Retracing extended sudoku matrix for high-capacity image steganography

Abstract

Numerous data hiding algorithms have been devised for imperceptibly embedding secret messages into the cover media so as to securely transmit user privacy information over the public communication channels. Among them, the reference matrix-based schemes in spatial domain draw extensive concern on account of the simple but efficient embedding and extraction procedure. The core idea of the planar matrix-based method is let two contiguous cover pixels conceal a base-N secret digit with the guidance of reference matrix, such as Sudoku, Turtle Shell, and so on. A novel image data hiding scheme with great embedding efficiency is presented in this paper, which is based on retracing extended Sudoku (RE-Sudoku) reference matrix. Owing to the number of Sudoku solutions and various extension directions, viz., the multiformity of RE-Sudoku matrix, this scheme is exceedingly more secure than the previous methods. More momentously, the proposed two-dimensional reference matrix can guide two 9-ary notational system secret digits to be embedded into each cover pixel pair simultaneously; thereby resulting in a larger embedding rate which converges to 3.169 bits per pixel. The experimental results reveal that this image steganography outperforms the other related works in terms of hiding capacity while maintaining a desirable image quality around 40 dB. Furthermore, the security of our proposed scheme is verified by demonstrating its resistance to the pixel-value difference histogram (PDH) and regular/singular (RS) steganalysis.

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References

  1. 1.

    Bender W, Gruhl D, Morimoto N, Lu A (1996) Techniques for data hiding. IBM Syst J 35(3&4):313–336

    Article  Google Scholar 

  2. 2.

    Chang CC, Chou YC, Kieu TD (2008) An information hiding scheme using Sudoku. In proceedings of the third international conference on innovative computing information and control (IEEE, Dalian, Liaoning, China, 2008):17–17

  3. 3.

    Chang CC, Liu Y, Nguyen TS (2014) A novel turtle Shell based scheme for data hiding. In proceedings of the tenth international conference on intelligent information hiding and multimedia signal processing (IEEE, Kitakyushu, Japan):89–93

  4. 4.

    Davis R (1978) The data encryption standard in perspective. IEEE Commun Soc Mag 16(6):5–9

    Article  Google Scholar 

  5. 5.

    Faez K, Khodaei M (2012) New adaptive steganographic method using least-significant-bit substitution and pixel-value differencing. IET Image Process 6(6):677–686

    Article  Google Scholar 

  6. 6.

    Fridrich J, Goljan M (2002) Practical steganalysis of digital images: state of the art. In Security and Watermarking of Multimedia Contents IV International Society for Optics and Photonics 4675:1–13

    Google Scholar 

  7. 7.

    Hou D, Wang H, Zhang W, Yu N (2018) Reversible data hiding in JPEG image based on DCT frequency and block selection. Signal Process 148:41–47

    Article  Google Scholar 

  8. 8.

    Huang CT, Lin LC, Sun DE, Wang SJ (2019) A security-based steganographic scheme in vector quantization coding between correlated neighboring blocks. Multimed Tools Appl 78(3):3131–3151

    Article  Google Scholar 

  9. 9.

    Hussain M, Wahab AWA, Idris YIB, Ho AT, Jung KH (2018) Image steganography in spatial domain: a survey. Signal Process Image Commun 65:46–66

    Article  Google Scholar 

  10. 10.

    Hussain M, Wahab AWA, Javed N, Jung KH (2018) Recursive information hiding scheme through LSB, PVD shift, and MPE. IETE Tech Rev 35(1):53–63

    Article  Google Scholar 

  11. 11.

    Kim HJ, Kim C, Choi Y, Wang S, Zhang X (2010) Improved modification direction methods. Comput Math Appl 60(2):319–325

    MathSciNet  Article  Google Scholar 

  12. 12.

    Liu Y, Chang CC, Nguyen TS (2016) High capacity turtle shell-based data hiding. IET Image Process 10(2):130–137

    Article  Google Scholar 

  13. 13.

    Liu Y, Chang CC, Huang PC (2017) Extended exploiting-modification-direction data hiding with high capacity. In Proceedings of the International Conference on Video and Image Processing (ACM press, Singapore):151–155

  14. 14.

    Mielikainen J (2006) LSB matching revisited. IEEE Signal Process Lett 13(5):285–287

    Article  Google Scholar 

  15. 15.

    Rivest RL, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public-key cryptosystems. Commun ACM 21(2):120–126

    MathSciNet  Article  Google Scholar 

  16. 16.

    Shen SY, Huang LH (2015) A data hiding scheme using pixel value differencing and improving exploiting modification directions. Comput Secur 48:131–141

    Article  Google Scholar 

  17. 17.

    Tavares R, Madeiro F (2016) Word-hunt: a LSB steganography method with low expected number of modifications per pixel. IEEE Lat Am Trans 14(2):1058–1064

    Article  Google Scholar 

  18. 18.

    Westfeld A, Pfitzmann A (2000) Attacks on Steganographic systems. In Proceedings of International workshop on information hiding (springer, Berlin, Heidelberg):61–76

  19. 19.

    Wu DC, Tsai WH (2003) A steganographic method for images by pixel-value differencing. Pattern Recogn Lett 24(9–10):1613–1626

    Article  Google Scholar 

  20. 20.

    Xia BB, Wang AH, Chang CC, Liu L (2016) An image steganography scheme using 3D-Sudoku. J Info Hiding Multimed Sign Proc 7(4):836–845

    Google Scholar 

  21. 21.

    Yang CH, Weng CY, Wang S-J, Sun H-M (2010) Varied PVD+LSB evading detection programs to spatial domain in data embedding systems. J Syst Softw 83:1635–1643

    Article  Google Scholar 

  22. 22.

    Zhang X, Wang S (2004) Vulnerability of pixel-value differencing steganography to histogram analysis and modification for enhanced security. Pattern Recogn Lett 25(3):331–339

    Article  Google Scholar 

  23. 23.

    Zhang X, Wang S (2006) Efficient Steganographic embedding by exploiting modification direction. IEEE Commun Lett 10(11):781–783

    MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

This research work has been supported by the National Natural Science Foundation of China (No.61972439, No.61702010, No.61672039).

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Correspondence to Yonglong Luo.

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Li, X., Luo, Y. & Bian, W. Retracing extended sudoku matrix for high-capacity image steganography. Multimed Tools Appl (2021). https://doi.org/10.1007/s11042-021-10675-9

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Keywords

  • Data hiding
  • Embedding capacity
  • Sudoku matrix
  • Image steganography