Vector space multisecret-sharing scheme based on Blakley’s method
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Keywords:
Secret Sharing, Multisecret-Sharing Scheme, Ideal Scheme, Blakley Method, Vector SpaceAbstract
Secret sharing schemes were introduced by Adi Shamir and George Blakley, independently, in 1979. In a (k,n)- threshold secret sharing scheme, any set of at least k out of n participants can retrieve the secret but no set of (k-1) or less can. Shamir’s secret sharing scheme is more popular than Blakley’s, even though the former is more complex than the latter. The practical reason is that Blakley’s scheme lacks determined, general and suitable matrices. In this paper, we present a multisecret-sharing scheme based on vector spaces over Rn and use Blakley’s method. This scheme is ideal in the sense that the size of each secret equals the size of any share.
References
H. Anton, C. Rorres, Elementary Linear Algebra, Applications Version, USA, 1994.
C. Asmuth and J. Bloom, A modular approach to key safeguarding, IEEE Trans. Information Theory, vol. 29, no. 2, pp. 208-210, 1993.
G. R. Blakley, Safeguarding Cryptographic Keys, in Proc. 1979 National Computer Conf., New York, pp. 313-317, Jun. 1979.
G. R. Blakley and G. A. Kabatianski, Linear algebra approach to secret sharing schemes, in Proc. of Error Control, Cryptology and Speech Compression, Lecture Notes in Computer Science, vol. 829, pp. 33-40, 1994.
I. N. Bozkurt, K. Kaya, A. A. Selçuk, A. M. Güloğlu, Threshold Cryptography Based on Blakley Secret Sharing, in Proc. of Information Security and Cryptology 2008, Ankara, Turkey, Dec. 2008.
C. C. Shen and W. Y. Fu, A geometry-based secret image sharing approach, Journal of Information Science and Engineering, vol. 24, no. 5, pp. 1567-1577, 2008.
S. Çalkavur, P. Solé, Multisecret-sharing schemes and bounded distance decoding of linear codes, International Journal of Computer Mathematics, vol. 94, no. 1, pp. 107-114, 2017.
C. Ding, T. Laihonen and A. Renvall, Linear multisecret-sharing schemes and error correcting codes, J. Comput. Sci. vol. 3, no. 9, pp. 1023-1036, 1997.
J. He and E. Dawson, Multistage secret sharing based on one-way function, Electronic Letters, vol. 30, no. 19, pp. 1591-1592, 1994.
X. Hei, X. Du, and B. Song, Two Matrices for Blakley’s Secret Sharing Scheme, IEEE ICC 2012-Communication and Information Systems Security Symposium, pp. 810-814, 2012.
L. Horn, Comment: Multistage secret sharing based on one-way function, Electronic Letters, vol. 31, no. 4, p. 262, 1995.
E. D. Karnin, J. W. Greene and M. E Hellman, On secret sharing systems, IEEE Trans. Inf. Theory IT, vol. 29, no. 1, pp. 35-41, 1983.
H. -X. Li, C. -.T. Cheng, and L. J. Pang, A New (t,n)- Threshold Multisecret Sharing Scheme, CIS 2005, vol. 3802, pp. 421-426, 2005.
C. Padro, Robust vector space secret sharing schemes, Information Processing Letters 68, pp. 107-111, 1998.
L. J. Pang and Y. -M. Wong, A New (t,n)- multisecret-sharing scheme based on Shamir’s secret sharing, Applied Math, vol. 167, pp. 840-848, 2005.
A. Shamir, How to share a secret, Comm. Of the ACM 22, pp. 612-613, 1979.
H. K. Tso, Sharing secret images using Blakley’s concept, Optical Engineering, vol. 47, no. 7, pp. 21-23, 2008.
M. Ulutaş, V. V. Nabiyev and G. Ulutaş, Improvements in Geometry-Based Secret Image Sharing Approach with Steganography, Mathematical Problems in Engineering, vol. 53, pp. 101-110, 2009.
C. -C. Yang, T. Y. Chang, M. -S. Hwang, A New (t,n)- multisecret sharing scheme, Applied Mathematics and Computation, vol. 151, pp. 483-490, 2004.
