A Verifiable Secret Image Sharing Scheme Based on Compressive Sensing

  • Xinyan Li
  • Di Xiao
  • Huajian Mou
  • Rui Zhang
Computer Science


This paper proposes a verifiable secret image sharing scheme based on compressive sensing, secret sharing, and image hashing. In this scheme, Toeplitz matrix generated by two chaotic maps is employed as measurement matrix. With the help of Shamir threshold scheme and image hashing, the receivers can obtain the stored values and the hash value of image. In the verifying stage and restoring stage, there must be at least t legal receivers to get the effective information. By comparing the hash value of the restored image with the hash value of original image, the scheme can effectively prevent the attacker from tampering or forging the shared images. Experimental results show that the proposed scheme has good recovery performance, can effectively reduce space, and is suitable for real-time transmission, storage, and verification.

Key words

compressive sensing secret sharing measurement matrix image hashing 

CLC number

TP 309 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Shamir A. How to share a secret [J]. Communication of ACM, 1979, 24(11): 612–613.CrossRefGoogle Scholar
  2. [2]
    Blakley R. Safeguarding cryptographic keys [C] // AFIPS National Computer Conference. Piscataway: IEEE, 1979: 313–317.Google Scholar
  3. [3]
    Chang C C, Huynh N T, Le H D. Lossless and unlimited multi-image sharing based on Chinese remainder theorem and Lagrange interpolation [J]. Signal Process, 2014, 99: 159–170.CrossRefGoogle Scholar
  4. [4]
    Chen C C, Wu W J. A secure Boolean-based multi secret image sharing scheme [J]. Journal of Systems and Software, 2014, 92: 107–114.CrossRefGoogle Scholar
  5. [5]
    Guo C, Chang C C, Qin C. A multi-threshold secret image sharing scheme based on MSP [J]. Pattern Recognition Letters, 2012, 3(12): 1594–1600.CrossRefGoogle Scholar
  6. [6]
    Islam N, Puech W, Hayat K, et al. Application of homomorphism to secure image sharing [J]. Optics Communications, 2011, 284(19): 4412–4429.CrossRefGoogle Scholar
  7. [7]
    Li L, Latif A A, Niu X. Elliptic curve ELGamal based homomorphic image encryption scheme for sharing secret images [J]. Signal Processing, 2012, 92(4): 1069–1078.CrossRefGoogle Scholar
  8. [8]
    Faraoun K M. Design of a new efficient and secure multi-secret images sharing scheme [J]. Multimedia Tools and Applications, 2017, 76: 1–15.CrossRefGoogle Scholar
  9. [9]
    Yang C N, Chen C H, Cai S R. Enhanced Boolean-based multi-secret image sharing scheme [J]. Journal of Systems and Software, 2016, 116: 22–24.CrossRefGoogle Scholar
  10. [10]
    Deng X, Wen W, Shi Z. Threshold multi-secret sharing scheme based on phase-shifting interferometry [J]. Optics Communications, 2017, 387(15): 409–414.CrossRefGoogle Scholar
  11. [11]
    Faraoun K M. A novel fast and provably secure (t,n)-threshold secret sharing construction for digital images [J]. Journal of Information Security and Applications, 2014, 19(6): 331–340.CrossRefGoogle Scholar
  12. [12]
    Liu L, Wang A H, Chang C C. A novel real-time and progressive secret image sharing with flexible shadows based on compressive sensing [J]. Signal Processing: Image Communication, 2014, 29(1): 128–134.Google Scholar
  13. [13]
    Huang C P, Li C C. A secret image sharing method using integer wavelet transform [J]. EURASIP Journal on Advances in Signal Processing, 2007, 2: 263–281.Google Scholar
  14. [14]
    Huang C P. Secure, error-resilient, and real-time progressive image transmission [J]. Optical Engineering, 2009, 48(12): 127–139.CrossRefGoogle Scholar
  15. [15]
    Donoho D L. Compressed sensing [J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306.CrossRefGoogle Scholar
  16. [16]
    Xiao D, Deng M, Zhu X. A reversible image authentication scheme based on compressive sensing [J]. Multimedia Tools and Applications, 2015, 74(18): 7729–7752.CrossRefGoogle Scholar

Copyright information

© Wuhan University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsYangtze Normal UniversityChongqingChina
  2. 2.College of Computer ScienceChongqing UniversityChongqingChina
  3. 3.College of Computer EngineeringYangtze Normal UniversityChongqingChina

Personalised recommendations