结果表明分数阶Fourier变换相较于Wigner-Ville分布和短时Fourier变换而言能够更好的分离和检测多分量chirp信号,对于含有加性噪声的单分量chirp信号,在信噪比较低时依然有较好的滤波效果；根据分数阶Fourier变换系数对阶数的敏感性和多样性,提出了基于分数阶Fourier变换的图像加密算法并仿真,结果表明该算法拥有较好的鲁棒性,能更好的抵抗统计特性攻击；在对混沌置乱图像加密技术做了一些研究后,提出基于混沌置乱的加密算法并仿真,该算法拥有较大的密钥空间,安全性好。通过对混沌置乱图像加密算法和分数阶Fourier图像加密算法进行仿真实验和分析对比,确定了优化加密算法的目的和思路,提出了改进的图像加密算法。仿真结果显示密文与明文相比灰度直方图更加平坦,均方误差与密钥极为敏感,相关性极低；算法具有较强的抗遮盖剪裁,抗噪声性能。最后,在DSP6711的平台上实现了加密算法,加密图像完全掩盖了明文的空频域信息。
As the rapid development of computer networks and communication technology, multimedia information is more widely used. Because digital information is easy to be stolen and tampered, the encryption and protection of digital information has become an important issue in information security field. Meanwhile, fractional Fourier transform is hot research topic both in optics and informatics, it is also a research direction in image processing. This paper studied the nature of fractional Fourier transform and its applications in signal processing, image analysis and image encryption. The application in modern image encryption of chaotic technology was studied. An image encryption algorithm was proposed after the analyzing the characteristics of the chaotic scrambling encryption technology and transform domain encryption technology.
This paper also discussed the detection, parameter estimation and separation about the single and multi-component chirp signal, and the filtering of LMF signal with noise based on fractional Fourier transform. Simulation results demonstrated that fractional Fourier transform can separate the multi-component chirp signal well compared with Wigner-Ville or Short-time Fourier transform, also, the single component chrip signal with additive noise still has a better filtering effect even though the SNR was low. This paper proposed and simulated an image encryption algorithm based on fractional Fourier transform by using its coefficient's sensitivity and diversity to initial value. This algorithm has good robustness and better ability to against statistical properties'attacks. An encryption algorithm based on chaotic scrambling was proposed and simulated, the algorithm has larger key space and better safty, but it seldom prevent clipping or noise, its robustness is poor in addition. An improved image encryption algorithm was present after analyzing the results of chaotic scrambling image encryption algorithm and fractional Fourier image encryption algorithm simulation experiment in this paper. The result show that the histogram of cryptograph became more flatter, the MSE and relativity was sensitived to the key. At last, the paper realized encryption algorithm on DSK6711. The result shows that the space and frequency information of original image were hidden perfectly.
本文对基于分数阶Fourier变换的单、多分量chirp信号检测、参数估计及分离,含噪LMF信号滤波进行了分析讨论,仿真结果表明分数阶Fourier变换相较于Wigner-Ville分布和短时Fourier变换而言能够更好的分离和检测多分量chirp信号,对于含有加性噪声的单分量chirp信号,在信噪比较低时依然有较好的滤波效果；根据分数阶Fourier变换系数对阶数的敏感性和多样性,提出了基于分数阶Fourier变换的图像加密算法并仿真,结果表明该算法拥有较好的鲁棒性,能更好的抵抗统计特性攻击；在对混沌置乱图像加密技术做了一些研究后,提出基于混沌置乱的加密算法并仿真,该算法拥有较大的密钥空间,安全性好。通过对混沌置乱图像加密算法和分数阶Fourier图像加密算法进行仿真实验和分析对比,确定了优化加密算法的目的和思路,提出了改进的图像加密算法。仿真结果显示密文与明文相比灰度直方图更加平坦,均方误差与密钥极为敏感,相关性极低；算法具有较强的抗遮盖剪裁,抗噪声性能。最后,在DSP6711的平台上实现了加密算法,加密图像完全掩盖了明文的空频域信息。
As the rapid development of computer networks and communication technology, multimedia information is more widely used. Because digital information is easy to be stolen and tampered, the encryption and protection of digital information has become an important issue in information security field. Meanwhile, fractional Fourier transform is hot research topic both in optics and informatics, it is also a research direction in image processing. This paper studied the nature of fractional Fourier transform and its applications in signal processing, image analysis and image encryption. The application in modern image encryption of chaotic technology was studied. An image encryption algorithm was proposed after the analyzing the characteristics of the chaotic scrambling encryption technology and transform domain encryption technology.
