Multimedia Tools and Applications

, Volume 77, Issue 7, pp 8805–8821 | Cite as

Reversible data hiding scheme using sub-sampled image exploiting Lagrange’s interpolating polynomial

  • Biswapati Jana


In this paper, a new reversible data hiding scheme has been proposed using lagrange’s interpolating polynomial on interpolated sub-sampled images. First, we generate sub-sampled images from original image and enlarge its size using image interpolation. Now, we convert secret message using lagrange interpolating polynomial and generate new secret message. The new secret message is divided and stored within interleaved pixel of each interpolated sub-sampled images. At the receiver end, new secret message is extracted from interleaved pixel of each sub-sampled stego images and then lagrange’s interpolation is applied to generate original secret message. The security has been enhanced due to the distributive nature of hidden data within multiple images. The original pixels are not effected during data embedding which assure reversibility. The proposed scheme provides average embedding capacity with good visual quality measured by peak signal to noise ratio (PSNR) which is greater than 50 dB. It is observed that the proposed scheme provides better performance than other existing data hiding schemes in terms of data embedding capacity, visual quality and security. We have analyzed our stego images through RS analysis, calculate relative entropy, standard deviation and correlation coefficient of original and stego image to show the robustness under various steganographic attacks.


Steganography Sub-sampled image Reversible data hiding Lagrange interpolation Image interpolation RS analysis Relative entropy 



The author is grateful to the anonymous reviewers for their invaluable comments and recommendations to improve our paper. This work is supported by UGC Innovative project grant under Vidyasagar University (Grant Nos: VU/Innovative/ Sc/06/2015, Dated: 17.06.2015).


  1. 1.
    Chan C, Cheng L (2004) Hiding data in images by simple LSB substitution. Pattern Recogn 37(3): 474–496CrossRefzbMATHGoogle Scholar
  2. 2.
    Chang C, Hsiao J, Chan C (2003) Finding optimal least-significant-bits substitutionin image hiding by dynamic programming strategy. Pattern Recogn 36(7):1583–1595CrossRefGoogle Scholar
  3. 3.
    Chang C, Chan C, Fan Y (2006) Image hiding scheme with modulus function and dynamic programming. Pattern Recogn 39(6):1155–1167CrossRefzbMATHGoogle Scholar
  4. 4.
    Fridrich J, Goljan J, Du R (2001) Invertible authentication. In: Proceedings of the SPIE, security and watermarking of multimedia contents, vol 4314. SanJose, pp 197208Google Scholar
  5. 5.
    Giri D, Jana B, Mondal SK (2016) Dual image based reversible data hiding scheme using three pixel value difference expansion Information systems design and intelligent applications. Springer, India, pp 403–412Google Scholar
  6. 6.
    Hwang J, Kim JW, Choi JU (2006) A reversible watermarking based on histogram shifting. International workshop on digital watermarking, lecture notes in computer science, vol 4283. Springer, Jeju Island, p 348361Google Scholar
  7. 7.
    Jana B (2016) Dual image based reversible data hiding scheme using weighted matrix. Int J Electron Inf Eng 5(1):6–19MathSciNetGoogle Scholar
  8. 8.
    Jana B, Giri D, Mondal SK (2016) Dual image based reversible data hiding scheme using (7, 4) hamming code. Multimed Tools Appl 1–23Google Scholar
  9. 9.
    Kim KS, Lee MJ, Lee HY, Lee HK (2009) Reversible data hiding exploiting spatial correlation between sub-sampled images. Pattern Recogn 42(11):3083–3096CrossRefzbMATHGoogle Scholar
  10. 10.
    Kuo WC, Jiang DJ, Huang YC (2007) Reversible data hiding based on histogram. International conference on intelligent computing, lecture notes in artificial intelligence, vol 4682. Springer, Qing Dao, pp 11521161Google Scholar
  11. 11.
    Lee CF, Chang CC, Gao CY (2013) A two-staged multi-level reversible data hiding exploiting lagrange interpolation. In: 2013 Ninth international conference on intelligent information hiding and multimedia signal processing. IEEE, pp 485–488Google Scholar
  12. 12.
    Lin CC, Tai WL, Chang CC (2008) Multilevel reversible data hiding based on histogram modification of difference images. Pattern Recogn 41(35):82–91zbMATHGoogle Scholar
  13. 13.
    Luo H, Yu FX, Chen H, Huang ZL, Li H, Wang PH (2011) Reversible data hiding based on block median preservation. Inform Sci 181(2):308328CrossRefGoogle Scholar
  14. 14.
    Ni Z, Shi Y Q, Ansari N, Su W (2006) Reversible data hiding. IEEE Trans Circ Syst Vid Technol 16(3):354–362CrossRefGoogle Scholar
  15. 15.
    Thien C, Lin J (2003) A simple and high-hiding capacity method for hiding digitby-digit data in images based on modulus function. Pattern Recogn 36 (12):2875–2881CrossRefzbMATHGoogle Scholar
  16. 16.
    Tsai PY, Hu YC, Yeh HL (2009) Reversible image hiding scheme using predictive coding and histogram shifting. Signal Process 89(11):29–43zbMATHGoogle Scholar
  17. 17.
    Varsaki E, Fotopoulos V, Skodras AN (2006) A reversible data hiding technique embedding in the image histogram. Technical Report HOU-CS-TR-2006-08-GR Hellenic Open UniversityGoogle Scholar
  18. 18.
    Wang R, Lin C, Lin J (2001) Image hiding by optimal LSB substitution andgenetic algorithm. Pattern Recogn 34(3):671–683CrossRefzbMATHGoogle Scholar
  19. 19.
    Wang SJ (2005) Steganography of capacity required using modulo operator forembedding secret image. Appl Math Comput 164(1):99–116MathSciNetzbMATHGoogle Scholar
  20. 20.
    Wang XT, Chang CC, Nguyen TS, Li MC (2013) Reversible data hiding for high quality images exploiting interpolation and direction order mechanism. Digit Signal Process 23(2):569–577MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceVidyasagar UniversityMidnaporeIndia

Personalised recommendations