搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一种基于压缩感知和多维混沌系统的多过程图像加密方案

石航 王丽丹

引用本文:
Citation:

一种基于压缩感知和多维混沌系统的多过程图像加密方案

石航, 王丽丹

Multi-process image encryption scheme based on compressed sensing and multi-dimensional chaotic system

Shi Hang, Wang Li-Dan
PDF
HTML
导出引用
  • 随着计算机科学的快速发展, 信息的存储和传播常常在各类计算机硬件以及多种网络之间进行, 传统的信息加密方案已逐渐不再适用. 因此, 基于计算机的信息加密算法近年来逐步成为研究热点. 通过结合小波包变换、压缩感知、混沌系统等理论, 一种基于压缩感知和多维混沌系统的多过程图像加密方案被提出. 该加密方案实现了针对灰度图像的压缩和加密及对应的解压、解密过程. 小波包变换理论被应用到图像的预处理阶段对原始图像进行小波包分解, 同时结合阈值处理方法对分解后所得的图像信号分量进行分类, 并在之后的处理过程中根据图像信号分量的特性对其有区分地进行压缩、加密或者保留. 在图像压缩阶段, 引入压缩感知算法克服传统采样定理采样成本高及重构质量偏低等弊端. 在图像加密阶段, 结合多类、多维度混沌系统对相关图像信号分量进行置乱. 最后, 应用压缩、加密以及小波包变换的逆过程实现对原始图像的完整重构. 仿真结果表明, 该图像加密方案在抵抗外界干扰时凭借算法鲁棒性有效地保护了密文图像的基本信息, 且在应对明文攻击等破解手段时不泄露任何有用信息. 此外, 经该加密方案加密后的密文图像的信息熵及相关系数等指标相比于参考文献中加密算法更加接近于理想值, 其加密性能有明显的提升.
    With the rapid development of computer science, the storage and dissemination of information are often carried out between various types of computer hardwares and various networks. The traditional information encryption scheme has gradually disappeared. Therefore, computer-based information encryption algorithms have gradually become a research hotspot in recent years. By combining the theory of wavelet packet transform, compressed sensing and chaotic system, a multi-process image encryption scheme based on compressed sensing and multi-dimensional chaotic system is proposed. The encryption scheme implements compression and encryption for grayscale images and corresponding decompression and decryption process. The wavelet packet transform theory is applied to the image preprocessing stage to perform wavelet packet decomposition on the original image. At the same time, the image signal components obtained by the decomposition are classified according to the threshold processing method, and the characteristics of the image signal components are processed in the subsequent processing. They are compressed, encrypted, or reserved in a differentiated manner. In the image compression stage, by introducing the compressed sensing algorithm to overcome the shortcomings of the traditional Nyquist sampling theorem, such as high sampling cost and low reconstruction quality, the compression efficiency and compression quality are improved while the ciphertext image reconstruction quality is guaranteed. In the image encryption stage, the encryption scheme combines multi-class and multi-dimensional chaotic systems to confuse and scramble the related image signal components, and introduces a high-dimensional chaotic system to make the encryption scheme have a large enough key space to further enhance the ciphertext image reliability. Finally, the complete reconstruction of the original image is achieved by applying the inverse of compression, encryption and wavelet packet transform. The simulation results show that the image encryption scheme effectively protects the basic information about ciphertext images by virtue of algorithm robustness against external interference, and does not reveal any useful information when dealing with cracking methods such as plaintext attacks. In addition, the information entropy and correlation coefficient of ciphertext images encrypted by this encryption scheme are closer to ideal values than those of the encryption algorithm in the references, and its encryption performance is significantly improved.
      通信作者: 王丽丹, ldwang@swu.edu.cn
    • 基金项目: 国家重点基础研究发展计划(批准号: 2018YFB1306600)、国家自然科学基金(批准号: 61571372, 61672436, 61601376)、重庆市基础科学与前沿技术研究专项重点项目(批准号: cstc2017jcyjBX0050, cstc2016jcyjA0547)和中央高校基本科研业务费(批准号: XDJK2016A001, XDJK2017A005)资助的课题
      Corresponding author: Wang Li-Dan, ldwang@swu.edu.cn
    • Funds: Project supported by the National Key Research & Development Program of China (Grant No. 2018YFB1306600), the National Natural Science Foundation of China (Grant Nos. 61571372, 61672436, 61601376), the Fundamental Science and Advanced Technology Research Foundation of Chongqing, China (Grant Nos. cstc2017jcyjBX0050, cstc2016jcyjA0547), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. XDJK2016A001, XDJK2017A005)
    [1]

