# A High-Capacity Coverless Information Hiding Based on the Lowest and Highest Image Fragments

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## Abstract

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## 1. Introduction

## 2. Proposed Method CIHLHF

#### 2.1. Embedding Procedures

_{i}. Then, for each C

_{i}, the lowest and highest, L

_{i}and H

_{i}, are determined. Second, secret data are converted into binary format M

_{i}. Lastly, a mapping operation is performed among the MSBs of L

_{i}, H

_{i}, and M

_{i}.

- Divide the cover picture I, of size K × L pixels, into m × n nonoverlapping segments, C
_{i}. - Determine the lowest and highest values, L
_{i}and H_{i}.$${\mathrm{L}}_{\mathrm{i}}=\mathrm{min}({\mathrm{v}}_{1}{\mathrm{C}}_{\mathrm{i}},{\mathrm{v}}_{2}{\mathrm{C}}_{\mathrm{i}},\dots ,{\mathrm{v}}_{\mathrm{m}\times \mathrm{n}}{\mathrm{C}}_{\mathrm{i}}\phantom{\rule{0ex}{0ex}}{\mathrm{H}}_{\mathrm{i}}=\mathrm{max}({\mathrm{v}}_{1}{\mathrm{C}}_{\mathrm{i}},{\mathrm{v}}_{2}{\mathrm{C}}_{\mathrm{i}},\dots ,{\mathrm{v}}_{\mathrm{m}\times \mathrm{n}}{\mathrm{C}}_{\mathrm{i}}$$ - Convert L
_{i}and H_{i}into an eight-bit binary. - Using Equation (2), calculate the hiding capacity of the cover picture:$$\mathrm{EC}=\left(\frac{\mathrm{K}\times \mathrm{L}}{\mathrm{m}\times \mathrm{n}}\right)\times 2$$

_{i}into a seven-binary (an ASCII code) format.

- Determine the predetermined mapping key Z between a sender and a receiver, where the length of Z is the same as EC.
- Create a mapping between T
_{i}and the MSB of L_{i}and H_{i}according to Z, which results in mapping flag U_{i}. The following is the mapping rule equation:U_{i}= Not (T_{i}⊕ C_{i-MSB})

_{i}= 4. Then, identify and convert the lowest and highest values, L

_{i}and H

_{i}. The cover image preparation is presented in Figure 2. Therefore, on the basis of Equation (1), we can embed 8 bits of secret data. Suppose the characters of secret data are A and B, and the decimal values are 65 and 66, respectively. Convert them into seven-binary format T

_{i}= 1,0,0,0,0,0,1,1,0,0,0,0,1,0. The embeddable T

_{i}= 1,0,0,0,0,0,1,1. Suppose that mapping key Z = 7,8,1,2,3,4,6,5. Lastly, on the basis of the rule in Table 1, U

_{i}= 0 0 1 1 1 1 0 0, as shown in Figure 3. Figure 3 is a continuation of Figure 2, in which the secret bits are mapped to the lowest and highest segment values. The first secret bit is mapped with the 7th MSB, so that 1 is mapped with 0 resulting in 0. This is followed by the second secret bit, which is mapped with the 8th MSB, the third secret bit mapped with the 1st MSB, the fourth secret bit mapped with the 2nd MSB, the fifth secret bit mapped with the 3rd MSB, the sixth secret bit mapped with the 4th MSB, the seventh secret bit mapped with the 6th MSB, and the eight secret bit mapped with the 5th MSB.

#### 2.2. Extracting Procedures

- Divide a stego picture S with size J × K pixels into j × k nonoverlapping segments, D
_{i}. - Determine the lowest and highest values, L
_{i}and H_{i}. - Convert L
_{i}and H_{i}into an eight-bit binary.

_{i}and the MSB of L

_{i}, H

_{i}in accordance with Z, resulting in secret data T

_{i}. The mapping rule of the extraction procedure is shown in Table 2.

