Abstract
The secret sharing scheme by Dileep et al. [19] uses Level ordered access structure which is missing in the existing access structures. In their scheme, sequential reconstruction of the secret is achieved by adding a virtual player at all the levels except at the first level. In this paper, we propose a variation of sequential secret sharing scheme for level ordered access structure (LOAS) [19], where multisecrets are distributed to multilevels each corresponding to a level by using the concepts of quadratic residues and discrete logarithm problem. The method consists of sharing of m secrets in m levels, each corresponding to a level. The distribution of secrets is based on quadratic residues concept and that of the discrete logarithm problem. The reconstruction of secrets is such that players of different levels find their respective level secrets individually only after they get their immediate higher level permission. Verification phase is also added at all the levels which guarantees the correctness of the shares in the presence of any cheater. The comparison of the proposed secret sharing scheme with existing secret sharing schemes, time complexity of the scheme and security analysis of the scheme for passive adversary model are discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Blakley, G.R.: Safeguarding cryptographic keys. AFIPS 48, 313–317 (1979)
Simmons, G.J.: How to (really) share a secret. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 390–448. Springer, New York (1990). https://doi.org/10.1007/0-387-34799-2_30
Tassa, T.: Hierarchical threshold secret sharing. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 473–490. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24638-1_26
Tassa, T., Dyn, N.: Multipartite secret sharing by bivariate interpolation. J. Cryptol. 22, 227–258 (2009)
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). https://doi.org/10.1007/BFb0053748
Tentu, A.N., Paul, P., Venkaiah, V.C.: Computationally perfect secret sharing scheme based on error-correcting codes. In: MartÃnez Pérez, G., Thampi, S.M., Ko, R., Shu, L. (eds.) SNDS 2014. CCIS, vol. 420, pp. 251–262. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54525-2_23
Tentu, A.N., Paul, P., Venkaiah, V.C.: Computationally perfect secret sharing schemes based on MDS codes. Int. J. Trust Manag. Comput. Commun. (IJTMCC) 2(4), 353–378 (2014)
Basit, A., Kumar, N.C., Venkaiah, V.C., Moiz, S.A., Tentu, A.N., Naik, W.: Multi-stage Multi-secret sharing scheme for hierarchical access structure. In: 2017 IEEE International Conference on Computing, Communication and Automation (ICCCA), Noida (2017, in press)
Iftene, S.: Compartmented secret sharing based on the Chinese remainder theorem, Cryptology ePrint Archive, Report 2005/4 08 (2005)
Singh, N., Tentu, A.N., Basit, A., Venkaiah, V.C.: Sequential secret sharing scheme based on Chinese remainder theorem. In: IEEE International Conference on Computational Intelligence and Computing Research (ICCIC), pp. 1–6 (2016)
He, J., Dawson, E.: Multistage secret sharing based on one-way function. Electron. Lett. 30(19), 1591–1592 (1994)
Harn, L.: Comment: multistage secret sharing based on one-way function. Electron. Lett. 31(4), 262 (1995)
Chang, T.-Y., Hwang, M.-S., Yang, W.-P.: A new multi-stage secret sharing scheme using one-way function. Oper. Syst. Rev. 39(1), 48–55 (2005)
Chanu, O.B., Tentu, A.N., Venkaiah, V.C.: Multi-stage multi-secret sharing schemes based on Chinese remainder theorem. In: International Conference on Advanced Research in Computer Science Engineering Technology (ICARCSET 2015), Unnao, India, vol. 17, no. 6 (2015)
Zhao, J., Zhang, J., Zhao, R.: A practical verifiable multi-secret sharing scheme. Comput. Stand. Interfaces 29(1), 138–141 (2007)
Tentu, A.N., Mahapatra, B., Venkaiah, V.C., Prasad, V.K.: New secret sharing scheme for multipartite access structures with threshold changeability. In: International Conference on Advances in Computing, Communications and Informatics, ICACCI 2015, Kochi, India, 10–13 Aug 2015
Nojoumian, M., Stinson, D.R.: Sequential secret sharing as a new hierarchical access structure. J. Internet Serv. Inf. Secur. (JISIS) 5(2), 23–31 (2015)
Dileep, K.P., Tentu, A.N., Venkaiah, V.C., Apparao, A.: Sequential secret sharing scheme based on level ordered access structure. J. Netw. Secur. 18(5), 874–881 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Tentu, A.N., Basit, A., Bhavani, K., Venkaiah, V.C. (2018). Multi-secret Sharing Scheme for Level-Ordered Access Structures. In: Kaczorowski, J., Pieprzyk, J., Pomykała, J. (eds) Number-Theoretic Methods in Cryptology. NuTMiC 2017. Lecture Notes in Computer Science(), vol 10737. Springer, Cham. https://doi.org/10.1007/978-3-319-76620-1_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-76620-1_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76619-5
Online ISBN: 978-3-319-76620-1
eBook Packages: Computer ScienceComputer Science (R0)