This paper also discussed the detection, parameter estimation and separation about the single and multi-component chirp signal, and the filtering of LMF signal with noise based on fractional Fourier transform. Simulation results demonstrated that fractional Fourier transform can separate the multi-component chirp signal well compared with Wigner-Ville or Short-time Fourier transform, also, the single component chrip signal with additive noise still has a better filtering effect even though the SNR was low. This paper proposed and simulated an image encryption algorithm based on fractional Fourier transform by using its coefficient's sensitivity and diversity to initial value. This algorithm has good robustness and better ability to against statistical properties'attacks. An encryption algorithm based on chaotic scrambling was proposed and simulated, the algorithm has larger key space and better safty, but it seldom prevent clipping or noise, its robustness is poor in addition. An improved image encryption algorithm was present after analyzing the results of chaotic scrambling image encryption algorithm and fractional Fourier image encryption algorithm simulation experiment in this paper. The result show that the histogram of cryptograph became more flatter, the MSE and relativity was sensitived to the key. At last, the paper realized encryption algorithm on DSK6711. The result shows that the space and frequency information of original image were hidden perfectly.
引文
[1]B.Furht and D.Kirovsk, editors. Multimedia Security Handbook[M]. CRC Press, Boca Raton, Florida,2004.
[2]Adress Uhi, Adress Pommer. Image and Video Encryption[M].Springer,1 st ed,2004.
[3]王军.博奇型计算全息在加密图像抗裁剪攻击中应用研究[D].北京：北京大学,2009.
[4]S.T.Liu, B.H.Zhu. Optical imgage encrption based on the generalized fractional convolution operation[J].Opt. Commun.2001,195:371-381.
[5]王长涛.复数阶分数傅里叶变换的实现[D].成都：四川大学,2002.
[6]曾阳素.分数傅里叶光学的应用研究[D].成都：四川大学,2002.
[7]谢世伟.变形分数相关及其光学和数字式实现研究[D].成都：四川大学,2003.
[8]M.Brunel,S.Coetmellec. Fractional-order Fourier formulation of the propagation of partially coherent light pluses[J].Opt.Commun.2004,230(4):1-5.
[9]郭斌,分数阶Fourier变换的基本原理与应用[D].成都：电子科技大学,2006.
[10]王银花.分数傅里叶变换的研究与应用[D].合肥：安徽大学,2007.
[11]Yi XIN,Ran TAO,Yue WANG.Image Encryption Based on a Novel Reality-Preserving Fractional Fourier Transform. International Conference on Innovative Computing,Information and Control.2006.
[12]王超.基于PCMCIA的RSA密码加速芯片的研究[D].杭州：浙江大学,2004.
[13]闫统江.伪随机序列的构造及其性质研究[D].西安：西安电子科技大学,2007.
[14]郑慧琴.计算机密码学的加密解密算法分析与改进[D].杭州：浙江大学,2001.
[15]于红梅.数论密码学历史分析与未来发展展望[D].济南：山东大学,2008.
[16]贺亮.RC4密钥扩展算法的不动点数分析[D].青岛大学,2008
[17]刘家胜.基于混沌的图像加密技术研究[D].安徽大学,2007.
[18]安丙辰.基于DSP的数字混沌加密系统的设计与实现[D].大连：大连理工大学,2006.
[19]王洪均.数字图像加密算法研究[D].南京：南京理工大学,2007.
[20]赵婷婷.基于神经网络的视频加密与压缩技术的研究[D].大连：大连理工大学,2009.
[21]赵德勤.非线性系统中的混沌控制与同步研究[D].上海：上海大学,2004.
[22]陶然,邓斌,王越.分数阶傅里叶变换及其应用[M].北京：清华大学出版社,2009.
[23]陈萍.分数阶Fourier变换在水雷目标特征提取中的应用[D].哈尔滨：哈尔滨工程大学,2007.
[24]张峰.基于分数阶Fourier变换的chirp类数字水印算法研究[D].郑州：郑州大学,2006.
[25]张琳.基于离散分数余弦变换的图像加密技术[D].南昌：南昌大学,2009.
[26]朱亚琼.分数阶Fourier变换的移动算法研究[D].郑州：郑州大学,2007.
[27]李进.分数阶Fourier变换在超声信号处理中的应用[D].合肥：中国科学技术大学,2009.
[28]李沙茹拉.基于DSP的图像增强技术[D].呼和浩特：内蒙古大学,2009.
[29]张士君.基于TMS320DM642的H.264编码器的实现和优化[D].北京：北京邮电大学,2008.
[30]徐伟,DSP的时空混沌信息加密的研究[D].南京：南京理工大学,2005.
[31]王中华,基于DSP的实时图像处理的研究[D].武汉：武汉理工大学,2006.
[32]Torre. The Fractional Fourier Transform and some of Its Applications to Optics Progress in optics.2002,43:531-596.
