
تعداد نشریات | 43 |
تعداد شمارهها | 1,685 |
تعداد مقالات | 13,838 |
تعداد مشاهده مقاله | 32,742,603 |
تعداد دریافت فایل اصل مقاله | 12,944,233 |
Ideal secret sharing schemes on graph-based $3$-homogeneous access structures | ||
Transactions on Combinatorics | ||
دوره 10، شماره 2، شهریور 2021، صفحه 107-120 اصل مقاله (297.71 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2021.123661.1739 | ||
نویسندگان | ||
Shahrooz Janbaz* 1؛ Bagher Bagherpour2؛ Ali Zaghian2 | ||
1Electrical and computer faculty, Malek Ashtar University of Technology, Tehran, Iran | ||
2Department of Mathematics and Cryptography, Malek Ashtar University of Technology, Isfahan, Iran | ||
چکیده | ||
The characterization of the ideal access structures is one of the main open problems in secret sharing and is important from both practical and theoretical points of views. A graph-based $3-$homogeneous access structure is an access structure in which the participants are the vertices of a connected graph and every subset of the vertices is a minimal qualified subset if it has three vertices and induces a connected graph. In this paper, we introduce the graph-based $3-$homogeneous access structures and characterize the ideal graph-based $3$-homogeneous access structures. We prove that for every non-ideal graph-based $3$-homogeneous access structure over the graph $G$ with the maximum degree $d$ there exists a secret sharing scheme with an information rate $\frac{1}{d+1}$. Furthermore, we mention three forbidden configurations that are useful in characterizing other families of ideal access structures. | ||
کلیدواژهها | ||
Cryptography؛ Secret sharing؛ Ideal access structures؛ Graph-based access structures؛ 3-homogeneous access structures | ||
مراجع | ||
[1] B. Bagherpour, S. Janbaz and A. Zaghian, Optimal information ratio of secret sharing schemes on Dutch Windmill graphs, Adv. Math. Commun., 13 (2019) 88–99. [2] G. R. Blakley, Safeguarding cryptographic keys, In proceeding of the AFIPS conference, 48 (1979) 313–317.
[3] C. Blundo, A. De Santis, R. De Simone and U. Vaccaro, Tight bounds on the information rate of the secret sharing scheme, Des. Codes Cryptogr., 11 (1997) 107-122. [4] C. Blundo, A. De Santis, D. R. Stinson and U. Vaccaro, Graph decomposition and secret sharing schemes, J. Cryptology, 8 (1998) 39–64. [5] E. F. Brickell and D. M. Davenport, On the classification of ideal secret sharing schemes, Journal of Cryptology, 4 (1991) 123–134. [6] L. Csirmas and G. Tardos, Optimal information rate of the secret sharing schemes on trees, IEEE Transaction on information theory, 59 (2013). [7] W. Jackson and K. M. Martin, Perfect secret sharing schemes on five participants, Des. Codes Cryptogr., 9 (1996) 267–286. [8] J. Martı́-Farré and C. Padró, Secret sharing schemes with three or four minimal qualified subsets, Des. Codes Cryptogr., 34 (2005) 17–34. [9] J. Martı́-Farré, A note on secret sharing schemes with three homogeneous access structure, Inform. Process. Lett., 102 (2007) 133–137. [10] J. Martı́-Farré and C. Padró, Ideal secret sharing scheme whose minimal qualified subsets have at most three participants, Des. Codes Cryptogr., 52 (2009) 1–14. [11] J. Martı́-Farré and C. Padró, Secret sharing schemes on access structures with intersection number equal to one, Discrete Appl. Math., 154 (2006) 552–563. [12] J. Martı́-Farré and C. Padró, Secret sharing schemes on sparse homogeneous access structures with rank three, Electron. J. Combin., 11 (2004) 16 pp. [13] M. Ito, A. Saito and T. Nishizeki, Secret sharing scheme realizing any access structure, Proc. IEEE Globecom, 87 (1987) 99–102. [14] C. Padró and G. Sáez, Secret sharing with bipartite access structure, IEEE Trans. Inform. Theory, 46 (2000) 2596–2604. [15] C. Padró and G. Sáez, Lower bounds on the information rate of secret sharing schemes with homogeneous access structure, Inform. Process. Lett., 83 (2002) 345-351. [16] A. Shamir, How to share a secret, Comm. ACM, 22 (1979) 612–613.
[17] D. R. Stinson, An explanation of secret sharing scheme, Designs, Codes and Cryptography, (1992) 157–390.
[18] D. R. Stinson, Decomposition construction for secret sharing schemes, IEEE Trans. Inform. Theory, 40 (1994) 118-125. [19] T. Tassa and N. Dyn, Multipartite secret sharing by bivariate interpolation, J. Cryptology, 22 (2009) 227-258.
[20] T. Tassa, Hierarchical Threshold Secret Sharing, J. Cryptology, 20 (2007) 237-264. | ||
آمار تعداد مشاهده مقاله: 271 تعداد دریافت فایل اصل مقاله: 284 |