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A (t,n)- Secret image sharing with steganography based on Rook polynomial and LWE problem

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Abstract

In a meaningful secret image sharing scheme with authentication, an image is distributed among the participants without raising adversaries suspicion. Additionally the cheats of the dealer and participants in the reconstruction of the image are discoverable, which means that the integration of the shares is verifiable. In this paper, we propose a novel meaningful secret image sharing with authentication property based on learning with errors problem and rook polynomial. Compared with the previous schemes, it has a higher embedding rate and a better visual quality.

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References

  1. Ahmadian AM, Amirmazlaghani M (2019) A novel secret image sharing with steganography scheme utilizing optimal asymmetric encryption padding and information dispersal algorithms. Signal Process Image Commun 74:78–88

    Article  Google Scholar 

  2. Charoghchi S, Mashhadi S (2021) Three (t,n)-secret image sharing schemes based on homogeneous linear recursion. Inf Sci 552:220–243

    Article  MathSciNet  MATH  Google Scholar 

  3. Chang Ch-Ch, Chen Y-H, Chuang L-Y (2014) Meaningful shadows for image secret sharing with steganography and authentication techniques. J Inform Hiding Multimed Signal Process 5(3):342–352

    Google Scholar 

  4. Chang Ch-Ch, Horng J-H, Shih Ch-Sh, Chang Ch-Ch (2020) A Maze Matrix-Based Secret Image Sharing Scheme with Cheater Detection, Sensors, 20(13). https://doi.org/10.3390/s20133802

  5. Chang C-C, Hsieh Y-P, Lin C-H (2008) Sharing secrets in stego images with authen-tication. Pattern Recognit. 41(10):3130–3137

    Article  MATH  Google Scholar 

  6. Chang C-C, Lin P-Y, Wang Z-H, Li M (2010) A sudoku-based secret image sharing scheme with reversibility. J Commun 5(1):5–12

    Article  Google Scholar 

  7. Chen Ch-Ch, Tsai Y-H (2016) An expandable essential secret image sharing structure. J Inform Hiding Multimed Signal Process 7(1):135–144

    Google Scholar 

  8. Chen S, Chang CC, Echizen I (2021) Steganographic Secret Sharing With GAN-Based Face Synthesis and Morphing for Trustworthy Authentication in IoT. IEEE Access 9:116427–116439

    Article  Google Scholar 

  9. Eslami Z, Razzaghi S, Ahmadabadi JZ (2010) Secret image sharing based on cellular automata and steganography. Pattern Recognit. 43(1):397–404

    Article  MATH  Google Scholar 

  10. Gao K, Horng J-H, Chang C-C (2021) An authenticatable (2, 3) secret sharing scheme using meaningful share images based on hybrid fractal matrix. IEEE Access 9:50112–50125

    Article  Google Scholar 

  11. Guo T, Liu F, Wu C-K, Yang C, Wang W, Ren Y-W (2013) Threshold Secret Image Sharing. In: Proceedings of the 15th International Conference on Information and Communications Security, Beijing, China, 20-22 November, pp 404–412, https://doi.org/10.1007/978-3-319-02726-5-29

  12. Guo Y, Ma Z, Zhao M (2019) Polynomial based progressive secret image sharing scheme with smaller shadow size. IEEE Access 7:73782–73789

    Article  Google Scholar 

  13. Hou YC, Quan ZY, Tsai CF, Tseng AY (2013) Block-based progressive visual secret sharing. Inf Sci 233:290–304

    Article  Google Scholar 

  14. Kanso A, Ghebleh M (2017) An efficient (t,n)-threshold secret image sharing scheme. Multimed Tools Appl. 76:16369–16388. https://doi.org/10.1007/s11042-016-3917-x

    Article  Google Scholar 

  15. Knospe H (2019) A course in cryptography. AMS

  16. Lee C-W, Tsai W-H (2013) A data hiding method based on information sharing via PNG images for applications of color image authentication and metadata embedding. Signal Process 93(7):2010–2025

    Article  Google Scholar 

  17. Lee J-S, Chen Y-R (2017) Selective scalable secret image sharing with verification. Multimed Tools Appl. 76(1):1–11

    Article  Google Scholar 

  18. Li X-S, Chang C-C, He M-X, Lin C-C (2019) A lightweight authenticable visual secret sharing scheme based on turtle shell structure matrix. Multimed Tools Appl 1–24

  19. Lin J, Lin C-C, Chang C-C (2019) Reversible Steganographic Scheme for AMBTC-compressed Image Based on (7,4) Hamming Code. Symmetry 11 (1):2361

    Google Scholar 

  20. Lin C-C, Tsai W-H (2004) Secret image sharing with steganography and authentication. J. Syst Softw 73(3):405–414

    Article  Google Scholar 

  21. Liu Y-X, Yang Ch-N, Chou Y-Sh, Wu S-Y, Sun Q-D (2018) Progressive (k,n) secret image sharing Scheme with meaningful shadow images by GEMD and RGEMD, J. Vis. Commun Image R.

