Abstract
An ideal conjunctive hierarchical secret sharing scheme, constructed based on the Maximum Distance Separable (MDS) codes, is proposed in this paper. The scheme, what we call, is computationally perfect. By computationally perfect, we mean, an authorized set can always reconstruct the secret in polynomial time whereas for an unauthorized set this is computationally hard. Also, in our scheme, the size of the ground field is independent of the parameters of the access structure. Further, it is efficient and requires O(n 3), where n is the number of participants.
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References
Belenkiy, M.: Disjunctive multi-level secret sharing.document, http://eprint.iacr.org/2008/018
Blakley, G.R.: Safeguarding cryptographic keys. In: AFIPS Conference Proceedings, vol. 48, pp. 313–317 (1979)
Blakley, G.R., Kabatianski, G.A.: Ideal perfect threshold schemes and MDS codes. In: IEEE Conf. Proc., Int. Symp. Information Theory, ISIT 1995, p. 488 (1995)
Brickell, E.F.: Some ideal secret sharing schemes. J. Comb. Math. Comb. Comput. 9, 105–113 (1989)
Farras, O., Padro, C.: Ideal hierarchical secret sharing schemes. IEEE Trans. Inf. Theory (January 2012)
Ghodosi, H., Pieprzyk, J., Safavi-Naini, R.: Secret sharing in multilevel and compartmented groups. In: Boyd, C., Dawson, E. (eds.) ACISP 1998. LNCS, vol. 1438, pp. 367–378. Springer, Heidelberg (1998)
Pieprzyk, J., Zhang, X.-M.: Ideal Threshold Schemes from MDS Codes. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 253–263. Springer, Heidelberg (2003)
Karnin, E.D., Greene, J.W., Hellman, M.E.: On secret sharing systems. IEEE Trans. Inf. Theory 29, 35–41 (1983)
Kothari, S.C.: Generalized linear threshold scheme. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 231–241. Springer, Heidelberg (1985)
Kaskaloglu, K., Ozbudak, F.: On hierarchical threshold access structures. IST panel symposium, Tallinn, Estonia, Nov.document (2010)
Lin, C., Harn, L.: Ideal perfect multilevel threshold secret sharing scheme. In: Proc. Fifth Intl. Conf. Inf. Assur. and Security, pp. 118–121 (2009)
Massey, J.L.: Minimal codewords and secret sharing. In: Proc. 6th Joint Swedish - Russian Workshop on Inform. Theory, pp. 269–279 (1993)
McEliece, R.J., Sarwate, D.V.: On sharing secrets and Reed Solomon codes. Comm. of ACM 24, 583–584 (1981)
Shamir, A.: How to share a secret. Comm. ACM 22, 612–613 (1979)
Tassa, T.: Hierarchical Threshold Secret Sharing. Journal of Cryptology, 237-264 (2007)
Tassa, T., Dyn, N.: Multipartite Secret Sharing by Bivariate Interpolation. Journal of Cryptology 22, 227–258 (2009)
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Tentu, A.N., Paul, P., Vadlamudi, C.V. (2013). Conjunctive Hierarchical Secret Sharing Scheme Based on MDS Codes. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_44
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