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基于深度学习的新混沌信号及其在图像加密中的应用

赵智鹏 周双 王兴元

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基于深度学习的新混沌信号及其在图像加密中的应用

赵智鹏, 周双, 王兴元

A new chaotic signal based on deep learning and its application in image encryption

Zhao Zhi-Peng, Zhou Shuang, Wang Xing-Yuan
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  • 为提高单一混沌系统图像加密的安全性, 本文提出了基于深度学习的图像加密算法. 首先, 利用超混沌Lorenz系统产生混沌序列. 其次, 利用长短期记忆人工神经网络(long-short term memory, LSTM)复杂的网络结构模拟混沌特征构造新的混沌信号. 然后, 利用最大Lyapunov指数, 0-1测试, 功率谱分析、相图以及NIST测试对新信号的动力学特征进行分析. 最后, 将新信号应用到图像加密中. 由于该方法生成的新信号不同于原有混沌信号, 而且加密系统具有很高的复杂结构和非线性特征, 故很难被攻击者攻击. 仿真实验结果表明, 本文提出的图像加密算法相比其他一些传统方法具有更高的安全性, 能够抵抗常见的攻击方式.
    To improve the security of image encryption in singular chaotic systems, an encryption algorithm based on deep-learning is proposed in this paper. To begin with, the chaos sequence is generated by using a hyperchaotic Lorenz system, prior to creating new chaotic signals based on chaotic characteristics obtained from he simulations of the powerful complex network structure of long-short term memory artificial neural network (LSTM-ANN). Then, dynamic characteristics of the new signals are analyzed with the largest Lyapunov exponent, 0-1 test, power spectral analysis, phase diagrams and NIST test. In the end, the new signals are applied to image encryption, the results of which verify the expected increased difficulty in attacking the encrypted system. This is attributable to the differences of the new signals generated using the proposed method from the original chaotic signals, as well as arises from the high complexity and nonlinearity of the system. Considering its ability to withstand common encryption attacks, it is hence reasonable to conclude that the proposed method exhibits higher safety and security than other traditional methods.
      通信作者: 周双, zhoushuang@cqnu.edu.cn ; 王兴元, xywang@dlmu.edu.cn
    • 基金项目: 国家自然科学基金 (批准号: 61672124)、国家密码学发展“十三五”密码理论基金(批准号: MMJJ20170203)、辽宁省科技创新领军人才基金(批准号: XLYC1802013)、辽宁省重点研发计划(批准号: 2019020105-JH2/103)、济南市“高校20条”资助项目引进创新团队计划(批准号: 2019GXRC031)和重庆市教委科学技术研究项目(批准号: KJQN201900529)资助的课题
      Corresponding author: Zhou Shuang, zhoushuang@cqnu.edu.cn ; Wang Xing-Yuan, xywang@dlmu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61672124), the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund, China (Grant No. MMJJ20170203), the Liaoning Province Science and Technology Innovation Leading Talents Program Project, China (Grant No. XLYC1802013), the Key R&D Projects of Liaoning Province, China (Grant No. 2019020105-JH2/103), the Jinan City’ 20 Universities’ Funding Projects-Introducing Innovation Team Program, China (Grant No. 2019GXRC031), and the Science and Technology Research Program of Chongqing Municipal Education Commission, China (Grant No. KJQN201900529)
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  • 图 1  超混沌Lorenz相图三维投影

    Fig. 1.  Three dimensional projection of hyperchaotic Lorenz phase diagram.

    图 2  LSTM训练模型示意

    Fig. 2.  LSTM training model diagram.

    图 3  混沌图像加密算法流程图(I)

    Fig. 3.  Chaotic image encryption flow chart algorithm (I).

    图 4  混沌图像加密算法流程图(Ⅱ)

    Fig. 4.  Chaotic image encryption flow chart algorithm (Ⅱ).

    图 5  $ \left\{ {y_i'} \right\} $LSTM模型训练过程

    Fig. 5.  LSTM model training process of $ \left\{ {y_i'} \right\} $.

    图 6  LSTM模型预测

    Fig. 6.  Forecast of LSTM model.

    图 7  截取的$ \left\{ {{y_i}} \right\} $

    Fig. 7.  Part of $ \left\{ {{y_i}} \right\} $.

    图 8  Wolf方法求$ \left\{ {y_i'} \right\} $最大Lyapunov指数过程图

    Fig. 8.  Using wolf method to find the largest Lyapunov exponent process of $ \left\{ {y_i'} \right\} $.

    图 9  新混沌信号0-1测试图

    Fig. 9.  0-1 test image of the new chaotic signal.

    图 10  超混沌Lorenz系统混沌信号0-1测试图

    Fig. 10.  0-1 test image of the hyperchaotic Lorenz signal.

    图 11  新混沌信号功率谱图

    Fig. 11.  The spectrum image of the new chaotic signal

    图 12  超混沌Lorenz信号功率谱图

    Fig. 12.  Spectrum image of hyperchaotic Lorenz signal.

    图 13  序列$ \left\{ {y_i'} \right\} $的相图

    Fig. 13.  Phase diagram of $ \left\{ {y_i'} \right\} $.

