Abstract
In this paper, we propose a secret sharing scheme for compartmented access structure with lower bounds. Construction of the scheme is based on the Maximum Distance Separable (MDS) codes. The proposed scheme is ideal and 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. This is in contrast to some of the existing schemes in the literature, in which an authorized set can recover the secret only with certain probability. Also, in our scheme unlike in some of the existing schemes, the size of the ground field need not be extremely large. This scheme is efficient and requires O(mn 3), where n is the number of participants and m is the number of compartments.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Beimel, A., Tassa, T., Weinreb, E.: Characterizing ideal weighted threshold secret sharing. SIAM J. Disc. Math. 22(1), 360–397 (2008)
Blakley, G.R.: Safeguarding cryptographic keys. AFIPS 48, 313–317 (1979)
Blakley, G.R., Kabatianski, A.: Ideal perfect threshold schemes and MDS codes. ISIT 1995, 488 (1995)
Brickell, E.F.: Some ideal secret sharing schemes. J. Comb. Math. Comb. Comput. 9, 105–113 (1989)
Collins, M.J.: A note on ideal tripartite access structures, manuscript available at http://eprint.iacr.org/2002/193/2002
Farràs, O., Martí-Farré, J., Padró, C.: Ideal multipartite secret sharing schemes. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 448–465. Springer, Heidelberg (2007)
Farràs, O., Padró, C., Xing, C., Yang, A.: Natural generalizations of threshold secret sharing. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 610–627. Springer, Heidelberg (2011)
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)
Herranz, J., Saez, G.: New results on multipartite access structures. IEEE Proc. Inf. Secur. 153, 153–162 (2006)
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, IT-29, 35–41 (1983)
Kaskaloglu, K., Ozbudak, F.: On hierarchical threshold access structures. In: IST Panel Symposium, Tallinn, Estonia (November 2010)
McEliece, R.J., Sarwate, D.V.: On sharing secrets and Reed Solomon codes. Communications of the ACM 24, 583–584 (1981)
Ng, S.-L.: Ideal Secret Sharing Schemes with multipartite access structures. IEEE Proc. Commun. 153, 165–168 (2006)
Ozadam, H., Ozbudak, F., Saygi, Z.: Secret sharing schemes and linear codes. In: ISC, Ankara, pp. 101–106 (2007)
Shamir, A.: How to share a secret. Comm. ACM 22, 612–613 (1979)
Simmons, G.J.: How to (Really) Share a secret. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 390–448. Springer, Heidelberg (1990)
Naidu, T.A., Paul, P., Venkaiah, V.C.: Ideal and Perfect Hierarchical Secret Sharing Schemes based on MDS codes. In: Proceeding of International Conference on Applied and Computaional Mathematics, Ankara, Turkey, pp. 256–272 (2012)
Tentu, A.N., Paul, P., Vadlamudi, C.V.: Conjunctive Hierarchical Secret Sharing Schemes based on MDS codes. In: Lecroq, T., Mouchard, L. (eds.) IWOCA 2013. LNCS, vol. 8288, pp. 463–467. Springer, Heidelberg (2013)
Naidu, T.A., Paul, P., Venkaiah, V.C.: Ideal and Perfect Hierarchical Secret Sharing Schemes based on MDS codes, eprint.iacr.org/2013/189.pdf
The Theory of Error-Correcting Codes. Macwilliams, Sloane (1981)
Tassa, T.: Hierarchical Threshold Secret Sharing. Journal of Cryptology 20, 237–264 (2007)
Tassa, T., Dyn, N.: Multipartite Secret Sharing by Bivariate Interpolation. Journal of Cryptology 22, 227–258 (2009)
Vinod, V., Narayanan, A., Srinathan, K., Pandu Rangan, C., Kim, K.: On the power of computational secret sharing. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 162–176. Springer, Heidelberg (2003)
Yu, Y., Wang, M.: A Probabilistic secret sharing scheme for a compartmented access structure. In: Qing, S., Susilo, W., Wang, G., Liu, D. (eds.) ICICS 2011. LNCS, vol. 7043, pp. 136–142. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tentu, A.N., Paul, P., Venkaiah, V.C. (2014). Computationally Perfect Secret Sharing Scheme Based on Error-Correcting Codes. In: Martínez Pérez, G., Thampi, S.M., Ko, R., Shu, L. (eds) Recent Trends in Computer Networks and Distributed Systems Security. SNDS 2014. Communications in Computer and Information Science, vol 420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54525-2_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-54525-2_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-54524-5
Online ISBN: 978-3-642-54525-2
eBook Packages: Computer ScienceComputer Science (R0)