# Reversible Data-Hiding Systems with Modified Fluctuation Functions and Reed-Solomon Codes for Encrypted Image Recovery

## Abstract

**:**

## 1. Introduction

## 2. System Model of the Proposed Scheme

#### 2.1. Image Encryption

#### 2.2. Rate Matching and RS Encoder

#### 2.3. Codeword Embedding

## 3. Fluctuation Function and Decoding of the Proposed System

#### 3.1. Image Decryption

#### 3.2. Codeword Extraction and Matching

#### 3.3. RS Decoder

#### 3.4. Image Recovery

## 4. Experimental Results

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Cheddad, A.; Condell, J.; Curran, K.; McKevitt, P. Digital image steganography: Survey and analysis of current methods. Signal Process.
**2010**, 90(3), 727–752. [Google Scholar] [CrossRef] - Memon, N.; Wong, P.W. A buyer-seller watermarking protocol. IEEE Trans. Image Process.
**2001**, 10, 643–649. [Google Scholar] [CrossRef] [PubMed] - Zhao, B.; Delp, E.J. Secret sharing in the encrypted domain with secure comparison. In Proceedings of the Global Telecommunications Conference (GLOBECOM 2011), Houston, TX, USA, 5–9 December 2011; pp. 1–5. [Google Scholar]
- Zhang, X. Reversible data hiding in encrypted images. IEEE Signal Process. Lett.
**2011**, 18(4), 255–258. [Google Scholar] [CrossRef] - Hong, W.; Chen, T.-S.; Wu, H.-Y. An improved reversible data hiding in encrypted images using side match. IEEE Signal Process. Lett.
**2012**, 19(4), 199–202. [Google Scholar] [CrossRef] - Liao, X.; Shu, C. Reversible data hiding in encrypted images based on absolute mean difference of multiple neighboring pixels. Vis. Commun. Image Represent.
**2015**, 28, 21–27. [Google Scholar] [CrossRef] - Zhang, X. Separable reversible data hiding in encrypted image. IEEE Trans. Inf. Forensics Secur.
**2012**, 7, 826–832. [Google Scholar] [CrossRef] - Pan, Z.; Wang, L.; Hu, S.; Ma, X. Reversible data hiding in encrypted image using new embedding pattern and multiple judgments. Multimed. Tools Appl.
**2016**, 75, 8595–8607. [Google Scholar] [CrossRef] - Zhang, X.; Qian, Z.; Feng, G.; Ren, Y. Efficient reversible data hiding in encrypted images. J. Vis. Commun. Image R.
**2014**, 25(2), 322–328. [Google Scholar] [CrossRef] - Zhang, W.; Chen, B.; Yu, N. Capacity-approaching codes for reversible data hiding. In Proceedings of the 13th Information Hiding (IH’2011) LNCS 6958, Prague, Czech Republic, 18–20 May 2011; pp. 255–269. [Google Scholar]
- Zhang, W.; Chen, B.; Yu, N. Improving various reversible data hiding schemes via optimal codes for binary covers. IEEE Trans. Image Process.
**2012**, 21, 2991–3003. [Google Scholar] [CrossRef] [PubMed] - Zhang, W.; Hu, X.; Li, X.; Yu, N. Optimal transition probability of reversible data hiding for general distortion metrics and its applications. IEEE Trans. Image Process.
**2015**, 24, 294–304. [Google Scholar] [CrossRef] [PubMed] - Tsai, T. Histogram-based reversible data hiding for vector quantisation-compressed images. IET Image Process.
**2009**, 3, 100–114. [Google Scholar] [CrossRef] - Ma, K.; Zhang, W.; Zhao, X.; Yu, N.; Li, F. Reversible data hiding in encrypted images by reserving room before encryption. IEEE Trans. Inf. Forensics Secur.
**2013**, 8, 553–562. [Google Scholar] [CrossRef] - Zhang, X. Reversible data hiding with optimal value transfer. IEEE Trans. Multimed.
**2013**, 15, 316–325. [Google Scholar] [CrossRef] - Ou, B.; Li, X.; Ni, R.; Shi, T.-Q. Pairwise prediction-error expansion for efficient reversible data hiding. IEEE Trans. Image Process.
**2013**, 22, 5010–5012. [Google Scholar] [CrossRef] [PubMed] - Zhang, W.; Hu, X.; Li, X.; Yu, N. Recursive histogram modification: establishing equivalency between reversible data hiding and lossless data compression. IEEE Trans. Image Process.
**2013**, 22, 2775–2785. [Google Scholar] [CrossRef] [PubMed] - Luo, L.; Chen, Z.; Chen, M.; Zeng, X.; Xiong, Z. Reversible image watermarking using interpolation technique. IEEE Trans. Inf. Forensics Secur.
**2010**, 5, 187–193. [Google Scholar] - Ni, Z.; Shi, Y.-Q.; Ansari, N.; Su, W. Reversible data hiding. IEEE Trans. Circuits Syst. Video Technol.
**2006**, 16, 354–362. [Google Scholar] - Nikolaidis, A. Reversible data hiding in JPEG images utilising zero quantised coefficients. IET Image Process.
**2015**, 9, 560–568. [Google Scholar] [CrossRef] - Hussain, M.; Wahab, A.W.A.; Javed, N.; Jung, K.H. Hybrid data hiding scheme using right-most digit replacement and adaptive least significant bit for digital images. Symmetry
**2016**, 8, 1–21. [Google Scholar] [CrossRef] - Kumar, M.; Agarwal, S. Reversible data hiding based on prediction error and expansion using adjacent pixels. Secur. Commun. Netw.
**2016**, 9, 3703–3712. [Google Scholar] [CrossRef] - Hong, W.; Chen, T.S.; Yin, Z.; Luo, B.; Ma, Y. Data hiding in AMBTC images using quantization level modification and perturbation technique. J. Vis. Commun. Image Represent.
**2017**, 76, 3761–3782. [Google Scholar] [CrossRef] - Khanam, F.-T.-Z.; Kim, S. Enhanced joint and separable reversible data hiding in encrypted images with high payload. Symmetry
**2017**, 9, 1–20. [Google Scholar] [CrossRef] - Cao, X.; Du, L.; Wei, X.; Meng, D.; Guo, X. High capacity reversible data hiding in encrypted images by patch-level sparse representation. IEEE Trans. Cybern.
**2016**, 46, 1132–1143. [Google Scholar] [CrossRef] [PubMed] - Qian, Z.; Zhang, X. Reversible data hiding in encrypted images with distributed source encoding. IEEE Trans. Circuits Syst. Video Technol.
**2016**, 26, 636–646. [Google Scholar] [CrossRef] - Xiao, D.; Xiang, Y.; Zheng, H.; Wang, Y. Separable reversible data hiding in encrypted image based on pixel value ordering and additive homomorphism. J. Vis. Commun. Image Represent.
**2017**. [Google Scholar] [CrossRef] - Proakis, J.G.; Salehi, M. Digital Communications; McGraw-Hil: New York, NY, USA, 2008; pp. 471–475. [Google Scholar]
- Wang, H.; Kim, S. New RLL decoding algorithm for multiple candidates in visible light communication. IEEE Photon. Technol. Lett.
**2015**, 27, 15–17. [Google Scholar] [CrossRef] - Moon, T.K. Error Correction Coding; Wiley-Interscience: Hoboken, NJ, USA, 2004. [Google Scholar]
- USC-SIPI Image Database. Available online: http//sipi.usc.edu/database/ (accessed on 2 March 2016).