[33]Ozaktas H.M., Kutay M.A., Bozdagi G. Digital computation of the fractional Fourier transform[J]. IEEE Trans.Sig.Proc.1996,44:2141-2150.
[34]Liu,Haifa Zhao,Shutian Zhengjun Liu. Continuous vs. discrete fractional Fourier transforms discrete fractional random transform[J]. Opt.Comm.2005,255:357-365.
[35]X.Wang, D.Zhao. Image Encryption Based on Anamorphic Fractional Fourier Transform and Three-step Phase-shifting Interferometry[J]. Opt.Comm.2006,268:240-244.
[36]Xu Guanlei, Wang Xiaotong, Xu Xiaogang, Fractional quaternion Fourier transform, convolution and correlation[J]. Signal Processing 88 (2008) 2511-2517.
[37]T. Alieva, M.L.Calvo. Importance of the Phase and Amplitude in the Fractional Fourier Domain[J].Opt.Soc.Am.A.2003,20(3):533-541.
[38]Rafael C. Gonzalez, Richard E. Woods Steven L. Eddins, Digital Image Processing Using MATLAB[M], Publishing House of Electronics Industry.2005.
[39]MATLAB link for code composer studio development tools[M]. Massachusetts:The MathWorks.2002.
[40]Code composer studio user's guide[M]. Texas:Texas instruments.2005.
[41]Madhusudan Joshi, Chandra Shakher, Kehar Singh. Logarithms-based RGB image encryption in the fractional Fourier domain:A non-linear approach[J]. Science Direct: Optics and Lasers in Engineering,2009,47:721-727.
[42]李南南,等,MATLAB7简明教程[M].北京：清华大学出版社,2006.
[43]冉启文,等.小波分析与分数阶傅里叶变换及应用[M].北京：北京国防工业出版社,2002.
[44]于力,朱邦和,刘树田.用于光学图像加密的分数Fourier变换双相位编码[J].光子学报,2001,30(7)：904-906.
[45]赵兴浩,陶然,邓兵.分数阶傅里叶变换数值计算中的量纲归一化[J].北京理工大学学报,2005,25(4)：360-364.
[46]李真芳.DSP程序开发MATLAB调试及直接目标代码生成[M].西安：西安电子科技大学,2003.
[47]李方慧,王飞.TMS320C6000系列DSPs原理与应用[M].北京：电子工业出版社,2003
[48]关心平.混沌控制及其在保密通信中的应用[M].北京：国防工业出版社,2002.
[49]李昌刚,韩正之,张浩然.图像加密技术综述[J].计算机研究与发展,2002,39：1317-1324.
[50]黄润生,黄浩.混沌理论及其应用[M].武汉大学出版社,2005.
[51]黄晓生.数字图像安全技术研究进展[J].华东交通大学学报,2006,23(1)：82-85.
[52]易开祥,孙鑫.石教英.一种基于混沌序列的图像加密算法[J].计算机辅助设计与图形学学报,2000,12(9)：672-676.
[2]Adress Uhi, Adress Pommer. Image and Video Encryption[M].Springer,1 st ed,2004.
[3]王军.博奇型计算全息在加密图像抗裁剪攻击中应用研究[D].北京：北京大学,2009.
[4]S.T.Liu, B.H.Zhu. Optical imgage encrption based on the generalized fractional convolution operation[J].Opt. Commun.2001,195:371-381.
[5]王长涛.复数阶分数傅里叶变换的实现[D].成都：四川大学,2002.
[6]曾阳素.分数傅里叶光学的应用研究[D].成都：四川大学,2002.
[7]谢世伟.变形分数相关及其光学和数字式实现研究[D].成都：四川大学,2003.
[8]M.Brunel,S.Coetmellec. Fractional-order Fourier formulation of the propagation of partially coherent light pluses[J].Opt.Commun.2004,230(4):1-5.
[9]郭斌,分数阶Fourier变换的基本原理与应用[D].成都：电子科技大学,2006.
[10]王银花.分数傅里叶变换的研究与应用[D].合肥：安徽大学,2007.
[11]Yi XIN,Ran TAO,Yue WANG.Image Encryption Based on a Novel Reality-Preserving Fractional Fourier Transform. International Conference on Innovative Computing,Information and Control.2006.
[12]王超.基于PCMCIA的RSA密码加速芯片的研究[D].杭州：浙江大学,2004.
[13]闫统江.伪随机序列的构造及其性质研究[D].西安：西安电子科技大学,2007.
[14]郑慧琴.计算机密码学的加密解密算法分析与改进[D].杭州：浙江大学,2001.
[15]于红梅.数论密码学历史分析与未来发展展望[D].济南：山东大学,2008.
[16]贺亮.RC4密钥扩展算法的不动点数分析[D].青岛大学,2008
[17]刘家胜.基于混沌的图像加密技术研究[D].安徽大学,2007.