    吴成茂 2014 物理学报 63 090504Google Scholar

    Wu C M 2014 Acta Phys. Sin. 63 090504Google Scholar

    [2]

    林青, 王延江, 王珺 2016 中国科学: 技术科学 46 910

    Lin Q, Wang Y J, Wang J 2016 Sci. China: Technol. Sci. 46 910

    [3]

    李静, 向菲, 张军朋 2019 电子设计工程 27 84Google Scholar

    Li J, Xian F, Zhang J P 2019 Int. Electr. Elem. 27 84Google Scholar

    [4]

    Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289Google Scholar

    [5]

    Chai X L, Zheng X Y, Gan Z H, Han D J, Chen Y R 2018 Signal Process 148 124Google Scholar

    [6]

    Zhu S Q, Zhu C X, Wang W H 2018 IEEE Access. 6 67095Google Scholar

    [7]

    Lü X P, Liao X F, Yang B 2018 Multimed Tools Appl. 77 28633Google Scholar

    [8]

    Hilton M L 1997 IEEE Trans. Bio-Med. Eng. 44 394Google Scholar

    [9]

    张祥, 张达永, 张刘辉, 潘栋 2016 气象水文海洋仪器 33 38Google Scholar

    Zhang X, Zhang D Y, Zhang L H, Pan D 2016 Meteorol. Hydrol. Mar. Instrum. 33 38Google Scholar

    [10]

    Goklani H S 2017 Int. J. Image, Graphics and Signal Processing 9 30

    [11]

    Huang R, Rhee K H, Uchida S 2012 Multimed Tools Appl. 7 2

    [12]

    Zhou N, Pan S, Cheng S, et al. 2016 Opt. Laser Technol. 82 121Google Scholar

    [13]

    禹思敏 2008 物理学报 57 3374Google Scholar

    Yu S M 2008 Acta Phys. Sin. 57 3374Google Scholar

    [14]

    禹思敏 2011 混沌系统与混沌电路 (西安:西安电子科技大学出版社) 第136−137页

    Yu S M 2011 Chaotic Systems and Chaotic Circuits (Xi’ an: Xi 'an University of Electronic Science and Technology Press) pp136−137 (in Chinese)

    [15]

    Chen G R 1999 Int. J. Bifurcat. Chaos 9 1465Google Scholar

    [16]

    王鸣天, 郭玉奇 2017 电子技术 46 69Google Scholar

    Wang M T, Guo Y Q 2017 Electr. Technol. 46 69Google Scholar

    [17]

    Li C Q 2013 Nonlinear Dyn. 73 2083Google Scholar

    [18]

    高展鸿, 徐文波 2011 基于MATLAB的图像处理案例教程 (北京: 清华大学出版社) 第99−101页

    Gao Z H, Xu W B 2011 MATLAB-Based Image Processing Case Tutorial (Beijing: Tsinghua University Press) pp99−101 (in Chinese)

    [19]

    张勇 2016 混沌数字图像加密 (北京: 清华大学出版社) 第50−59页

    Zhang Y 2016 Chaotic Digital Image Crptosystem (Beijing: Tsinghua University Press) pp50−59 (in Chinese)

    [20]

    王静, 蒋国平 2011 物理学报 60 060503Google Scholar

    Wang J, Jiang G P 2011 Acta Phys. Sin. 60 060503Google Scholar

    [21]

    Zhang Y, Xiao D 2013 Opt. Lasers Eng. 51 472Google Scholar

  • 图 1  Lena图像及其二阶小波包变换 (a)原图; (b)二阶小波包变换

    Fig. 1.  Lena and its second-order wavelet packet transformation: (a) Original Lena; (b) second order wavelet packet transformation of Lena.

