# Research on Image Steganography Based on Sudoku Matrix

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## Abstract

**:**

## 1. Introduction

## 2. Research Status

## 3. Research Methods

#### 3.1. Research Plan

#### 3.1.1. Design of Magic Matrices

- 16 × 16 Sudoku matrix

- 2.
- Double-layer magic matrix

#### 3.1.2. Determination of Traversal Area

#### 3.2. Evaluation Methods

- Visual effect

- 2.
- Embedding rate (ER)

- 3.
- Peak signal-to-noise ratio (PSNR)

## 4. Experimental Analysis

#### 4.1. Turtle Shell Magic Matrix-Based Image Steganography

#### 4.2. 4 × 4 Magic Matrix-Based Image Steganography

#### 4.3. 4-2 Double-Layer Magic Matrix-Based Image Steganography

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) Basic magic matrix as traversal area. (

**b**) Traversal area with origin on the inside lower right.

**Figure 5.**Image contrast according to 4 × 4 magic matrix-based data hiding method, with stego-images displayed in green box; they should be listed as (

**a**) original image of baboon, (

**b**) stego-image of (

**a**), (

**c**) original image of pepper, (

**d**) stego-image of (

**c**), (

**e**) original image of airplane, (

**f**) stego-image of (

**e**), (

**g**) original image of house, and (

**h**) stego-image of (

**g**).

Cover Image | Chang et al.′s Scheme (TDH) | Low-Com-Cost-2020 | Low-Com-Cost_TS | |||
---|---|---|---|---|---|---|

EC (bpp) | PSNR (dB) | EC (bpp) | PSNR (dB) | EC (bpp) | PSNR (dB) | |

Airplane | 1.5 | 49.76 | 1.5 | 50.17 | 1.5 | 49.2 |

Baboon | 1.5 | 49.76 | 1.5 | 50.17 | 1.5 | 49.2 |

Boat | 1.5 | 49.76 | 1.5 | 50.17 | 1.5 | 49.24 |

House | 1.5 | 49.75 | 1.5 | 50.17 | 1.5 | 49.2 |

Paper | 1.5 | 49.76 | 1.5 | 50.17 | 1.5 | 49.2 |

Average | 1.5 | 49.76 | 1.5 | 50.17 | 1.5 | 49.21 |

Cover Image | ER (bpp) | PSNR (dB) | Hiding Duration | Extraction Duration |
---|---|---|---|---|

Baboon | 2 | 46.3651 | 0.0256 | 0.0121 |

Paper | 2 | 46.3604 | 0.0282 | 0.0137 |

Airplane | 2 | 46.3658 | 0.0266 | 0.0135 |

House | 2 | 46.3583 | 0.0305 | 0.0128 |

Avg | 2 | 46.3624 | 0.0277 | 0.0130 |

Cover Image | ER (bpp) | PSNR (dB) | Hiding Duration | Extraction Duration |
---|---|---|---|---|

Airplane | 3 | 40.73 | 0.041 | 0.0188 |

Baboon | 3 | 40.731 | 0.0417 | 0.0221 |

Boat | 3 | 40.725 | 0.0419 | 0.0187 |

House | 3 | 40.727 | 0.0429 | 0.0193 |

Paper | 3 | 40.728 | 0.0421 | 0.0185 |

Avg | 3 | 40.728 | 0.0419 | 0.0195 |

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**MDPI and ACS Style**

Hsiao, T.-C.; Liu, D.-X.; Chen, T.-L.; Chen, C.-C.
Research on Image Steganography Based on Sudoku Matrix. *Symmetry* **2021**, *13*, 387.
https://doi.org/10.3390/sym13030387

**AMA Style**

Hsiao T-C, Liu D-X, Chen T-L, Chen C-C.
Research on Image Steganography Based on Sudoku Matrix. *Symmetry*. 2021; 13(3):387.
https://doi.org/10.3390/sym13030387

**Chicago/Turabian Style**

Hsiao, Tsung-Chih, Dong-Xu Liu, Tzer-Long Chen, and Chih-Cheng Chen.
2021. "Research on Image Steganography Based on Sudoku Matrix" *Symmetry* 13, no. 3: 387.
https://doi.org/10.3390/sym13030387