# A Maze Matrix-Based Secret Image Sharing Scheme with Cheater Detection

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## Abstract

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## 1. Introduction

## 2. Related Work

## 3. The Proposed Secret Image Sharing Scheme

#### 3.1. The Maze Matrix

#### 3.2. The Data Embedding and Extraction Scheme

#### 3.3. The Sshare Construction Algorithm

#### 3.4. The Data Extraction Algorithm

#### 3.5. The Cheat Event Detection and Cheater Detection Mechanism

## 4. Experimental Results

#### 4.1. Share Construction and Data Extraction

#### 4.2. Cheat Event Detection and Cheater Detection

#### 4.3. Comparison with Liu et al.’s Scheme [26]

#### 4.4. Time Efficiency Evaluation

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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$\mathit{s}{\mathit{g}}_{\mathit{j}}$ | $\left({\mathit{p}}_{\mathit{x}}^{\prime},{\mathit{p}}_{\mathit{y}}^{\prime}\right)$ | $\mathit{s}{\mathit{g}}_{\mathit{j}}$ | $\left({\mathit{p}}_{\mathit{x}}^{\prime},{\mathit{p}}_{\mathit{y}}^{\prime}\right)$ | $\mathit{s}{\mathit{g}}_{\mathit{j}}$ | $\left({\mathit{p}}_{\mathit{x}}^{\prime},{\mathit{p}}_{\mathit{y}}^{\prime}\right)$ | $\mathit{s}{\mathit{g}}_{\mathit{j}}$ | $\left({\mathit{p}}_{\mathit{x}}^{\prime},{\mathit{p}}_{\mathit{y}}^{\prime}\right)$ |
---|---|---|---|---|---|---|---|

0 | $\left(0,\text{}0\right)$ | 4 | $\left(0,\text{}5\right)$ | 8 | $\left(5,5\right)$ | 12 | $\left(5,\text{}0\right)$ |

1 | $\left(0,\text{}2\right)$ | 5 | $\left(1,\text{}5\right)$ | 9 | $\left(5,\text{}4\right)$ | 13 | $\left(3,\text{}0\right)$ |

2 | $\left(0,\text{}3\right)$ | 6 | $\left(2,\text{}5\right)$ | 10 | $\left(5,\text{}3\right)$ | 14 | $\left(2,\text{}0\right)$ |

3 | $\left(0,\text{}4\right)$ | 7 | $\left(3,\text{}5\right)$ | 11 | $\left(5,\text{}2\right)$ | 15 | $\left(1,\text{}0\right)$ |

Cover Image 1 | Cover Image 2 | PSNR (dB) | Embedding Capacity (bits) | ||
---|---|---|---|---|---|

Shadow 1 | Shadow 2 | ||||

Pair 1 | Lena | baboon | 39.88 | 39.89 | 1,048,576 |

Pair 2 | Tiffany | Barbara | 39.86 | 39.90 | 1,048,576 |

Pair 3 | airplane | peppers | 39.87 | 39.88 | 1,048,576 |

Pair 4 | boat | Goldhill | 39.88 | 39.88 | 1,048,576 |

Pair 5 | toys | girl | 39.90 | 39.88 | 1,048,576 |

Pair 6 | Elaine | sailboat | 39.88 | 39.88 | 1,048,576 |

Tampered Shadow | DR_{J} |
---|---|

Lena | 0.42 |

Tiffany | 0.42 |

airplane | 0.42 |

boat | 0.42 |

toys | 0.42 |

Elaine | 0.42 |

Tampered Shadow | DR_{B1} |
---|---|

Lena | 0.20 |

Tiffany | 0.20 |

airplane | 0.20 |

boat | 0.20 |

toys | 0.20 |

Elaine | 0.20 |

Shadow 1 | Shadow 2 | $\mathit{D}{\mathit{R}}_{1}$ | $\mathit{D}{\mathit{R}}_{2}$ | $\mathit{D}{\mathit{R}}_{1\cap 2}$ | $\mathit{D}{\mathit{R}}_{1\cup 2}$ | |
---|---|---|---|---|---|---|

Pair 1 | Lana | baboon | 0.43 | 0.43 | 0.72 | 0.52 |

Pair 2 | Tiffany | Barbara | 0.42 | 0.42 | 0.73 | 0.52 |

Pair 3 | airplane | peppers | 0.44 | 0.42 | 0.73 | 0.53 |

Pair 4 | boat | Goldhill | 0.43 | 0.43 | 0.71 | 0.52 |

Pair 5 | toys | girl | 0.43 | 0.43 | 0.71 | 0.53 |

Pair 6 | Elaine | sailboat | 0.43 | 0.43 | 0.72 | 0.53 |

Hiding Scheme | PSNR | EC | $\mathit{D}{\mathit{R}}_{\mathit{J}\mathit{S}}$ | $\mathit{D}{\mathit{R}}_{\mathit{J}\mathit{C}}$ | $\mathit{D}{\mathit{R}}_{\mathit{B}}$ |
---|---|---|---|---|---|

Maze matrix | 39.88 | 4 | 0.43 | 0.72 | 0.20 |

Turtle shell [26] | 41.71 | 3 | 0.50 | 0.50 | — |

Cover Images | Execution Time (sec) | |
---|---|---|

Conventional Scheme | Proposed Scheme | |

Pair 1 | 0.1297 | 0.0692 |

Pair 2 | 0.1425 | 0.0747 |

Pair 3 | 0.1074 | 0.0737 |

Pair 4 | 0.1030 | 0.0703 |

Pair 5 | 0.1110 | 0.0708 |

Pair 6 | 0.1055 | 0.0709 |

Average | 0.1165 | 0.0716 |

Stego Images | Execution Time (sec) |
---|---|

Pair 1 | 0.0366 |

Pair 2 | 0.0361 |

Pair 3 | 0.0382 |

Pair 4 | 0.0366 |

Pair 5 | 0.0411 |

Pair 6 | 0.0348 |

Average | 0.0372 |

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## Share and Cite

**MDPI and ACS Style**

Chang, C.-C.; Horng, J.-H.; Shih, C.-S.; Chang, C.-C. A Maze Matrix-Based Secret Image Sharing Scheme with Cheater Detection. *Sensors* **2020**, *20*, 3802.
https://doi.org/10.3390/s20133802

**AMA Style**

Chang C-C, Horng J-H, Shih C-S, Chang C-C. A Maze Matrix-Based Secret Image Sharing Scheme with Cheater Detection. *Sensors*. 2020; 20(13):3802.
https://doi.org/10.3390/s20133802

**Chicago/Turabian Style**

Chang, Ching-Chun, Ji-Hwei Horng, Chia-Shou Shih, and Chin-Chen Chang. 2020. "A Maze Matrix-Based Secret Image Sharing Scheme with Cheater Detection" *Sensors* 20, no. 13: 3802.
https://doi.org/10.3390/s20133802