# An Efficient Separable Reversible Data Hiding Using Paillier Cryptosystem for Preserving Privacy in Cloud Domain

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## Abstract

**:**

## 1. Introduction

## 2. Paillier Cryptosystem

#### 2.1. Key Generation

#### 2.2. Encryption

#### 2.3. Decryption

#### 2.4. Homomorphic Property

## 3. Proposed Scheme

#### 3.1. Image Encryption

#### 3.2. Data Embedding

#### Padding Procedure

#### 3.3. Data Extraction

#### 3.4. Image Recovery

#### 3.5. Exemplifying Our Proposed Scheme

#### 3.6. Proposed Scheme in Cloud Domain

## 4. Experimental Results

#### 4.1. Results Showing Independence of the Proposed Scheme for Different Images

#### 4.2. Comparative Analysis with Other Standard Schemes in RDHEI

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Vacating room after encryption (VRAE); and (

**b**) vacating room before encryption (VRBE).

**Figure 6.**Data embedding process in our proposed scheme after getting an encrypted image $C$ of size $(4\times 4)$ from the content-owner. ${C}_{1}^{0}$ and ${C}_{1}$ are the values for index $k=1$ of ${C}^{0}$ and $C$, respectively.

**Figure 8.**(

**a**–

**d**) The four original standard gray-scale images of size 512 × 512; and (

**e**–

**h**) the directly decrypted images (DDI) to check embedding rate, peak signal noise ratio (PSNR), structural similarity index matrix (SSIM) for different images in our scheme.

Notations | Description |
---|---|

$(\mathit{N},g)$ | A public key for encryption |

$(D{h}_{k})$ | A data hiding key for hiding and recovery of additional data |

$\lambda $ | A private key possessed by the receiver for image recovery |

$I$ | An original image of size $L\times B$ |

$k$ | Index for each pixel where $1\le k\le L\times B$ |

${I}_{k}$ | kth pixel of the original image $I$ |

${C}_{k}$ | An encrypted value of ${I}_{k}$ i.e., kth encrypted pixel of the encrypted image $C$ |

$E[\xb7]$ | An encryption function |

$D[\xb7]$ | A decryption function |

${r}_{k}$ | A randomly selected integer for each ${I}_{k}$ such that ${r}_{k}\in {\mathbb{Z}}_{\mathit{N}}^{*}$ |

$C$ | An encrypted image generated from all ${C}_{k}$ achieved by pixel by pixel encryption |

$D$ | Additional data of size $L\times B$ bits to be embedded |

$E(D)$ | Encrypted additional data using $(D{h}_{k})$ |

${M}^{0}$ | A zero matrix of size $L\times B$ where all the elements are zero |

${C}^{0}$ | A matrix resulting from encryption of matrix ${M}^{0}$ |

${C}_{k}^{0}$ | kth encrypted value of “0” from the matrix ${C}^{0}$ |

$PU$ | A padded unit |

$P{U}_{k}$ | kth padded unit consisting of pair $({C}_{k}^{0},{C}_{k})$ where $1\le k\le L\times B$ |

${C}^{\prime}$ | A marked encrypted image (MEI) constituted from all the padded units (PUs) |

$DDI$ | A directly decrypted image |

$DD{I}_{k}$ | kth pixel of directly decrypted image (DDI) |

**Table 2.**Embedding rate, peak signal noise ratio (PSNR), structural similarity index matrix (SSIM) for four distinct standard test images (Figure 8a–d) in the proposed scheme.

Test Images | Embedding Rate (bpp) | PSNR | SSIM |
---|---|---|---|

Lena, Baboon, Boat and Airplane | 1.0 | +∞ | 1 |

Schemes | Image Pre-Processing | Encryption | Receiver | Maximum Embedding Rate (bpp) | PSNR (dB) of Directly Image | Data Expansion |
---|---|---|---|---|---|---|

Zhang [9] | No | Stream cipher | Separable | 0.033 | 38.0 | No |

Zhang et al. [12] | Yes | Stream cipher | Separable | 0.04 | 55.34 | No |

Yin et al. [10] | No | Stream cipher | Separable | 0.1294 | 50.51 | No |

Ma et al. [11] | Yes | Stream cipher | Separable | 0.7 | 33.273 | No |

Cao et al. [16] | Yes | Stream cipher | Separable | 0.8 | 37.375 | No |

Tai et al. [24] | Yes | Public key | Separable | 1.0 | $+\infty $ | Yes |

Proposed | No | Public key | Separable | 1.0 | $+\infty $ | Yes |

**Table 4.**Comparative analysis of our scheme in terms of bit-size for image (L × B) with Tai et al. [24].

Schemes | Size (in bits) | ||
---|---|---|---|

Content-Owner | Data-Hider | Receiver | |

Tai et al. [24] | $2\times L\times B\times (\lfloor {\mathrm{log}}_{2}{\mathit{N}}^{2}\rfloor +1)$ | $2\times L\times B\times (\lfloor {\mathrm{log}}_{2}{\mathit{N}}^{2}\rfloor +1)$ | $2\times L\times B\times (\lfloor {\mathrm{log}}_{2}{\mathit{N}}^{2}\rfloor +1)$ |

Proposed | $1\times L\times B(\lfloor {\mathrm{log}}_{2}{\mathit{N}}^{2}\rfloor +1)$ | $2\times L\times B\times (\lfloor {\mathrm{log}}_{2}{\mathit{N}}^{2}\rfloor +1)$ | $2\times L\times B\times (\lfloor {\mathrm{log}}_{2}{\mathit{N}}^{2}\rfloor +1)$ |

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## Share and Cite

**MDPI and ACS Style**

Khan, A.N.; Fan, M.Y.; Nazeer, M.I.; Memon, R.A.; Malik, A.; Husain, M.A.
An Efficient Separable Reversible Data Hiding Using Paillier Cryptosystem for Preserving Privacy in Cloud Domain. *Electronics* **2019**, *8*, 682.
https://doi.org/10.3390/electronics8060682

**AMA Style**

Khan AN, Fan MY, Nazeer MI, Memon RA, Malik A, Husain MA.
An Efficient Separable Reversible Data Hiding Using Paillier Cryptosystem for Preserving Privacy in Cloud Domain. *Electronics*. 2019; 8(6):682.
https://doi.org/10.3390/electronics8060682

**Chicago/Turabian Style**

Khan, Ahmad Neyaz, Ming Yu Fan, Muhammad Irshad Nazeer, Raheel Ahmed Memon, Asad Malik, and Mohammed Aslam Husain.
2019. "An Efficient Separable Reversible Data Hiding Using Paillier Cryptosystem for Preserving Privacy in Cloud Domain" *Electronics* 8, no. 6: 682.
https://doi.org/10.3390/electronics8060682