    图 14  序列$ \left\{ {{y_i}} \right\} $的相图

    Fig. 14.  Phase diagram of $ \left\{ {{y_i}} \right\} $.

    图 15  数字图像加密解密实验图 (a)鸟(256 × 256)原图; (b)鸟(256 × 256)加密图; (c)鸟(256 × 256)解密图; (d)辣椒(256 × 256)原图; (e)辣椒(256 × 256)加密图; (f)辣椒(256 × 256)解密图; (g)Lena(512 × 512)原图; (h) Lena(512 × 512)加密图; (i) Lena(512 × 512)解密图; (j) 液体泼洒(512 × 512)原图; (k) 液体泼洒(512 × 512)加密图; (l) 液体泼洒(512 × 512)解密图; (m)机场(1024 × 1024)原图; (n) 机场(1024 × 1024)加密图; (o) 机场(1024 × 1024)解密图; (p)飞机(1024 × 1024)原图; (q)飞机(1024 × 1024)加密图; (r)飞机(1024 × 1024)解密图

    Fig. 15.  Experimental picture of digital image encryption and decryption: (a) Original bird image; (b) encrypted bird image; (c) decrypted bird image; (d) original pepper (256 × 256) image; (e) encrypted pepper (256 × 256) image; (f) decrypted pepper (256 × 256) image; (g) original Lena (512 × 512) image; (h) encrypted Lena (512 × 512) image; (i) decrypted Lena (512 × 512) image; (j) original splash (512 × 512) image; (k) encrypted splash (512 × 512) image; (l) decrypted splash (512 × 512) image; (m) original airport (1024 × 1024) image; (n) encrypted airport (1024 × 1024) image; (o) decrypted airport (1024 × 1024) image; (p) original airplane (1024 × 1024) image; (q) encrypted airplane (1024 × 1024) image; (r) decrypted airplane (1024 × 1024) image.

    图 16  密钥敏感性 (a)明文图像; (b)密文用$ x_0' $解密结果; (c)密文用$ \left\{ {{y_i}} \right\} $解密结果

    Fig. 16.  Sensitivity of secret key: (a) Original image; (b) error key $ x_0' $ restoring diagram; (c) error key $ \left\{ {{y_i}} \right\} $ restoring diagram.

    图 17  加密解密图像直方图 (a)鸟(256 × 256)原图与明文直方图; (b)鸟(256 × 256)加密图和密图直方图; (c)辣椒(256 × 256)原图与明文直方图; (d)辣椒(256 × 256)加密图和密图直方图; (e) Lena(512 × 512)原图与明文直方图; (f) Lena(512 × 512)加密图和密图直方图; (g)水滴泼洒(512 × 512)原图与明文直方图; (h)水滴泼洒(512 × 512)加密图和密图直方图; (i)机场(1024 × 1024)原图与明文直方图; (j)机场(1024 × 1024)加密图和密图直方图; (k)飞机(1024 × 1024)原图与明文直方图; (l)飞机(1024 × 1024)加密图和密图直方图

    Fig. 17.  Histograms of plain images and ciphered images: (a) Original image and histogram of bird (256 × 256); (b)cipher image and histogram of bird (256 × 256); (c) original image and histogram of pepper (256 × 256); (d) cipher image and histogram of pepper(256 × 256); (e) original image and histogram of Lena (512 × 512); (f) cipher image and histogram of Lena (512 × 512); (g) original image and histogram of splash (512 × 512); (h) cipher image and histogram of splash (512 × 512); (i) original image and histogram of airport (1024 × 1024); (j) cipher image and histogram of airport (1024 × 1024); (k) original image and histogram of airplane (1024 × 1024); (l) cipher image and histogram of airplane (1024 × 1024).

    图 18  Lena图相关性分析 (a)明文; (b)密图

    Fig. 18.  Correlation coefficients of Lena: (a) Original image; (b) encrypted image

    图 19  抗攻击性检验 (a) 10%剪切; (b) 30%剪切; (c) 80%剪切; (d) 0.001高斯白噪声攻击; (e) 0.01高斯白噪声攻击; (f) 0.1高斯白噪声攻击

    Fig. 19.  Anti attack test: (a) 10% data missed; (b) 30% date missed; (c) 80% data missed; (d) attack of 0.001 Gaussian white noise; (e) attack of 0.01 Gaussian white noise; (f) attack of 0.1 Gaussian white noise.

    图 20  全黑全白图加密解密图像

    Fig. 20.  Encryption and decryption image of all black and all white image.

    表 1  新混沌时间序列NIST测试

    Table 1.  NIST test of the new chotic time series

    统计测试p 结果
    单比特频率测试0.8752通过
    块内频率测试0.8523通过
    游程测试0.6121通过
    块内最长1游程测试0.0828通过
    二进制矩阵秩测试0.1445通过
    离散傅里叶(谱)测试0.8152通过
    非重叠模板匹配测试0.3527通过
    重叠模板匹配测试0.4305通过
    Maurer通用统计测试0.4214通过
    线性复杂度测试0.2341通过
    序列测试0.3053通过
    近似熵测试0.1568通过
    累加和测试0.3257通过
    随机旅行测试0.1523通过
    随机旅行变种测试0.1057通过
    下载: 导出CSV

    表 2  超混沌Lorenz混沌序列NIST测试

    Table 2.  NIST test of the hyperchaotic Lorenz time series.