    图 2  分类算法流程图

    Fig. 2.  Flow chart of classification algorithm.

    图 3  一次置乱加密流程图

    Fig. 3.  One scrambling encryption algorithm flow chart.

    图 4  S信号的密文图像 (a) 一次置乱密文图像; (b) 二次置乱密文图像

    Fig. 4.  Ciphertext image of the S signal: (a) Scrambling ciphertext image once; (b) secondary scrambling ciphertext image.

    图 5  S信号二次置乱加密流程图

    Fig. 5.  Secondary scrambling encryption flow chart of S signal

    图 6  图像重构流程图

    Fig. 6.  Image reconstruction flow chart.

    图 7  Lena图像的明文图像、重构图像 (a)原始图像; (b) Lena重构图像

    Fig. 7.  Original, reconstructed image of Lena: (a) Original image; (b) reconstructed image.

    图 8  更多加密方案运行实例 (a) Pepper原始图像; (b) Pepper重构图像; (c) Cameraman原始图像; (d) Cameraman重构图像

    Fig. 8.  More encryption scheme running examples: (a) Original image of Pepper; (b) reconstructed image of Pepper; (c) original image of Cameraman; (d) reconstructed image of Cameraman.

    图 9  Lena图像的明文(S信号)、密文图像在水平、竖直、斜线三个方向的相关分布图 (a)明文图像相关分布图; (b) S信号的密文图像相关分布图

    Fig. 9.  Correlation distribution of plaintext, ciphertext image in horizontal, vertical and oblique directions of S signal of Lena: (a) Correlation distribution of plaintext of S signal; (b) correlation distribution of ciphertext of S signal.

    图 11  Cameraman图像的明文(S信号)、密文图像在水平、竖直、斜线三个方向的相关分布图 (a)明文图像相关分布图; (b) S信号的密文图像相关分布图

    Fig. 11.  Correlation distribution of plaintext, ciphertext image in horizontal, vertical and oblique directions of S signal of Cameraman: (a) Correlation distribution of plaintext of S signal; (b) correlation distribution of ciphertext of S signal

    图 10  Pepper图像的明文(S信号)、密文图像在水平、竖直、斜线三个方向的相关分布图 (a)明文图像相关分布图; (b) S信号的密文图像相关分布图

    Fig. 10.  Correlation distribution of plaintext, ciphertext image in horizontal, vertical and oblique directions of S signal of Pepper: (a) Correlation distribution of plaintext of S signal; (b) correlation distribution of ciphertext of S signal.

    图 12  Lena, Pepper, Cameraman图像的S信号的明文、密文的灰度直方图 (a) S信号的明文灰度直方图; (b) S信号的密文图像相关分布图

    Fig. 12.  Gray histogram of plaintext and ciphertext of S signal of Lena, Pepper, Cameraman: (a) Gray histogram of plaintext of S signal; (b) gray histogram of plaintext of ciphertext of S signal

    图 13  不同图像的S信号嵌入噪声后的重构结果 (a) Lena原始图像、嵌入噪声的S信号密文、重构图像; (b) Pepper原始图像、嵌入噪声的S信号密文、重构图像; (c) Cameraman原始图像、嵌入噪声的S信号密文、重构图像

    Fig. 13.  Reconstruction results of S signals of different images embedded with noise: (a) Reconstruction results of Lena with corresponding Cipher S signal embedded noise; (b) reconstruction results of Pepper with corresponding Cipher S signal embedded noise; (c) reconstruction results of Cameraman with corresponding Cipher S signal embedded noise

