# Data Hiding Based on a Two-Layer Turtle Shell Matrix

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## Abstract

**:**

## 1. Introduction

## 2. Chang et al.’s Scheme

#### 2.1. Construction of the Turtle Shell Matrix

#### 2.2. Data Embedding and Data Extraction

#### 2.3. Example of Data Embedding and Data Extraction

## 3. Proposed Scheme

#### 3.1. Construction of the Two-Layer Matrix

#### 3.2. Data Embedding and Data Extraction Procedures

**Data embedding procedure**

**Input:**A cover image $I$ sized $W\times H$, the binary secret stream $S$ with length $L$.

**Output:**A stego-image ${I}^{\prime}$.

**Data extraction procedure**

**Input:**A stego-image ${I}^{\prime}$ sized $W\times H$, the construction information.

**Output:**The secret binary stream $S$.

#### 3.3. Example of Data Embedding and Data Extraction

## 4. Experimental Results

- ${\mu}_{x}$, ${\mu}_{y}$ are the average of $x$ and $y$, respectively;
- ${\sigma}_{x}^{2}$, ${\sigma}_{y}^{2}$ are the variance of $x$ and $y$, respectively;
- ${\sigma}_{xy}$ is the covariance of $x$ and $y$;
- ${c}_{1}={\left({k}_{1}L\right)}^{2},{c}_{2}={\left({k}_{2}L\right)}^{2}$ are two variables to stabilize the division with weak denominator;
- $L$ is the dynamic range of the pixel-values; and
- ${k}_{1}=0.01$ and ${k}_{2}=0.03$ by default.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 8.**Six original cover images: (

**a**) Lena; (

**b**) Peppers; (

**c**) Baboon; (

**d**) Sailboat; (

**e**) Airplane; (

**f**) Boat.

**Figure 9.**Six stego-images with maximum embedding capacity of 2.5 bpp. (

**a**) Stego Lena with PSNR = 47.13; (

**b**) Stego Peppers with PSNR = 47.13; (

**c**) Stego Baboon with PSNR = 47.09; (

**d**) Stego Sailboat with PSNR = 47.12; (

**e**) Stego Airplane with PSNR = 47.11; (

**f**) Stego Boat with PSNR = 47.15.

**Table 1.**Cases of embedding using the turtle shell in Figure 2.

Cases | Original Pixel Pair | To-Be-Embedded Data | Stego Pixel Pair | |
---|---|---|---|---|

Case 1: $m\left({p}_{k},{p}_{k+1}\right)={s}_{t}$ | Rule 0 | (2,4) | (100)_{2} → (4)_{8} | (2,4) |

Case 2: $m\left({p}_{k},{p}_{k+1}\right)\ne {s}_{t}$ | Rule 1 | (2,7) | (110)_{2} → (6)_{8} | (2,8) |

Rule 2 | (5,3) | (000)_{2} → (0)_{8} | (6,4) | |

Rule 3 | (2,0) | (101)_{2} → (5)_{8} | (3,1) |

**Table 2.**Example of data embedding using the two-layer turtle shell matrix in Figure 7.

Original Pixel Pair | Secret Bit Stream | Stego Pixel Pair |
---|---|---|

(9,2) | (11)_{2} (110)_{2} (is converted to) → (3)_{4} (6)_{8} | (9,2) |

(7,5) | (10)_{2} (000)_{2} (is converted to) → (2)_{4} (0)_{8} | (9,6) |

(1,0) | (10)_{2} (011)_{2} (is converted to) → (2)_{4} (3)_{8} | (4,3) |

Test Images | [23] | [24] | [25] | [26] | The Proposed | |||||
---|---|---|---|---|---|---|---|---|---|---|

EC | PSNR | EC | PSNR | EC | PSNR | EC | PSNR | EC | PSNR | |

Lena | 1.5 | 49.42 | 2 | 45.55 | 2 | 45.57 | 2.5 | 41.87 | 2.5 | 47.13 |

Peppers | 1.5 | 49.40 | 2 | 45.54 | 2 | 45.56 | 2.5 | 41.90 | 2.5 | 47.13 |

Baboon | 1.5 | 49.39 | 2 | 45.55 | 2 | 45.57 | 2.5 | 41.85 | 2.5 | 47.09 |

Sailboat | 1.5 | 49.40 | 2 | 45.55 | 2 | 45.58 | 2.5 | 41.89 | 2.5 | 47.12 |

Airplane | 1.5 | 49.39 | 2 | 45.58 | 2 | 45.57 | 2.5 | 41.85 | 2.5 | 47.11 |

Boat | 1.5 | 49.40 | 2 | 45.54 | 2 | 45.58 | 2.5 | 41.88 | 2.5 | 47.15 |

Average | 1.5 | 49.40 | 2 | 45.55 | 2 | 45.57 | 2.5 | 41.87 | 2.5 | 47.12 |

Test Images | EMD [17] | EMD-2 [18] | [20] | [21] | The Proposed | |||||
---|---|---|---|---|---|---|---|---|---|---|

EC | PSNR | EC | PSNR | EC | PSNR | EC | PSNR | EC | PSNR | |

Lena | 1 | 52.12 | 1.37 | 50.86 | 1.5 | 44.97 | 1.585 | 48.68 | 1.6 | 49.06 |

Peppers | 1 | 52.11 | 1.37 | 50.78 | 1.5 | 44.67 | 1.585 | 48.67 | 1.6 | 49.06 |

Baboon | 1 | 52.11 | 1.37 | 50.69 | 1.5 | 44.68 | 1.585 | 48.66 | 1.6 | 49.04 |

Airplane | 1 | 52.11 | 1.37 | 50.79 | 1.5 | 45.02 | 1.585 | 48.68 | 1.6 | 49.05 |

Average | 1 | 52.11 | 1.37 | 50.78 | 1.5 | 44.84 | 1.585 | 48.67 | 1.6 | 49.05 |

Test Image | Lena | Baboon | Peppers | Airplane | Sailboat | Boat | Average |
---|---|---|---|---|---|---|---|

[26] | 0.940 | 0.964 | 0.943 | 0.940 | 0.951 | 0.952 | 0.948 |

The proposed | 0.973 | 0.991 | 0.974 | 0.970 | 0.980 | 0.981 | 0.978 |

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**MDPI and ACS Style**

Xie, X.-Z.; Lin, C.-C.; Chang, C.-C.
Data Hiding Based on a Two-Layer Turtle Shell Matrix. *Symmetry* **2018**, *10*, 47.
https://doi.org/10.3390/sym10020047

**AMA Style**

Xie X-Z, Lin C-C, Chang C-C.
Data Hiding Based on a Two-Layer Turtle Shell Matrix. *Symmetry*. 2018; 10(2):47.
https://doi.org/10.3390/sym10020047

**Chicago/Turabian Style**

Xie, Xiao-Zhu, Chia-Chen Lin, and Chin-Chen Chang.
2018. "Data Hiding Based on a Two-Layer Turtle Shell Matrix" *Symmetry* 10, no. 2: 47.
https://doi.org/10.3390/sym10020047