光学仪器  2023, Vol. 45 Issue (1): 60-66 PDF

1. 上海理工大学 光电信息与计算机工程学院，上海 200093;
2. 上海理工大学 出版印刷与艺术设计学院，上海 200093;
3. 中船勘察设计研究院有限公司，上海 200063;
4. 上海工程技术大学 图书馆，上海 201620

Multiple image encryption studies based on a cascaded phase retrieval and ghost imaging
ZHANG Leihong1, SU Yahui2, WANG Kaimin1, ZHANG Dawei1, PENG Wei3, WU Fengshou3, ZHOU Jie4
1. School of Optical-Electrical and computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;
2. College of Communication and Art Design, University of Shanghai for Science and Technology, Shanghai 200093, China;
3. China Shipbuilding Industry Institute of the Engineering Investigation and Design Co., Ltd., Shanghai 200063, China;
4. Library, Shanghai University of Engineering Science, Shanghai 201620, China
Abstract: Optical information processing technology has the characteristics of high speed and parallelism. The wavelength of light is short and the information capacity is large. At the same time, it has many attributes such as amplitude, phase, wavelength and polarization, which could be the carrier of multi-dimensional information. Therefore, optical encryption is of great significance in the field of information security transmission and is widely used in the field of image encryption. For multiple image encryption, this paper proposes a multi image encryption algorithm based on cascaded phase iteration and computational ghost imaging. This method can encrypt multiple images efficiently at the same time, which is simple, safe and reliable, and has less transmission data. The encryption effect of this method is evaluated by using correlation coefficient, and the effectiveness and security of this method are verified by simulation.
Key words: cascaded phase retrieval algorithm    computational ghost imaging    image processing    multi-image encryption

1 基于CPRA与CGI的多图像加密原理 1.1 CPRA加密原理

 图 1 4f相关器的光学加密系统 Figure 1 Optical encryption system for the 4f correlator
 $\begin{split} {{\displaystyle g}}^{k}\left(x,y\right) &\mathrm{exp}\left[{\rm{i}}{{\displaystyle \phi }}^{k}\left(x,y\right)\right]=\\ &{{\displaystyle IFT}}\left(FT\left\{f\left(x,y\right)\mathrm{exp}\left[{\rm{i}}{{\displaystyle \theta }}^{k}\left(x,y\right)\right]\right\}\times \right.\\ & \left.\mathrm{exp}\left[{\rm{i}}{{\displaystyle \varphi }}^{k}\left(u,v\right)\right]\right) \end{split}$ (1)

 $\begin{split} \varphi ^{k + 1} \left( {u,v} \right) =& angle\left\{ {\dfrac{{FT\left\{ {g\left( {x,y} \right)\exp \left[ {{\rm{i}} \phi ^k \left( {x,y} \right)} \right]} \right\}}}{{FT\left\{ {f\left( {x,y} \right)\exp \left[ {{\rm{i}}\theta ^k \left( {x,y} \right)} \right]} \right\}}}} \right\} \\ \theta ^{k + 1} \left( {x,y} \right) =& angle\left\{ { {IFT} \left( {FT\left\{ {g\left( {x,y} \right)\exp \left[ {{\rm{i}}\phi ^k \left( {x,y} \right)} \right]} \right\} \times}\right.}\right.\\ &\left.{\left.{\exp \left[ { - {\rm{i}} \varphi ^{k + 1} \left( {u,v} \right)} \right]} \right)} \right\} \\[-13pt] \end{split}$ (2)

 $CC = \dfrac{{{cov} \left[ {g\left( {x,y} \right),\mathop g\nolimits^k \left( {x,y} \right)} \right]}}{{\mathop \sigma \nolimits_g \mathop \sigma \nolimits_{\mathop g\nolimits^k } }}$ (3)

1.2 CGI加密原理

GI作为一种非局域成像方式，在成像时，经过空间光调制器调制的光束先被分成参考光路和物体所在光路，然后经光学器件收集光学信息。参考光路和物体光路的光学信息经过二阶关联计算，可以实现对信息的重构[14]。而CGI方法则简化了装置，省略了参考光路，见图2

 图 2 CGI原理图 Figure 2 Schematic diagram of CGI

 $\mathop B\nolimits_i = \displaystyle\int {T\left( {x,y} \right)} \mathop I\nolimits_i \left( {x_p,y_q} \right){\rm{d}}x{\rm{d}}y$ (4)

 $\mathop {\boldsymbol{I}}\nolimits_i = \left | {\begin{array}{*{20}{c}} {\mathop I\nolimits_{11}^i }& \cdots &{\mathop I\nolimits_{1n}^i } \\ \vdots & & \vdots \\ {\mathop I\nolimits_{n1}^i }& \cdots &{\mathop I\nolimits_{nn}^i } \end{array}} \right|$ (5)

 $\begin{split} \mathop {\boldsymbol{I}}\nolimits_i =& \left[ \begin{array}{*{20}{c}} {\mathop I\nolimits_{11}^i } & {\mathop I\nolimits_{12}^i } & \cdots & {\mathop I\nolimits_{1n}^i } & {\mathop I\nolimits_{21}^i } & {\mathop I\nolimits_{22}^i } & \cdots \end{array} \right. \\ & \left. \begin{array}{*{20}{c}} & {\mathop I\nolimits_{nn - 1}^i } & {\mathop I\nolimits_{nn}^i} \end{array} \right] \end{split}$ (6)