**Figure 5.**Example of error recovery by using RS codes in the Lena image. (

**a**) Error pattern in Figure 4c; (

**b**) Analysis of the codeword for the error pattern.

**Figure 6.**BER performances of referenced and proposed fluctuation functions for the three images. (

**a**) Lena; (

**b**) Peppers; (

**c**) Jet.

**Figure 7.**BER performances of the proposed reversible data-hiding (RDH) systems with Reed–Solomon (RS) codes for the three images. (

**a**) Lena; (

**b**) Peppers; (

**c**) Jet.

**Figure 8.**PSNR performances of the proposed RDH systems with RS codes for the three images. (

**a**) Lena; (

**b**) Peppers; (

**c**) Jet.

Rate | Min. s | No. Messages | Gain (%) | ||
---|---|---|---|---|---|

Ref. Zhang [4] | 1 | 16 | 1024 | G1 | G2 |

Ref. Hong [5] | 1 | 14 | 1296 | ||

Pro. RS(15, 11) | 0.73 | 8 | 3004 | 293.3 | 231.8 |

Pro. RS(15, 7) | 0.47 | 6 | 3372 | 329.3 | 260.2 |

Pro. RS(31, 23) | 0.74 | 6 | 5360 | 523.5 | 413.6 |

Pro. RS(31, 15) | 0.48 | 6 | 3496 | 341.4 | 269.8 |

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**MDPI and ACS Style**

Kim, S.
Reversible Data-Hiding Systems with Modified Fluctuation Functions and Reed-Solomon Codes for Encrypted Image Recovery. *Symmetry* **2017**, *9*, 61.
https://doi.org/10.3390/sym9050061

**AMA Style**

Kim S.
Reversible Data-Hiding Systems with Modified Fluctuation Functions and Reed-Solomon Codes for Encrypted Image Recovery. *Symmetry*. 2017; 9(5):61.
https://doi.org/10.3390/sym9050061

**Chicago/Turabian Style**

Kim, Sunghwan.
2017. "Reversible Data-Hiding Systems with Modified Fluctuation Functions and Reed-Solomon Codes for Encrypted Image Recovery" *Symmetry* 9, no. 5: 61.
https://doi.org/10.3390/sym9050061