A generalization of the Mignotte's scheme over Euclidean domains and applications to secret image sharing
DOI:
https://doi.org/10.13069/jacodesmath.617239Keywords:
Mignotte sequences, Secret image sharing, Secret sharing scheme, Euclidean domainAbstract
Secret sharing scheme is an efficient method to hide secret key or secret image by partitioning it into parts such that some predetermined subsets of partitions can recover the secret but remaining subsets cannot. In 1979, the pioneer construction on this area was given by Shamir and Blakley independently. After these initial studies, Asmuth-Bloom and Mignotte have proposed a different $(k,n)$ threshold modular secret sharing scheme by using the Chinese remainder theorem. In this study, we explore the generalization of Mignotte's scheme to Euclidean domains for which we obtain some promising results. Next, we propose new algorithms to construct threshold secret image sharing schemes by using Mignotte's scheme over polynomial rings. Finally, we compare our proposed scheme to the existing ones and we show that this new method is more efficient and it has higher security.
Received: 10 February 2019 Accepted: 19 August 2019Downloads
References
C. Asmuth and J. Bloom, A modular approach to key safeguarding, IEEE Trans. Inform. Theory 29(2) (1983) 208–210.
G. R. Blakley, Safeguarding cryptographic keys, In: Proc. AFIPS 1979 National Computer Conf., AFIPS Press, Montvale, NJ (1979) 313–317.
D. Pei, A. Salomaa, and C. Ding, Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography, World Scientific, Singapore, 1996.
T. W. Hungerford, Abstract Algebra: An Introduction, 3rd ed., Cengage Learning, Boston, 2012.
S. Iftene, General secret sharing based on the Chinese Remainder Theorem with applications in E–Voting, Electron. Notes Theor. Comput. Sci. 186 (2007) 67–84.
E. V. Krishnamurthy, Error–Free Polynomial Matrix Computations, Texts and Monographs in Computer Science, Springer-Verlag, New York, 1985.
J. B. Lima and R. M. Campello de Souza, Histogram uniformization for digital image encryption, In: 25th SIBGRAPI Conference on Graphics, Patterns and Images, Ouro Preto, Brazil (2012) 55–62.
P. K. Meher and J. C. Patra, A new approach to secure distributed storage, sharing and dissemination of digital image, In: 2006 IEEE International Symposium on Circuits and Systems (ISCAS), Kos, Greece (2006) 373–376.
M. Mignotte, How to share a secret, In: Cryptography, EUROCRYPT 1982, Lecture Notes in Comput. Sci., vol. 149, Springer, Berlin, Heidelberg (1983) 371–375.
M. Naor and A. Shamir, Visual cryptography, In: Advances in Cryptology – EUROCRYPT 1994, Lecture Notes in Comput. Sci., vol. 950, Springer, Berlin, Heidelberg (1994) 1–12.
O. Ore, The general Chinese remainder theorem, Amer. Math. Monthly 59(6) (1952) 365–370.
A. Shamir, How to share a secret, Comm. ACM 22(11) (1979) 612–613.
S. J. Shyu and Y. R. Chen, Threshold secret image sharing by Chinese remainder theorem, In: 2008 IEEE Asia-Pacific Services Computing Conference, Yilan, Taiwan (2008) 1332–1337.
D. R. Stinson, An explication of secret sharing schemes, Des. Codes Cryptogr. 2(4) (1992) 357–390.
S. Somaraj and M. A. Hussain, Performance and Security Analysis for Image Encryption using Key Image, Indian J. Sci. Technol. 8(35) (2015) 1–10.
T. G. Mironova and G. M. Agayan, Generalized Mignotte's sequences over polynomial rings, Electron. Notes Theor. Comput. Sci. 186 (2007) 43–48.
C. C. Thien and J. C. Lin, Secret image sharing, Comput. & Graphics 26(5) (2002) 765–770.
G. Ulutas, M. Ulutas, and V. Nabiyev, Secret sharing scheme based on Mignotte's scheme, In: 2011 19th Signal Processing and Communications Applications Conference (SIU), Antalya, Turkey (2011) 291–294.
R. Z. Wang and C. H. Su, Secret image sharing with smaller shadow images, Pattern Recognition Lett. 27(6) (2006) 551–555.
Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Trans. Image Process. 13(4) (2004) 600–612.
