Abstract
When traditional secret image sharing techniques reconstructed the secret, they input the shares over t. While less than t shares can know nothing about the secret, the problem arises when there are more than t shares. The cheater can use this to put their share in the last. Therefore, fairness is a important objective of the secret image sharing. Tian et al. proposed the fairness secret sharing scheme in 2012. However, they generated v polynomials for one secret data and performed v-times to reconstruct the polynomial using Lagrange interpolation. Therefore, their scheme is unsuitableness in the real-time processing. The proposed scheme generates one polynomial for the one secret data based on the fairness concept of Tian et al.’s scheme. For the providing fairness, the proposed scheme hides the verification value at the random coefficient of the polynomial. During the secret image reconstruction procedure, each shadow image brought by a participant is verified for its fairness using XOR operation. Our scheme not only satisfies the fairness, but also is suitable for the real-time process. This helps to detect the participant from intentional provision of a false or cheating. In addition, our scheme uses the steganography technique for increasing the security protection purpose. The proposed scheme as a whole offers a high secure and effective mechanism for the secret image sharing that is not found in existing secret image sharing methods. In the experimental result, PSNR of the proposed scheme is average 44.67 dB. It is higher 4 dB than the previous schemes. The embedding capacity is also similar to the other schemes.
Similar content being viewed by others
References
Stinson, D.R.: Cryptography theory and practice. 3rd edn. Chapman & Hall/CRC Press (2006)
William, S.: Cryptography and Network Security. 4th edn. Prentice Hall (2006)
Menezes, A.J., Van Oorschot, P.C., Vanstone, S.A.: Handbook of applied cryptography. CRC press (1996)
Shamir, A.: How to share a secret. Commun. ACM 22, 612–613 (1979)
Thien, C.C., Lin, J.C.: Secret image sharing. Comput. Graph. 26(5), 765–770 (2002)
Thien, C.C., Lin, J.C.: An image sharing method with user-friendly shadow images. IEEE Trans. Circuit Syst. Video Technol. 13(12), 1161–1169 (2003)
Lin, C.C., Tsai, W.H.: Secret image sharing with steganography and authentication. J. Syst. Softw. 73(3), 405–414 (2004)
Yang, C.N., Chen, T.S., Yu, K.H., Wang, C.C.: Improvements of image sharing with steganography and authentication. J. Syst. Softw. 80(7), 1070–1076 (2007)
Chang, C.C., Hsieh, Y.P., Lin, C.H.: Sharing secrets in stego images with authentication. J. Pattern Recognit. 41(10), 3130–3137 (2008)
Wang, R.Z., Shyu, S.J.: Scalable secret image sharing. J. Signal Process. Image Commun. 22(4), 363–373 (2008)
Mustafa, U., Ulutas, G., Nabiyev, V.V.: Invertible secret image sharing for gray level and dithered cover images. J. Syst. Softw. 86(2), 485–500 (2013)
Lin, P.Y., Chan, C.S.: Invertible secret image sharing with steganography. Pattern Recognit. Lett. 31(13), 1887–1893 (2010)
Blakley, G.R.: Safeguarding cyptographic keys. Manag. Requir. Knowl. Int. Workshop IEEE Comput. Soc. 31(13), 1887–1893 (1979)
Mignotte, M.: How to share a secret. Cryptography, pp 371-375 (1983)
Pang, L.J., Wang, Y.M.: A new \((t, n)\) multi-secert sharing scheme base on Shamir’s secret sharing. Appl. Math. Comput. 167–1, 840–848 (2005)
Beimel, A.: Secret sharing schemes : a survey. Coding Cryptol, 11–46 (2011)
Yang, C.N., Ouyang, J.F., Harn, L.: Steganography and authentication in image sharing without parity bits. Optics Commun., 1725–1735 (2011)
Chang, C.C., Chen, Y.H., Wang, H.C.: Meaningful secret sharing technique with authentication and remedy abilities. Inf. Sci., 3073–3084 (2011)
Tian, Y., Ma, J., Peng, C., Jiang, Q.: Fair \((t,n)\) threshold secret sharing scheme. IET Inf. Secur., 106–112 (2012)
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. Adv. Cryptol. 576, 129–140 (1992)
Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: Proceedings of the 28th Annual Symposium on Foundations of Computer Science, pp 427-437 (1987)
Harn, L., Lin, C.: Detection and identification of cheaters in \((t, n)\) secret sharing scheme. Des. Codes Cryptogr. 52(1), 15–24 (2009)
Harn, L., Lin, C.: Fair reconstruction of a secret. Inf. Process. Lett. 55, 45–47 (1995)
Naor, M., Shamir, A.: Visual cryptography. Ad. Cryptol. EuroCrypt’94. 950, 1–2 (1995)
Lin, C.C., Tsai, W.H.: Visual cryptography for gray-level images by dithering techniques. Pattern Recognit. Lett. 24, 349–358 (2003)
Hou, Y.C.: Visual cryptography for color images. Pattern Recognit. 36(7), 1619–1629 (2003)
Tompa, M., Woll, H.: How to share a secret with cheaters. J. Cryptol. 1(3), 133–138 (1988)
Benaloh, J.C.: Secret sharing homomorphisms: keeping shares of a secret sharing. In: Odlyzko, A.M. (ed.) Advances in Cryptology - CRYPTO '86, vol. 263, pp. 251–260. Springer, Berlin, Heidelberg (1987)
Ghodosi, H., Pieprzyk, J., Safavi-Naini, R.: Remarks on the multiple assignment secret sharing scheme. ICICS 97. 1334, 72–80 (1997)
Harn, L., Lin, C.: Strong \((n, t,n)\) verifiable secret sharing scheme. Inf. Sci. 180, 3059–3064 (2010)
Acknowledgments
This work was supported by the IT R&D program of MSIP / IITP [10041145, Self-Organized Software platform (SoSp) for Welfare Devices] and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2015R1D1A1A01060801).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lee, GJ., Yoon, EJ., Kim, C. et al. A real-time secret image sharing with fairness. J Real-Time Image Proc 14, 5–12 (2018). https://doi.org/10.1007/s11554-015-0558-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11554-015-0558-7