 $\begin{split} \left[ {\begin{array}{*{20}{c}} {\mathop B\nolimits_1 } \\ {\begin{array}{*{20}{c}} {\mathop B\nolimits_2 } \\ {\begin{array}{*{20}{c}} \vdots \\ {\mathop B\nolimits_M } \end{array}} \end{array}} \end{array}} \right] =& \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\mathop I\nolimits_{11}^1 } \\ {\mathop I\nolimits_{11}^2 } \\ \vdots \\ {\mathop I\nolimits_{11}^M } \end{array}}&{\begin{array}{*{20}{c}} \cdots \\ \cdots \\ \\ \cdots \end{array}} \end{array}}&{\begin{array}{*{20}{c}} {\mathop I\nolimits_{1n}^1 } \\ {\mathop I\nolimits_{1n}^2 } \\ \vdots \\ {\mathop I\nolimits_{1n}^M } \end{array}}&{\begin{array}{*{20}{c}} \cdots \\ \cdots \\ \\ \cdots \end{array}}&{\begin{array}{*{20}{c}} {\mathop I\nolimits_{nn}^1 } \\ {\mathop I\nolimits_{nn}^2 } \\ \vdots \\ {\mathop I\nolimits_{nn}^M } \end{array}} \end{array}} \right] \cdot \\ &\left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\mathop T\nolimits_{11} } \\ \vdots \end{array}} \\ {\mathop T\nolimits_{1n} } \\ \vdots \\ {\mathop T\nolimits_{nn} } \end{array}} \right]\\[-45pt] \end{split}$ (7)

 ${T_{{\rm{CS}}}}\left( {x,y} \right) = \left\langle {\mathop B\nolimits_i \mathop I\nolimits_i \left( {x,y} \right)} \right\rangle - \left\langle {\mathop B\nolimits_i } \right\rangle \left\langle {\mathop I\nolimits_i \left( {x,y} \right)} \right\rangle$ (8)

 $\mathop T\nolimits_{{\rm{CS}}} = \mathop T\nolimits' ,\arg \min \left\| {{\mathit{\Psi}} \left\{ {\mathop T\nolimits' \left( {x,y} \right)} \right\}} \right\|$ (9)
2 基于CPRA与CGI的多图像加解密流程

 图 3 CPRA加密系统 Figure 3 CPRA encryption system
 $g_{0n + 1}^k \exp \left( {{\rm{i}} \phi _n } \right) = IFT\left\{ {FT\left[ { g_{0n}^k \exp \left( {{\rm{i}} \theta _n } \right)} \right]\exp( {\rm{i }}\varphi _n) } \right\}$ (10)

 $\begin{split} g_{0n + 1}^k \exp \left( {{\rm{i}} \phi _n } \right) =& IFT\left\{ {FT\left[ { g_{0n}^k \exp \left( {{\rm{i}} \phi _{n - 1} } \right)\exp \left( { - {\rm{i}} \phi _{n - 1} } \right) \times } \right.} \right.\\ & \left.{ \left.{ \exp \left( {{\rm{i}} \theta _n } \right)} \right]\exp \left( {{\rm{i}} \varphi _n } \right)} \right\}\\[-10pt] \end{split}$ (11)

 $\begin{split} g_{0n + 1}^k \exp \left( {{\rm{i}} \phi _n } \right) =& IFT\left[ {FT\left\{ { g_{0n}^k \exp \left( {{\rm{i}} \phi _{n - 1} } \right) } \right.} \right.\times\\ &\left.{\left.{\exp \left[ {{\rm{i}}\left( { \theta _n - \phi _{n - 1} } \right)} \right]} \right\}} \right]\exp \left( {{\rm{i}} \varphi _n } \right) \end{split}$ (12)

 $\begin{split} g_{0n}^k \exp \left( {{\rm{i}} \phi _{n - 1} } \right) =& IFT\left[ {FT\left\{ { g_{0n + 1}^k \exp \left( {{\rm{i}} \phi _n } \right) \times} \right.} \right.\\ & \left.{ \left.{\exp \left( { - {\rm{i}} \varphi _n } \right)} \right\}} \right] \times \exp \left[ { - {\rm{i}}\left( { \theta _n - \theta _{n - 1} } \right)} \right] \end{split}$ (13)

3 仿真与分析

 （a）输入图像，（b）~（d）目标图像，（e）~（h）解密图像 图 4 加解密结果 Figure 4 Encryption and decryption of the results

 图 5 CPRA阶段不同阶次相位掩码错误时的解密情况 Figure 5 Decryption of different orders of subphase mask errors in the CPRA

 （a1）~（a4）、（b1）~（b4）、（c1）~（c4）、（d1）~（d4）、（e1）~（e4）裁剪比例分别是10%，20%，30%，40%，50% 图 6 不同裁剪程度下的明文图像解密结果 Figure 6 Decryption results of plaintext images under different cropping degrees

4 结 论

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