    图 14  不同图像的S信号像素剪切后的重构结果 (a) Lena原始图像、剪切12.5%像素点后的S信号密文、重构图像; (b) Pepper原始图像、剪切12.5%像素点后的S信号密文、重构图像; (c) Cameraman原始图像、剪切12.5%像素点后的S信号密文、重构图像

    Fig. 14.  Reconstruction results of S signals of different images after pixel shearing: (a) Reconstruction results of Lena with corresponding Cipher S signal with 12.5% pixels lost; (b) reconstruction results of Pepper with corresponding Cipher S signal with 12.5% pixels lost; (c) reconstruction results of Cameraman with corresponding Cipher S signal with 12.5% pixels lost

    图 15  针对本文加密算法的选择明文攻击

    Fig. 15.  The CPA against the encryption algorithm in this paper

    表 1  Lena图像Ci信号分量0像素点的个数及占比

    Table 1.  The number and proportion of 0 pixels in Ci signals in Lena.

    信号分量0像素点个数0像素点占比/%
    C13298.03
    C255413.53
    C370317.16
    C468216.65
    C543610.64
    C691722.39
    C784220.56
    C878919.26
    下载: 导出CSV

    表 2  比较不同加密方案的相关系数

    Table 2.  Comparisons for the correlation coefficients of different encryption scheme.

    图像明文图像密文图像
    水平竖直斜线水平竖直斜线
    Lena (本文)0.91890.73390.8097–0.0002 –0.0004 0.0001
    Lena[16]0.91800.73450.80830.00320.00250.0173
    Lena[17]0.91510.80970.74840.02740.00510.0117
    Pepper (本文)0.88490.75670.8323–0.0003 –0.0004 0.0003
    Pepper[16]0.88270.83740.74820.02100.00100.0071
    Pepper[17]0.88640.83980.74660.00700.01980.0228
    Cameraman (本文)0.92750.83640.88660.0004 0.0001 0.0002
    Cameraman [16]0.93390.88980.84590.00350.00140.0159
    Cameraman[17]0.92800.88350.84110.02770.01410.0281
    下载: 导出CSV

    表 3  比较不同加密方案的信息熵

    Table 3.  Comparisons for the entropy of different encryption scheme.

    加密方案明文图像密文图像
    Lena (本文)7.30357.9544
    Lena[16]7.9642
    Lena[17]7.9531
    Pepper (本文)7.43447.9633
    Pepper[16]7.9586
    Pepper[17]7.9543
    Cameraman (本文)6.95717.9554
    Cameraman[16]7.9636
    Cameraman[17]7.9538
    下载: 导出CSV

    表 4  修改1 bit像素点后不同图像(S信号)的NPCR, UACI, BACI

    Table 4.  NPCR, UACI, BACI of different images after changed 1 bit.

    图像NPCRUACIBACI
    Lena0.99540.33030.2682
    Pepper0.99440.33050.2657
    Cameraman0.99660.33940.2684
    下载: 导出CSV

    表 5  本文算法处理下不同图像的wPSNR和SSIM

    Table 5.  wPSNR and SSIM of different images after processed by scheme in this paper.

    图像wPSNRSSIM
    Lena48.900.9898
    Pepper50.330.9927
    Cameraman43.340.9736
    下载: 导出CSV

    表 6  本文算法处理不同图像时的时间复杂度

    Table 6.  Algorithm proposed deals with the time complexity of different images.