[18]安丙辰.基于DSP的数字混沌加密系统的设计与实现[D].大连：大连理工大学,2006.
[19]王洪均.数字图像加密算法研究[D].南京：南京理工大学,2007.
[20]赵婷婷.基于神经网络的视频加密与压缩技术的研究[D].大连：大连理工大学,2009.
[21]赵德勤.非线性系统中的混沌控制与同步研究[D].上海：上海大学,2004.
[22]陶然,邓斌,王越.分数阶傅里叶变换及其应用[M].北京：清华大学出版社,2009.
[23]陈萍.分数阶Fourier变换在水雷目标特征提取中的应用[D].哈尔滨：哈尔滨工程大学,2007.
[24]张峰.基于分数阶Fourier变换的chirp类数字水印算法研究[D].郑州：郑州大学,2006.
[25]张琳.基于离散分数余弦变换的图像加密技术[D].南昌：南昌大学,2009.
[26]朱亚琼.分数阶Fourier变换的移动算法研究[D].郑州：郑州大学,2007.
[27]李进.分数阶Fourier变换在超声信号处理中的应用[D].合肥：中国科学技术大学,2009.
[28]李沙茹拉.基于DSP的图像增强技术[D].呼和浩特：内蒙古大学,2009.
[29]张士君.基于TMS320DM642的H.264编码器的实现和优化[D].北京：北京邮电大学,2008.
[30]徐伟,DSP的时空混沌信息加密的研究[D].南京：南京理工大学,2005.
[31]王中华,基于DSP的实时图像处理的研究[D].武汉：武汉理工大学,2006.
[32]Torre. The Fractional Fourier Transform and some of Its Applications to Optics Progress in optics.2002,43:531-596.
[33]Ozaktas H.M., Kutay M.A., Bozdagi G. Digital computation of the fractional Fourier transform[J]. IEEE Trans.Sig.Proc.1996,44:2141-2150.
[34]Liu,Haifa Zhao,Shutian Zhengjun Liu. Continuous vs. discrete fractional Fourier transforms discrete fractional random transform[J]. Opt.Comm.2005,255:357-365.
[35]X.Wang, D.Zhao. Image Encryption Based on Anamorphic Fractional Fourier Transform and Three-step Phase-shifting Interferometry[J]. Opt.Comm.2006,268:240-244.
[36]Xu Guanlei, Wang Xiaotong, Xu Xiaogang, Fractional quaternion Fourier transform, convolution and correlation[J]. Signal Processing 88 (2008) 2511-2517.
[37]T. Alieva, M.L.Calvo. Importance of the Phase and Amplitude in the Fractional Fourier Domain[J].Opt.Soc.Am.A.2003,20(3):533-541.
[38]Rafael C. Gonzalez, Richard E. Woods Steven L. Eddins, Digital Image Processing Using MATLAB[M], Publishing House of Electronics Industry.2005.
[39]MATLAB link for code composer studio development tools[M]. Massachusetts:The MathWorks.2002.
[40]Code composer studio user's guide[M]. Texas:Texas instruments.2005.
[41]Madhusudan Joshi, Chandra Shakher, Kehar Singh. Logarithms-based RGB image encryption in the fractional Fourier domain:A non-linear approach[J]. Science Direct: Optics and Lasers in Engineering,2009,47:721-727.
[42]李南南,等,MATLAB7简明教程[M].北京：清华大学出版社,2006.
[43]冉启文,等.小波分析与分数阶傅里叶变换及应用[M].北京：北京国防工业出版社,2002.
[44]于力,朱邦和,刘树田.用于光学图像加密的分数Fourier变换双相位编码[J].光子学报,2001,30(7)：904-906.
[45]赵兴浩,陶然,邓兵.分数阶傅里叶变换数值计算中的量纲归一化[J].北京理工大学学报,2005,25(4)：360-364.
[46]李真芳.DSP程序开发MATLAB调试及直接目标代码生成[M].西安：西安电子科技大学,2003.
[47]李方慧,王飞.TMS320C6000系列DSPs原理与应用[M].北京：电子工业出版社,2003
[48]关心平.混沌控制及其在保密通信中的应用[M].北京：国防工业出版社,2002.
[49]李昌刚,韩正之,张浩然.图像加密技术综述[J].计算机研究与发展,2002,39：1317-1324.
[50]黄润生,黄浩.混沌理论及其应用[M].武汉大学出版社,2005.
[51]黄晓生.数字图像安全技术研究进展[J].华东交通大学学报,2006,23(1)：82-85.
[52]易开祥,孙鑫.石教英.一种基于混沌序列的图像加密算法[J].计算机辅助设计与图形学学报,2000,12(9)：672-676.