## 3. Experimental Results and Comparison

_{i}). When a cover image and a stego image are exactly the same, Q

_{i}can obtain the optimal value of 1. The following is a definition of Q

_{i}:

_{i}) and hiding capacity. As shown in Table 3, the PSNR, SSIM, and Q

_{i}of the CIHMSB and CIHLHF techniques achieved optimal values of $\infty $, 1, and 1, respectively. The fundamental reason is that neither the CIHMSB nor the CIHLHF procedure modified the cover image, in accordance with the concept of coverless data hiding, in which the cover image is identical to the stego image. PSNR value $\infty $ indicates that the pixel values of the original and stego images were the same.

_{i}. In this experiment, the cover image is a grayscale image with a size of 512 × 512. If the fragment size is 8 × 8, the number of segments C

_{i}is 4096.

_{i}is 49,152. So, when attackers need to extract 49,152 bits of secret data from the 4096th fragment, they would use the brute-force method because they have no information regarding mapping key Z. When the adversary needs to extract T

_{i}bits of secret information from C

_{i}image fragments, they must use brute-force attacks without knowing mapping key Z. Therefore, brute-force attacks can be calculated as follows:

_{i}with m bits. In the proposed CIHLHF, the hiding capacity of the cover image is 2 m, and the extra cost is needed to store the mapping flag U

_{i}with 2 m bits. Although the mapping flag’s size in the proposed CIHLHF is double that of CIHMSB, the hiding capacity in the proposed CIHLHF is double that of CIHMSB. In addition, the mapping flag’s size is significantly smaller than that of the cover and stego images. Therefore, if we want to hide a secret message as with the proposed CIHLHF, 2 m bits, in CIHMSB, the size of a cover image needs to with 2(W × H) pixels, which is double the proposed CIHLHF size.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Grayscale test images: (

**a**) Airplane; (

**b**) Baboon; (

**c**) Barbara; (

**d**) Boat; (

**e**) Lena; (

**f**) Pepper.

T_{i} | MSB of L_{i}, H_{i} | U_{i} |
---|---|---|

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

U_{i} | MSB of L_{i}, H_{i} | T_{i} |
---|---|---|

1 | 0 | 0 |

0 | 1 | 0 |

0 | 0 | 1 |

1 | 1 | 1 |

Methods | Bits | ${\mathbf{Carrirer}}^{-1}$ | Hiding Capacity $(\mathbf{Bits}\ast {\mathbf{Carrirer}}^{-1})$ | PSNR (dB) | SSIM | Q_{i} |
---|---|---|---|---|---|---|

CIHMSB [35] | 4 | (512 × 512)/(8 × 8) = 4096 | 16,384 | ∞ | 1 | 1 |

CIHLHF | 12 | 49,152 (3 times higher) | ∞ | 1 | 1 |

Method | Total Bits | Time (Years) |
---|---|---|

CIHMSB [35] | 16,384 | $4.83\times {10}^{\mathrm{31,916}}$ |

CIHLHF | 49,152 | $2.69\times {10}^{\mathrm{177,113}}$ |

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**MDPI and ACS Style**

Anggriani, K.; Chiou, S.-F.; Wu, N.-I.; Hwang, M.-S.
A High-Capacity Coverless Information Hiding Based on the Lowest and Highest Image Fragments. *Electronics* **2023**, *12*, 395.
https://doi.org/10.3390/electronics12020395

**AMA Style**

Anggriani K, Chiou S-F, Wu N-I, Hwang M-S.
A High-Capacity Coverless Information Hiding Based on the Lowest and Highest Image Fragments. *Electronics*. 2023; 12(2):395.
https://doi.org/10.3390/electronics12020395

**Chicago/Turabian Style**

Anggriani, Kurnia, Shu-Fen Chiou, Nan-I Wu, and Min-Shiang Hwang.
2023. "A High-Capacity Coverless Information Hiding Based on the Lowest and Highest Image Fragments" *Electronics* 12, no. 2: 395.
https://doi.org/10.3390/electronics12020395