A Jigsaw Puzzle SolverBased Attack on Image Encryption Using Vision Transformer for PrivacyPreserving DNNs
Abstract
:1. Introduction
2. Preparation
2.1. PrivacyPreserving DNNs
2.2. Image Encryption for PrivacyPreserving DNNs
 Divide the RGB color image I into blocks of $M\times M$ pixels.
 Separate each pixel into upper and lower 4 bit pixel values to form sixchannel blocks.
 Reverse the intensities of the pixel values in each block randomly by a secret key.
 Shuffle the pixel values in each block randomly by a secret key.
 Combine six channels in each block into three channel to generate an encrypted image.
 Divide RGB color image I into blocks of $M\times M$ pixels.
 Permute randomly the divided blocks by using a secret key.
 The same procedure of LE is applied to the permuted blocks to generate an encrypted image.
 Divide RGB color image I into $X\times Y$ pixels.
 Apply negative–positive transformations to each pixel of the three color channels randomly by using a secret key. In this scheme, the secret key is independently used for all color components. In this step, a pixel q is transformed to ${q}^{\prime}$ by$${q}^{\prime}=\left(\right)open="\{"\; close>\begin{array}{cc}q\hfill & \left(r\right(i)=0)\hfill \\ q\oplus ({2}^{8}1)\hfill & \left(r\right(i)=1)\hfill \end{array},$$
 Shuffle three color components of each pixel by using a secret key.
 Combine $X\times Y$ pixels to generate an encrypted image.
 Divide RGB color image I into blocks of $M\times M$ pixels.
 Permute randomly the divided blocks using a secret key.
 Rotate and invert randomly each block by using a secret key.
 Apply negative–positive transformations to each block by using a secret key according to Equation (1).
 Shuffle three color components of each block by using a secret key.
 Integrate the encrypted blocks to generate an encrypted image.
 Divide an RGB color image I into blocks $B=\{{B}_{1},\dots ,{B}_{i},\dots ,{B}_{n}\}$, $i\in \{1,\dots ,n\}$ with $M\times M$ pixels, where n is the number of divided blocks calculated by$$n=\lfloor \frac{X}{M}\rfloor \times \lfloor \frac{Y}{M}\rfloor .$$
 Permute the divided blocks by using a secret key ${K}_{VTE1}$, where ${K}_{VTE1}$ is commonly used for all color components. Accordingly, the scrambled blocks ${B}^{\prime}=\{{B}_{1}^{\prime},\dots ,{B}_{i}^{\prime},\dots ,{B}_{n}^{\prime}\}$ are generated.
 Divide each scrambled block ${B}_{i}^{\prime}$ into four nonoverlapping square subblocks ${S}_{ij},j\in \{UL,UR,LL,LR\}$ with $\frac{M}{2}\times \frac{M}{2}$ pixels, where ${S}_{iUL}$ is defined as the upper left position of the ith blocks, ${S}_{iUR}$ as the upper right, ${S}_{iLL}$ as the lower left, and ${S}_{iLR}$ as the lower right. Thereby, scrambled blocks divided into subblocks $S=\{{S}_{1j},\dots ,{S}_{ij},\dots ,{S}_{nj}\}$ are generated. The number of subblocks m is described as$$m=4n.$$
 Shuffle the pixel position within a subblock by using a secret key ${K}_{VTE2}$ to generate pixel shuffled subblocks ${S}^{\prime}=\{{S}_{1j}^{\prime},\dots ,{S}_{ij}^{\prime},\dots ,{S}_{nj}^{\prime}\}$, where ${K}_{VTE2}$ is commonly used for all subblocks and color components. As a result, each scrambled block is divided into four encrypted subblocks, denoted by ${S}_{i}^{\prime}=\{{S}_{iUL}^{\prime},{S}_{iUR}^{\prime},{S}_{iLL}^{\prime},{S}_{iLR}^{\prime}\}$.
 Merge all blocks to generate an encrypted image.
3. Proposed Attacks
3.1. Threat Models
Algorithm 1 FRattack [14] 

3.2. Jigsaw Puzzle SolverBased Attack
4. Experiments
4.1. Experimental Conditions
4.2. Experimental Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Plain  LE [11]  PE [12]  ELE [13]  EtC [28]  VTE [20]  

Block scrambling  √  √  √  
Key type  Same  Different  Different  Same  Same  
Key space  $({M}^{2}\xb76)!\phantom{\rule{0.166667em}{0ex}}\xb7{2}^{{M}^{2}\xb76}$  ${2}^{3\xb7X\xb7Y}\xb7{6}^{X\xb7Y}$  ${(({M}^{2}\xb76)!\phantom{\rule{0.166667em}{0ex}}\xb7{2}^{{M}^{2}\xb76})}^{n}$$\xb7n!\phantom{\rule{0.166667em}{0ex}}$  ${8}^{n}\xb7{2}^{n}\xb7{6}^{n}\xb7n!\phantom{\rule{0.166667em}{0ex}}$  $n!\phantom{\rule{0.166667em}{0ex}}\xb7{\left(\frac{M}{2}\right)}^{2}!$  
Example  
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Chuman, T.; Kiya, H. A Jigsaw Puzzle SolverBased Attack on Image Encryption Using Vision Transformer for PrivacyPreserving DNNs. Information 2023, 14, 311. https://doi.org/10.3390/info14060311
Chuman T, Kiya H. A Jigsaw Puzzle SolverBased Attack on Image Encryption Using Vision Transformer for PrivacyPreserving DNNs. Information. 2023; 14(6):311. https://doi.org/10.3390/info14060311
Chicago/Turabian StyleChuman, Tatsuya, and Hitoshi Kiya. 2023. "A Jigsaw Puzzle SolverBased Attack on Image Encryption Using Vision Transformer for PrivacyPreserving DNNs" Information 14, no. 6: 311. https://doi.org/10.3390/info14060311