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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.
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Keywords:
- chaotic system/
- image encryption/
- deep learning
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统计测试 p值 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 
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统计测试 p值 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:
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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Lorenz 0.3381[52] 0.7937 混沌 混沌 随机 深度学习 2.6002 0.9250 混沌 混沌 随机 下载:
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图片 改变$ P(256, 256) $ NPCR/% UACI/% Bird ($ 256 \times 256 $) 99.56 33.35 Cameraman ($ 256 \times 256 $) 99.63 33.30 Pepper ($ 256 \times 256 $) 99.62 33.39 House ($ 256 \times 256 $) 99.63 33.37 Lena ($ 512 \times 512 $) 99.58 33.38 Airplane ($ 512 \times 512 $) 99.59 33.42 Tank ($ 512 \times 512 $) 99.61 33.49 Splash ($ 512 \times 512 $) 99.64 33.54 Truck ($ 512 \times 512 $) 99.60 33.47 Airport ($ 1024 \times 1024 $) 99.62 33.48 Airplane ($ 1024 \times 1024 $) 99.60 33.47 下载:
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图片 明文 密文 水平 垂直 对角 反对角 水平 垂直 对角 反对角 Lena 0.9844 0.9668 0.9620 0.9790 –0.0016 0.0014 –0.0014 –0.0010 Bird 0.9889 0.9826 0.9713 0.9519 0.0114 0.0103 0.0104 –0.0031 Cameraman 0.9591 0.9335 0.9101 0.9377 –0.0099 0.0141 –0.0165 –0.0028 Pepper 0.9638 0.9585 0.9368 0.9339 –0.0127 –0.0014 –0.0079 0.0134 Airport 0.9066 0.9072 0.8446 0.8752 –0.0091 0.0088 –0.0014 –0.0054 Splash 0.9925 0.9850 0.9797 0.9507 0.0082 0.0016 0.0039 –0.0060 Airplane 0.9476 0.9664 0.9418 0.9299 –0.0278 –0.0105 0.0013 –0.0083 House 0.9549 0.9780 0.9399 0.9027 0.0141 –0.0115 –0.0176 0.0005 Tank 0.8678 0.8815 0.8414 0.7949 –0.0036 0.0003 –0.0098 –0.0065 Truck 0.9258 0.9561 0.9114 0.8194 0.0028 –0.0041 0.0018 0.0074 下载:
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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:
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NPCR UACI 信息熵 相关系数 水平 垂直 对角 全黑图 0.9958 0.3332 7.9970 0.0016 0.0003 0.0036 全白图 0.9961 0.3351 7.9971 0.0070 0.0004 0.0070 下载:
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