基于Bezier曲线的数字图像加密研究
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摘要
分析了数字图像加密在国内外的发展现状和面临的问题,在此基础上深入讨论并提出了一种基于有理二次Bezier曲线的数字图像加密算法。根据该曲线内权因子的特殊性质给出了一个有理映射函数,经计算当权因子在一定范围内取值时,该映射具有正的Lyapunov指数,即具有混沌性质。随后利用其混沌特性生成混沌序列进而构造加密因子与像素灰度进行运算并置换,最终得到加密图像。该算法不仅保留了一维混沌系统形式简单的特点,而且具有加密解密效率高的优点。通过对直方图、相邻像素之间的相关性及信息熵等进行的详细分析可以看出,该算法安全性高,加密图像的灰度直方图较为均匀,加密图像中相邻像素之间的相关性强度显著降低。仿真结果表明该算法取得了较好的加密效果。
We analyze the development status and problems of digital image encryption at home and abroad. On the basis,we discuss in depth and propose a digital image encryption algorithm based on rational quadratic Bezier curves. According to the special property of the inner weight factor,a rational mapping function is given. When the weight factor is evaluated in a certain range,the mapping has a positive Lyapunov exponent,that is,it has the property of chaos. Then,the chaotic sequence is generated by the mapping function. The pixel gray values are replaced by the encryption factor,and the encrypted image is obtained finally. The algorithm proposed not only maintains the virtue of simple form,but also has high efficiency because of the encryption and decryption algorithm both are the same one. Finally,the gray histogram and the correlation between adjacent pixels and the entropy are analyzed in detail. The proposed algorithm has high security. The gray histogram of the encrypted image is more uniform,and the intensity of the correlation between adjacent pixels in the encrypted image is significantly reduced. The simulation shows that the proposed algorithm achieves better encryption effect.
We analyze the development status and problems of digital image encryption at home and abroad. On the basis,we discuss in depth and propose a digital image encryption algorithm based on rational quadratic Bezier curves. According to the special property of the inner weight factor,a rational mapping function is given. When the weight factor is evaluated in a certain range,the mapping has a positive Lyapunov exponent,that is,it has the property of chaos. Then,the chaotic sequence is generated by the mapping function. The pixel gray values are replaced by the encryption factor,and the encrypted image is obtained finally. The algorithm proposed not only maintains the virtue of simple form,but also has high efficiency because of the encryption and decryption algorithm both are the same one. Finally,the gray histogram and the correlation between adjacent pixels and the entropy are analyzed in detail. The proposed algorithm has high security. The gray histogram of the encrypted image is more uniform,and the intensity of the correlation between adjacent pixels in the encrypted image is significantly reduced. The simulation shows that the proposed algorithm achieves better encryption effect.
引文
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[14] ZHANG Yong,TANG Yingjun.A plaintext-related image encryption algorithm based on chaos[J].Multimedia Tools and Applicaions,2018,77:6647-6669.
[15] LAI Dejian,CHEN Guanrong.Generating different statistical distributions by the chaotic skew tent map[J].International Journal of Bifurcation and Chaos,2000,10(6):1509-1512.
[16] GóRA P,BOYARSKY A.On the significance of the tent map[J].Internationa Journal of Bifurcation and Chaos,2003,13(5):1299-1301.
[17] 于万波,杨灵芝.二次函数混沌特性分析及其图像加密应用[J].计算机工程,2013,39(4):5-8.
[18] 施法中.CAGD&NURBS[M].北京:高等教育出版社,2013.
[2] 陈燕梅,张胜元.基于AES的数字图像置乱方法[J].中国图象图形学报,2006,11(8):1077-1080.
[3] NORCEN R,UHL A.Selective encryption of the JPEG2000 bitstream[C]//Proceedings of communications and multimedia security.Berlin:Springer,2003:194-204.
[4] 徐亚,张绍武.基于Arnold映射的分块双层自适应扩散图像加密算法[J].中国图象图形学报,2015,20(6):740-748.
[5] LIU Zhengjun,GONG Min,DOU Yongkang,et al.Double image encryption by using Arnold transform and discrete fraction alangular transform[J].Optics and Lasers in Engineering,2012,50(2):248-255.
[6] 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(10):1318-1324.
[7] SASAKI M,WATANABE Y.Visual secret sharing schemes encrypting multiple images[J].IEEE Transactions on Information Forensics and Security,2018,13(2):356-365.
[8] 张晓强,王蒙蒙,朱贵良.图像加密算法研究新进展[J].计算机工程与科学,2012,34(5):1-6.
[9] 廖琪男,卢守东,孙宪波.结合超混沌序列和移位密码的数字图像加密算法[J].小型微型计算机系统,2015,36(2):332-337.
[10] 黄冬梅,耿霞,魏立斐,等.基于Henon映射的加密遥感图像的安全检索方案[J].软件学报,2016,27(7):1729-1740.
[11] ABANDA Y,TIEDEU A.Image encryption by chaos mixing[J].IET Image Processing,2016,10(10):742-750.
[12] CHEN Guanrong,MAO Yaobin,CHUI C K.A symmetric image encryption scheme based on 3D chaotic cat maps[J].Chaos,Solitons and Fractals,2004,21(3):749-761.
[13] PAK C,HUANG Liliang.A new color image encryption using combination of the 1D chaotic map[J].Signal Processing,2017,138:129-137.
[14] ZHANG Yong,TANG Yingjun.A plaintext-related image encryption algorithm based on chaos[J].Multimedia Tools and Applicaions,2018,77:6647-6669.
[15] LAI Dejian,CHEN Guanrong.Generating different statistical distributions by the chaotic skew tent map[J].International Journal of Bifurcation and Chaos,2000,10(6):1509-1512.
[16] GóRA P,BOYARSKY A.On the significance of the tent map[J].Internationa Journal of Bifurcation and Chaos,2003,13(5):1299-1301.
[17] 于万波,杨灵芝.二次函数混沌特性分析及其图像加密应用[J].计算机工程,2013,39(4):5-8.
[18] 施法中.CAGD&NURBS[M].北京:高等教育出版社,2013.