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Some New Bounds on the Information Ratio of the Cartesian Product of Some Classes of Graphs | ||
پدافند الکترونیکی و سایبری | ||
Article 11, Volume 6, Issue 4 - Serial Number 24, April 2019, Pages 135-142 PDF (1.32 M) | ||
Document Type: Original Article | ||
Authors | ||
Abbas Cheraghi Chaleshtari* ; Mohammad Gholami | ||
Receive Date: 13 January 2018, Accept Date: 27 May 2018 | ||
Abstract | ||
In this paper, we find a lower-bound for the information ratio of the cartesian product of an arbitrary tree with diameter at least 3 and a cycle Cm for every m³3. Moreover, we determine the best information ratio of the perfect secret sharing scheme based on the graph constructed from the cartesian product of a cycle of length 6 with the d -dimensional cube Qd . More precisely, it is shown that for every d³1 , the information ratio of is exactly | ||
Keywords | ||
Secret Sharing Scheme; Information Ratio; Cartesian Product | ||
References | ||
[1] A. Shamir, “How to share a secret,” Comm. ACM, vol. 22, pp. 612-613, 1979.## [2] G. R. Blakley, “Safe guarding cryptographic keys,” in AFIPS Conference Proceedings, New York, United States of America, pp. 313-317, June 4-7, 1979.## [3] C. Blundo, et al., “On the information rate of secret sharing schemes,” Theor. Comput. Sci., vol. 154, no. 2, pp. 283-306, 1996.## [4] L. Csirmaz, “The size of a share must be large,” J. Cryptol, vol. 10, pp. 223-231, 1997.## [5] C. Blundo, A. De Santis, D. R. Stinson, and U. Vaccaro, “Graph decomposition and secret sharing schemes,” J. Cryptol, vol. 8, pp. 39-64, 1995.## [6] E. F. Brickell and D. M. Davenport, “On the classification of ideal secret sharing schemes,” J. Cryptol, vol. 4, pp. 123-134, 1991.## [7] E. F. Brickell and D. R. Stinson, “Some improved bounds on the information rate of perfect secret sharing schemes,” J. Cryptol, vol. 5, pp. 153-166, 1992.## [8] J. Martí-Farré and P. Carles “On secret sharing schemes, matroids and polymatroids,” J. Math. Cryptol, vol. 4, pp. 95-120, 2010.## [9] M. Van Dijk, “On the information rate of perfect secret sharing schemes,” Design. Code. Cryptogr., vol. 6, pp. 143-160, 1995.## [10] W. A. Jackson and K. M. Martin, “Perfect secret sharing schemes on five participants,” Design. Code. Cryptogr, vol. 9, pp. 267-286, 1996.## [11] C. Padro, “Lecture notes in secret sharing,” Available at http://eprint.iacr.org/2012/674, 2012.## [12] M. Gharahi and S. Khazaei, “Reduced access structures with four minimal qualified subsets on six participants,” Adv. Math. Commun. vol. 12, pp. 199-214, 2018.## [13] L. Csirmaz and G. Tardos, “Optimal information rate of secret sharing schemes on trees,” IEEE Trans. Inf. Theory, vol. 59, pp. 2527-2530, 2013.## [14] L. Csirmaz and P. Ligeti, “On an infinite family of graphs with information ratio 2−1/k,” Computing, vol. 85, pp. 127-136, 2009.## [15] L. Csirmaz, “Secret sharing on the d-dimensional cube,” Design. Code. Cryptogr, vol. 74, pp. 719-729, 2015.## [16] A. Cheraghi, G. Raeisi and M. Gholami, “On the information ratio of a class of graphs,” First International Conference on Combinatorics, Cryptography and Computation, I4C2016, IUST, Nour branch, Mazandaran, Iran, Sep. 2016.## [17] D. R. Stinson, “Decomposition construction for secret sharing schemes,” IEEE Trans. Inf. Theory, vol 40, pp. 118-125, 1994.## [18] W. Wang, Z. Li, and Y. Song, “The optimal information rate of perfect secret sharing schemes,” In 2011 International Conference on Business Management and Electronic Information (BMEI), Guangzhou, China, May 13-15, pp. 207-212, 2011.## [19] Z. Karimifard, S. Mashhadi, and D. Ebrahimi Bagha, “Semiquantum Secret Sharing Using Three Particles Without [20] H. Maimani, Z. Norozi, “Secret sharing based on Cartesian product of graphs”, Iranian J. Math. Sci. Info, vol. 8, pp. 31-38, 2013.## [21] L. Csirmaz, “Secret sharing on infinite graphs,” Tetra Mount. Math. Pub, vol. 41, pp.1-18, 2008.## | ||
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