CSA  >> Vol. 7 No. 8 (August 2017)

    基于改进标准映射的图像加密算法
    A Novel Image Encryption Algorithm Based on Improved Standard Mapping

  • 全文下载: PDF(13801KB) HTML   XML   PP.753-773   DOI: 10.12677/CSA.2017.78087  
  • 下载量: 83  浏览量: 896  

作者:  

陈裕城,叶瑞松:汕头大学数学系,广东 汕头

关键词:
标准映射混沌图像加密Standard Mapping Chaos Image Encryption

摘要:

本文提出一种基于改进标准映射的图像加密算法。首先,针对标准映射用于图像置乱加密时的密钥空间小等不足,通过引进变量的非线性项和含参量的线性组合对标准映射进行改进。改进标准映射的相位空间图、Lyapunov指数、时间序列测试均表明了改进标准映射具有良好的随机性能。同时,利用改进标准映射设计了一种新的灰度图像加密算法,在置换阶段,采用改进的标准映射实现置乱得到较好的置乱效果;在扩散阶段,采用动态反馈方式的机制使得扩散过程有很好的扩散加密效果。最后,本文还提出了与本文灰度图像加密算法相关的性能分析,包括密钥空间分析、密钥敏感性分析、统计分析等,所有的仿真实验均表明,本文提出的加密算法对各种已知攻击具有非常强的鲁棒性,并且具有密钥空间大、密钥敏感性强、可抵抗统计分析攻击、蛮力攻击、差分攻击、已知明文和选择明文攻击等优良特性。

This paper proposes an image encryption algorithm based on improved standard mapping. The standard mapping is improved by introducing the nonlinear term of the variables and the linear combination of the parameters. The phase space diagram, Lyapunov exponent and time series tests of the improved standard mapping show that improved standard mapping has good random performance. A new gray image encryption algorithm is then designed using the improved standard mapping. In the permutation stage, the improved standard map is applied to disorder the pixels positions to achieve good scrambling effect. In the diffusion stage, the mechanism of dynamic feedback is used to make the diffusion process have fair diffusion and encryption effect. Finally, the performance analysis is carried out, including key space analysis, key sensitivity analysis, statistical analysis, etc. Simulation experiments show that the encryption algorithm proposed has a large key space, strong key sensitivity, strong robustness against statistical analysis attack, brute force attack, differential analysis attack, and chosen\known plaintext attacks, etc.

文章引用:
陈裕城, 叶瑞松. 基于改进标准映射的图像加密算法[J]. 计算机科学与应用, 2017, 7(8): 753-773. https://doi.org/10.12677/CSA.2017.78087

参考文献

[1] http://www.xinhuanet.com/world/ljm2013/index.htm
[2] http://finance.qq.com/a/20170119/003242.htm
[3] 张同锋. 基于一维复合混沌映射的数字图像加密算法研究[D]: [博士学位论文]. 兰州: 兰州大学, 2016.
[4] Liu, W., Sun, K. and Zhu, C. (2016) A Fast Image Encryption Algorithm Based on Chaotic Map. Optics and Lasers in Engineering, 84, 26-36.
[5] 张强, 田小平. 基于图像位平面分解的混沌加密方法研究[J]. 西安邮电学院学报, 2010, 15(5): 83-86.
[6] Robinson, R.C., 韩茂安, 邢业朋, 等. 动力系统导论[M]. 北京: 机械工业出版社, 2007.
[7] Alvarez, G. and Li, S. (2006) Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems. International Journal of Bifurcation and Chaos, 16, 2129-2151.
https://doi.org/10.1142/S0218127406015970
[8] Matthews, R. (1989) On the Derivation of a “Chaotic” Encryption Algorithm. Cryptologia, 13, 29-42.
https://doi.org/10.1080/0161-118991863745
[9] Fridrich, J. (1998) Symmetric Ciphers Based on Two-Dimensional Chaotic Maps. International Journal of Bifurcation and Chaos, 8, 1259-1284.
https://doi.org/10.1142/S021812749800098X
[10] Ye, R. (2011) A Novel Chaos-Based Image Encryption Scheme with an Efficient Permutation-Diffusion Mechanism. Optics Communications, 284, 5290-5298.
[11] Wong, K.W., Kwok, B.S.H. and Law, W.S. (2008) A Fast Image Encryption Scheme Based on Chaotic Standard Map. Physics Letters A, 372, 2645-2652.
[12] 李昌刚, 韩正之, 张浩然. 一种基于随机密钥及“类标准映射”的图像加密算法[J]. 计算机学报, 2003, 26(4): 465- 470.
[13] Xu, L., Gou, X., Li, Z., et al. (2017) A Novel Chaotic Image Encryption Algorithm Using Block Scrambling and Dynamic Index Based Diffusion. Optics and Lasers in Engineering, 91, 41-52.
[14] Hamdi, M., Rhouma, R. and Belghith, S. (2017) A Selective Compression-Encryption of Images Based on SPIHT Coding and Chirikov Standard Map. Signal Processing, 131, 514-526.
[15] Fu, C., Chen, J., Zou, H., et al. (2012) A Chaos-Based Digital Image Encryption Scheme with an Improved Diffusion Strategy. Optics Express, 20, 2363-2378.
https://doi.org/10.1364/OE.20.002363
[16] Chai, X., Chen, Y. and Broyde, L. (2017) A Novel Chaos-Based Image Encryption Algorithm Using DNA Sequence Operations. Optics and Lasers in Engineering, 88, 197-213.
[17] Patidar, V., Pareek, N.K., Purohit, G., et al. (2011) A Robust and Secure Chaotic Standard Map Based Pseudorandom Permutation-Substitution Scheme for Image Encryption. Optics Communications, 284, 4331-4339.
[18] Lian, S., Sun, J. and Wang, Z. (2005) A Block Cipher Based on a Suitable Use of the Chaotic Standard Map. Chaos, Solitons & Fractals, 26, 117-129.
[19] 吴成茂. 离散Arnold变换改进及其在图像置乱加密中的应用[J]. 物理学报, 2014, 63(9): 090504.
[20] Ye, R. (2014) A Novel Image Encryption Scheme Based on Generalized Multi-Sawtooth Maps. Fundamenta Informaticae, 133, 87-104.
[21] Wang, Y., Wong, K.W., Liao, X., et al. (2009) A Chaos-Based Image Encryption Algorithm with Variable Control Parameters. Chaos, Solitons & Fractals, 41, 1773-1783.
[22] Zhang, Y. and Xiao, D. (2013) Double Optical Image Encryption Using Discrete Chirikov Standard Map and Chaos-Based Fractional Random Transform. Optics and Lasers in Engineering, 51, 472-480.
[23] Ye, R. and Huang, H. (2010) Application of the Chaotic Ergodicity of Standard Map in Image Encryption and Watermarking. International Journal of Image, Graphics and Signal Processing, 2, 19.
https://doi.org/10.5815/ijigsp.2010.01.03
[24] Zhao, J., Guo, W. and Ye, R. (2014) A Chaos-Based Image Encryption Scheme Using Permutation-Substitution Architecture. International Journal of Computer Trends and Technology, 15, 174-185.
https://doi.org/10.14445/22312803/IJCTT-V15P137
[25] Rannou, F. (1974) Numerical Study of Discrete Plane Ar-ea-Preserving Mappings. Astronomy and Astrophysics, 31, 289.
[26] http://www.scholarpedia.org/article/Chirikov_standard_map
[27] http://sipi.usc.edu/database/
[28] 张弘. 数字图像处理与分析[M]. 北京: 机械工业出版社, 2013.