    图像WPT分解及分类压缩及重构加密及解密整体重构总耗时/s
    Lena0.600 s8.893 s1.098 s0.377 s10.968
    Pepper0.734 s7.815 s1.105 s0.362 s10.016
    Cameraman0.617 s3.908 s1.901 s0.353 s6.799
    下载: 导出CSV
  • [1]

    吴成茂 2014 物理学报 63 090504Google Scholar

    Wu C M 2014 Acta Phys. Sin. 63 090504Google Scholar

    [2]

    林青, 王延江, 王珺 2016 中国科学: 技术科学 46 910

    Lin Q, Wang Y J, Wang J 2016 Sci. China: Technol. Sci. 46 910

    [3]

    李静, 向菲, 张军朋 2019 电子设计工程 27 84Google Scholar

    Li J, Xian F, Zhang J P 2019 Int. Electr. Elem. 27 84Google Scholar

    [4]

    Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289Google Scholar

    [5]

    Chai X L, Zheng X Y, Gan Z H, Han D J, Chen Y R 2018 Signal Process 148 124Google Scholar

    [6]

    Zhu S Q, Zhu C X, Wang W H 2018 IEEE Access. 6 67095Google Scholar

    [7]

    Lü X P, Liao X F, Yang B 2018 Multimed Tools Appl. 77 28633Google Scholar

    [8]

    Hilton M L 1997 IEEE Trans. Bio-Med. Eng. 44 394Google Scholar

    [9]

    张祥, 张达永, 张刘辉, 潘栋 2016 气象水文海洋仪器 33 38Google Scholar

    Zhang X, Zhang D Y, Zhang L H, Pan D 2016 Meteorol. Hydrol. Mar. Instrum. 33 38Google Scholar

    [10]

    Goklani H S 2017 Int. J. Image, Graphics and Signal Processing 9 30

    [11]

    Huang R, Rhee K H, Uchida S 2012 Multimed Tools Appl. 7 2

    [12]

    Zhou N, Pan S, Cheng S, et al. 2016 Opt. Laser Technol. 82 121Google Scholar

    [13]

    禹思敏 2008 物理学报 57 3374Google Scholar

    Yu S M 2008 Acta Phys. Sin. 57 3374Google Scholar

    [14]

    禹思敏 2011 混沌系统与混沌电路 (西安:西安电子科技大学出版社) 第136−137页

    Yu S M 2011 Chaotic Systems and Chaotic Circuits (Xi’ an: Xi 'an University of Electronic Science and Technology Press) pp136−137 (in Chinese)

    [15]

    Chen G R 1999 Int. J. Bifurcat. Chaos 9 1465Google Scholar

    [16]

    王鸣天, 郭玉奇 2017 电子技术 46 69Google Scholar

    Wang M T, Guo Y Q 2017 Electr. Technol. 46 69Google Scholar

    [17]

    Li C Q 2013 Nonlinear Dyn. 73 2083Google Scholar

    [18]

    高展鸿, 徐文波 2011 基于MATLAB的图像处理案例教程 (北京: 清华大学出版社) 第99−101页

    Gao Z H, Xu W B 2011 MATLAB-Based Image Processing Case Tutorial (Beijing: Tsinghua University Press) pp99−101 (in Chinese)

    [19]

    张勇 2016 混沌数字图像加密 (北京: 清华大学出版社) 第50−59页

    Zhang Y 2016 Chaotic Digital Image Crptosystem (Beijing: Tsinghua University Press) pp50−59 (in Chinese)

    [20]

    王静, 蒋国平 2011 物理学报 60 060503Google Scholar

    Wang J, Jiang G P 2011 Acta Phys. Sin. 60 060503Google Scholar

    [21]