  22. Liu Y, Chang C-C (2018) A turtle shell-based visual secret sharing scheme with reversibility and authentication. Multimed Tools Appl 77(19):25295–25310

    Article  Google Scholar 

  23. Liu Q, Xiang X, Qin J, Tan Y, Zhang Q (2021) A robust coverless steganography scheme using camouflage image. IEEE transactions on circuits and systems for video technology. https://doi.org/10.1109/TCSVT.2021.3108772

  24. Maan VK, Dhaliwal HS (2013) Vector quantization in image steganography. International Journal Of Engineering Research & Technology (IJERT) 2 (4):421–424

    Google Scholar 

  25. Meng K, Miao F, Xiong Y, Chang C-C (2021) A reversible extended secret image sharing scheme based on Chinese remainder theorem. Signal Process: Image Commun 95. https://doi.org/10.1016/j.image.2021.116221

  26. Priyanka S, Balasubramanian R, Manoj M (2018) A (n,n) threshold non-expansible XOR based visual cryptography with unique meaningful shares. Signal Process 142:301–319

    Article  Google Scholar 

  27. Riordan J (1980) Introduction to combinatorial analysis, Princeton University Press

  28. Sardar MK, Adhikari A (2020) A new lossless secret color image sharing scheme with small shadow size. J Visual Commun Image Represent 68(10):2768. https://doi.org/10.1016/j.jvcir.2020.102768

    Google Scholar 

  29. Strang G (2016) Introduction to Linear Algebra. Cambridge Press, Fifth edition

  30. Singh P, Raman B (2018) Reversible data hiding based on Shamir’s secret sharing for color images over cloud. Inf Sci 422:77–97

    Article  MATH  Google Scholar 

  31. Shamir A (1979) How to share a secret. Commun ACM 22(11):612–613

    Article  MathSciNet  MATH  Google Scholar 

  32. Shiu P-F, Tai W-L, Jan J-K, Chang C-C, Lin C-C (2019) An Interpolative AMBTC-based high-payload RDH scheme for encrypted images. Signal Process: Image Commun 74:64–77

    Google Scholar 

  33. Thien C-C, Lin J-C (2002) Secret image sharing. Comput Graphics 26(5):765–770

    Article  Google Scholar 

  34. Wang Z-H, Pizzolatti MS, Chang Ch-Ch (2014) Efficient and meaningful multisecret image sharing based on block imitation. J Inform Hiding Multimed Signal Process 5(1):47–60

    Google Scholar 

  35. Wu X, Yang CN (2019) Partial reversible AMBTC-based secret image sharing with steganography. Digit Signal Process 93:22–33

    Article  Google Scholar 

  36. Wu X, Yang C (2019) Invertible secret image sharing with steganography and authentication for AMBTC compressed images. Signal Process Image Commun 78:437–447

    Article  Google Scholar 

  37. Xiong L, Han X, Yang CN (2021) CP-PSIS: CRT And polynomial-based progressive secret image sharin. Signal Processing 185. https://doi.org/10.1016/j.sigpro.2021.108064

  38. Xiong L, Han X, Yang CN (2021) Transform Domain-Based invertible and lossless secret image sharing with authentication. IEEE Trans Inform Forensics Secur 16:2912–2925

    Article  Google Scholar 

  39. Xiong L, Zhong X, Yang C (2020) DWT-SISA: a secure and effective discrete wavelet transform-based secret image sharing with authentication. Signal Process 173:107571. https://doi.org/10.1016/j.sigpro.2020.107571

    Article  Google Scholar 

  40. Yan X, Lu Y, Liu L, Song X (2020) Reversible image secret sharing. IEEE Trans Inform Forensics Secur 15:3848–3858

    Google Scholar 

  41. Yan X, Li J, Pan Z, Zhong X, Yang G (2021) Multiparty verification in image secret sharing. Inf Sci 562:475–490

    Article  MathSciNet  Google Scholar 

  42. Yang C, Chen T, Yu K, Wang C (2007) Improvements of image sharing with steganography and authentication. J Syst Softw 80:1070–1076

    Article  Google Scholar 

  43. Yang C-N, Ouyang J-F, Harn L (2012) Steganography and authentication in image sharing without parity bits. Opt Commun 285(7):1725–1735

    Article  Google Scholar 

  44. Yang C-N, Wu C, Lin Y, Kim C (2012) Enhanced Matrix-Based secret image sharing scheme. IEEE Signal Process Lett 19:789–792

    Article  Google Scholar 

  45. Yuan HD (2014) Secret sharing with multi-cover adaptive steganography. Inf Sci 254:197–212

    Article  MathSciNet  MATH  Google Scholar 

  46. Zarepour-Ahmadabadi J, Ahmadabadi MS, Latif A (2016) An adaptive secret image sharing with a new bitwise steganographic property. Inf Sci 369:467–480

    Article  MathSciNet  Google Scholar 

  47. Zhou X, Lu Y, Yan X, Wang Y, Liu L (2018) Lossless and efficient Polynomial-Based secret image sharing with reduced shadow size. Symmetry 10. https://doi.org/10.3390/sym10070249

  48. Zhu L, Luo X, Zhang Y, Yang C, Liu F (2021) Inverse interpolation and its application in robust image steganography. IEEE Transactions on Circuits and Systems for Video Technology. https://doi.org/10.1109/TCSVT.2021.3107342

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Correspondence to Samaneh Mashhadi.

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Mashhadi, S., Saeedi, Z. A (t,n)- Secret image sharing with steganography based on Rook polynomial and LWE problem. Multimed Tools Appl 82, 39077–39097 (2023). https://doi.org/10.1007/s11042-023-15016-6

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  • DOI: https://doi.org/10.1007/s11042-023-15016-6

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