    统计测试p 结果
    单比特频率测试0.8815通过
    块内频率测试0.7253通过
    游程测试0.5986通过
    块内最长1游程测试0.0823通过
    二进制矩阵秩测试0.1263通过
    离散傅里叶(谱)测试0.8164通过
    非重叠模板匹配测试0.3580通过
    重叠模板匹配测试0.5216通过
    Maurer通用统计测试0.4418通过
    线性复杂度测试0.5052通过
    序列测试0.6015通过
    近似熵测试0.1435通过
    累加和测试0.4863通过
    随机旅行测试0.3997通过
    随机旅行变种测试0.2265通过
    下载: 导出CSV

    表 3  混沌信号统计参数对比

    Table 3.  Comparison of statistical parameters of chaotic signals.

    信号来源最大Lyapunov
    指数
    0-1
    测试
    功率谱
    分析
    相图NIST
    测试
    超混沌Lorenz0.3381[52]0.7937混沌混沌随机
    深度学习2.60020.9250混沌混沌随机
    下载: 导出CSV

    表 4  NPCR和UACI

    Table 4.  NPCR and UACI.

    图片改变$ P(256, 256) $
    NPCR/%UACI/%
    Bird ($ 256 \times 256 $)99.5633.35
    Cameraman ($ 256 \times 256 $)99.6333.30
    Pepper ($ 256 \times 256 $)99.6233.39
    House ($ 256 \times 256 $)99.6333.37
    Lena ($ 512 \times 512 $)99.5833.38
    Airplane ($ 512 \times 512 $)99.5933.42
    Tank ($ 512 \times 512 $)99.6133.49
    Splash ($ 512 \times 512 $)99.6433.54
    Truck ($ 512 \times 512 $)99.6033.47
    Airport ($ 1024 \times 1024 $)99.6233.48
    Airplane ($ 1024 \times 1024 $)99.6033.47
    下载: 导出CSV

    表 5  NPCR和UACI的平均值与其他加密算法的比较

    Table 5.  The average of NPCR and UACI and comparison with other algorithms.

    本文平均值文献[10]文献[13]文献[58]文献[59]
    NPCR/%99.60499.6199.664199.6199.6114
    UACI/%33.4633.4833.612433.4633.4523
    下载: 导出CSV

    表 6  图像相关系数

    Table 6.  Correlation coefficients of images.

    图片明文 密文
    水平垂直对角反对角水平垂直对角反对角
    Lena0.98440.96680.96200.9790 –0.00160.0014–0.0014–0.0010
    Bird0.98890.98260.97130.95190.01140.01030.0104–0.0031
    Cameraman0.95910.93350.91010.9377–0.00990.0141–0.0165–0.0028
    Pepper0.96380.95850.93680.9339–0.0127–0.0014–0.00790.0134
    Airport0.90660.90720.84460.8752–0.00910.0088–0.0014–0.0054
    Splash
    0.99250.98500.97970.95070.00820.00160.0039–0.0060
    Airplane0.94760.96640.94180.9299–0.0278–0.01050.0013–0.0083
    House0.95490.97800.93990.90270.0141–0.0115–0.01760.0005
    Tank0.86780.88150.84140.7949–0.00360.0003–0.0098–0.0065
    Truck0.92580.95610.91140.81940.0028–0.00410.00180.0074
    下载: 导出CSV

    表 7  密文图像相关系数比较

    Table 7.  Comparison of the correlation coefficients of images.

    Lena文献[10]文献[13]文献[58]文献[59]
    水平–0.0016–0.000070.00047–0.00251–0.038118
    垂直0.0014–0.0024–0.03911–0.00292–0.029142
    对角–0.00140.00190.00305–0.001560.002736
    下载: 导出CSV

    表 8  信息熵

    Table 8.  Information entropy of images.

    图片图片大小信息熵
    House$ 256 \times 256 $7.9969
    Cameraman$ 256 \times 256 $7.9971
    Bird$ 256 \times 256 $7.9968
    Pepper$ 256 \times 256 $7.9971
    Lena$ 512 \times 512 $7.9993
    Splash$ 512 \times 512 $7.9993
    Airplane$ 512 \times 512 $7.9993
    Tank$ 512 \times 512 $7.9994
    Truck$ 512 \times 512 $7.9993
    Airport$ 1024 \times 1024 $7.9998
    Airplane$ 1024 \times 1024 $7.9998
    下载: 导出CSV

    表 9  全黑全白图的统计分析

    Table 9.  The statistical analysis of all-black image and all-white image.

    NPCRUACI信息熵相关系数
    水平垂直对角
    全黑图0.99580.33327.99700.00160.00030.0036
    全白图0.99610.33517.99710.00700.00040.0070
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-03-25
  • 修回日期:  2021-07-08
  • 上网日期:  2021-08-17
  • 刊出日期:  2021-12-05

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