图 1  Lyapunov指数谱

Fig. 1.  Lyapunov exponent diagram.

图 2  系统(2)随$f$变化的分岔图

Fig. 2.  Bifurcation diagram of system (2) variation with $f$.

图 3  时间序列图　(a) $x\text- t$时间序列; (b) $y \text- t$时间序列; (c) $z \text- t$时间序列; (d) $w \text- t$时间序列; (e) $v \text- t$时间序列

Fig. 3.  Time series diagram: (a) $x \text- t$ time series; (b) $y \text- t$ time series; (c) $z \text- t$ time series; (d) $w \text- t$ time series; (e) $v \text- t$time series

图 4  三维相图　(a) $x \text- y \text- z$三维图; (b) $x \text- y \text- w$三维图; (c) $x \text- y \text- v$三维图; (d) $x \text- z \text- w$三维图; (e) $x \text- z \text- v$三维图; (f) $x \text- w \text- v$三维图; (g) $y \text- z \text- w$三维图; (h) $y \text- z \text- v$三维图; (i) $y \text- w \text- v$三维图; (j) $z \text- w \text- v$三维图

Fig. 4.  Three-dimensional phase diagram: (a) $x \text- y \text- z$ Three-dimensional map; (b) $x \text- y \text- w$ Three-dimensional map; (c) $x \text- y \text- v$ Three-dimensional map; (d) $x \text- z \text- w$ Three-dimensional map; (e) $x \text- z \text- v$ Three-dimensional map; (f) $x \text- w \text- v$ Three-dimensional map; (g) $y \text- z \text- w$ Three-dimensional map; (h) $y \text- z \text- v$ Three-dimensional map; (i) $x \text- y \text- z$ Three-dimensional map; (j) $z \text- w \text- v$ Three-dimensional map.

图 5  二维平面相图　(a) $x \text- y$平面; (b) $x \text- z$平面; (c) $x \text- v$平面; (d) $y \text- z$平面; (e) $y \text- w$平面; (f) $z \text- w$平面; (g) $z \text- v$平面

Fig. 5.  Two-dimensional plane phase diagram: (a) $x \text- y$ flat; (b) $x \text- z$ flat; (c) $x \text- v$ flat; (d) $y \text- z$ flat; (e) $y \text- w$ flat; (f) $z \text- w$ flat; (g) $z \text- v$ flat.

图 6  数字图像加解密实验图　(a) lena原图; (b) lena加密图像; (c) lena解密图像; (d) baboon原图; (e) baboon加密图像; (f) baboon解密图像; (g) boat原图; (h) boat加密图像; (i) boat解密图像

Fig. 6.  Digital image encryption and decryption experiment: (a) Original Lena image; (b) encrypted Lena image; (c) decrypted Lena image; (d) original baboon image; (e) encrypted baboon image; (f) decrypted baboon image; (g) original boat image.; (h) encrypted boat image; (i)decrypted boat image.

图 7  明文图像和密文图像直方图　(a) lena明文直方图; (b) lena密文直方图; (c) baboon明文直方图; (d) baboon密文直方图; (e) boat明文直方图; (f) boat密文直方图

Fig. 7.  Histogram of plaintext and ciphertext images (a) Plaintext Lena image histogram; (b) ciphertext Lena image histogram; (c) plaintext baboon image histogram; (d) ciphertext baboon image histogram; (e) plaintext boat image histogram; (f) ciphertext boat image histogram.

图 8  密钥敏感性测试图　(a)明文图像; (b)密文${{{Y}}_1}$(密钥为${y_0}$); (c)密文${{{Y}}_2}$(密钥为${y_1}$); (d) ${{{Y}}_1}$正确解密结果; (e) ${{{Y}}_1}$用${y_1}$错误解密结果; (f) ${{{Y}}_2}$用${y_0}$错误解密结果

Fig. 8.  Key sensitivity tests: (a) Plain-image; (b) cipher ${{{Y}}_1}$ with key ${y_0}$; (c) cipher ${{{Y}}_2}$ with key ${y_1}$; (d) right decrypted ${{{Y}}_1}$; (e) decrypted ${{{Y}}_1}$ with ${y_1}$; (f) decrypted${{{Y}}_2}$ with${y_0}$.

图 9  baboon图像加密前后三个方向上的相关性分析图　(a), (b)对角相邻; (c), (d)水平相邻; (e), (f)垂直相邻;

Fig. 9.  Correlation analysis chart in three directions before and after baboon image encryption: (a), (b) Diagonally adjacent; (c), (d) horizontally adjacent; (e), (f) vertically adjacent.

图 10  抗剪切攻击能力分析图　(a)剪切前密文; (b)剪切后密文; (c)剪切前解密; (d)剪切后解密

Fig. 10.  Anti-shear attack capability analysis chart: (a) Ciphertext before cutting; (b) ciphertext after cutting; (c) decrypted image before cutting; (d) decrypted image after cutting.

图 11  抗噪声攻击能力分析图　(a)加噪前密文; (b)加噪后密文; (c)加噪前解密; (d)加噪后解密

Fig. 11.  Anti-noise attack capability analysis chart: (a) Ciphertext before adding noise; (b) ciphertext after adding noise; (c) decrypted image before adding noise; (d) decrypted image after adding noise.