    Zhang Y, Xiao D 2013 Opt. Lasers Eng. 51 472Google Scholar

  • [1] 王攀, 王仲根, 孙玉发, 聂文艳. 新型压缩感知计算模型分析三维电大目标电磁散射特性. 物理学报, 2023, 72(3): 030202. doi: 10.7498/aps.72.20221532
    [2] 凡洪剑, 李江, 王丽华, 樊春海, 柳华杰. 基于DNA折纸模板的铁原子阵列构建及其信息加密应用. 物理学报, 2021, 70(6): 068702. doi: 10.7498/aps.70.20201438
    [3] 胡耀华, 刘艳, 穆鸽, 秦齐, 谭中伟, 王目光, 延凤平. 基于多模光纤散斑的压缩感知在光学图像加密中的应用. 物理学报, 2020, 69(3): 034203. doi: 10.7498/aps.69.20191143
    [4] 陈炜, 郭媛, 敬世伟. 基于深度学习压缩感知与复合混沌系统的通用图像加密算法. 物理学报, 2020, 69(24): 240502. doi: 10.7498/aps.69.20201019
    [5] 李少东, 陈永彬, 刘润华, 马晓岩. 基于压缩感知的窄带高速自旋目标超分辨成像物理机理分析. 物理学报, 2017, 66(3): 038401. doi: 10.7498/aps.66.038401
    [6] 冷雪冬, 王大鸣, 巴斌, 王建辉. 基于渐进添边的准循环压缩感知时延估计算法. 物理学报, 2017, 66(9): 090703. doi: 10.7498/aps.66.090703
    [7] 李慧, 赵琳, 李亮. 基于贝叶斯压缩感知的周跳探测与修复方法. 物理学报, 2016, 65(24): 249101. doi: 10.7498/aps.65.249101
    [8] 时洁, 杨德森, 时胜国, 胡博, 朱中锐. 基于压缩感知的矢量阵聚焦定位方法. 物理学报, 2016, 65(2): 024302. doi: 10.7498/aps.65.024302
    [9] 庄佳衍, 陈钱, 何伟基, 冒添逸. 基于压缩感知的动态散射成像. 物理学报, 2016, 65(4): 040501. doi: 10.7498/aps.65.040501
    [10] 李广明, 吕善翔. 混沌信号的压缩感知去噪. 物理学报, 2015, 64(16): 160502. doi: 10.7498/aps.64.160502
    [11] 康荣宗, 田鹏武, 于宏毅. 一种基于选择性测量的自适应压缩感知方法. 物理学报, 2014, 63(20): 200701. doi: 10.7498/aps.63.200701
    [12] 陈明生, 王时文, 马韬, 吴先良. 基于压缩感知的目标频空电磁散射特性快速分析. 物理学报, 2014, 63(17): 170301. doi: 10.7498/aps.63.170301
    [13] 王哲, 王秉中. 压缩感知理论在矩量法中的应用. 物理学报, 2014, 63(12): 120202. doi: 10.7498/aps.63.120202
    [14] 张新鹏, 胡茑庆, 程哲, 钟华. 基于压缩感知的振动数据修复方法. 物理学报, 2014, 63(20): 200506. doi: 10.7498/aps.63.200506
    [15] 李龙珍, 姚旭日, 刘雪峰, 俞文凯, 翟光杰. 基于压缩感知超分辨鬼成像. 物理学报, 2014, 63(22): 224201. doi: 10.7498/aps.63.224201
    [16] 冯丙辰, 方晟, 张立国, 李红, 童节娟, 李文茜. 基于压缩感知理论的非线性γ谱分析方法. 物理学报, 2013, 62(11): 112901. doi: 10.7498/aps.62.112901
    [17] 白旭, 李永强, 赵生妹. 基于压缩感知的差分关联成像方案研究. 物理学报, 2013, 62(4): 044209. doi: 10.7498/aps.62.044209
    [18] 马原, 吕群波, 刘扬阳, 钱路路, 裴琳琳. 基于主成分变换的图像稀疏度估计方法. 物理学报, 2013, 62(20): 204202. doi: 10.7498/aps.62.204202
    [19] 宁方立, 何碧静, 韦娟. 基于lp范数的压缩感知图像重建算法研究. 物理学报, 2013, 62(17): 174212. doi: 10.7498/aps.62.174212
    [20] 刘 强, 方锦清, 赵耿, 李永. 基于FPGA技术的混沌加密系统研究. 物理学报, 2012, 61(13): 130508. doi: 10.7498/aps.61.130508
计量
  • 文章访问数:  9478
  • PDF下载量:  168
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-04-16
  • 修回日期:  2019-07-15
  • 上网日期:  2019-10-01
  • 刊出日期:  2019-10-20

/

返回文章
返回