Abstract
Secret sharing scheme is a cryptographic primitive or a method for increasing the security of crucial information or data. It is used to share a secret among a set of participants, such that specific sets of participants can uniquely reconstruct the secret by pooling their shares. In this paper, we have proposed a new multi-secret sharing scheme for compartment access structure. In this access structure, the set of participants is partitioned into different compartments. The secret can be obtained only if the threshold number of participants from each of the compartments reconstruct their compartment secret, and participate in recovering the actual secret. The proposed scheme uses Shamir’s scheme first to retrieve partial secrets and combines them to form the requested secret. The scheme can also verify whether the retrieved secret is valid or not. Security analysis of the scheme is carried out and showed that the scheme resists both the insider as well as outsider attacks. Our proposed scheme is simple and easy to understand as we have used only the modular inverse concept.
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, vol. 48, pp. 313–317 (1979)
Brickell, E.F.: Some ideal secret sharing schemes. In: Workshop on the Theory and Application of Cryptographic Techniques, pp. 468–475, Springer, Berlin, Heidelberg, 10 Apr 1989
Iftene, S.: General secret sharing based on the chinese remainder theorem with applications” in e-voting. Electron. Notes Theor. Comput. Sci. 186, 67–84 (2007)
Farras, O., Padro, C., Xing, C., Yang, A.: Natural generalizations of threshold secret sharing. IEEE Trans. Inf. Theory. 60(3):1652–64 (2004)
Dawson, E., Donovan, D.: The breadth of Shamir’s secret-sharing scheme. Comput. Secur. 13(1), 69–78 (1994)
Karnin, E., Greene, J., Hellman, M.: On secret sharing systems. IEEE Trans. Inf. Theory 29(1), 35–41 (1983)
Franklin, M., Yung, M.: Communication complexity of secure computation. In: Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, pp. 699–710, ACM, 1 July 1992
Yang, C.-C., Chang, T.-Y., Hwang, M.-S.: A (t, n) multi-secret sharing scheme. Appl. Math. Comput. 151(2), 483–490 (2004)
Chien, H.-Y., Jan, J.-K., Tseng, Y.-M.: A practical (t, n) multi-secret sharing scheme. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 83(12), 2762–2765 (2000)
Endurthi, A., Chanu, O.B., Tentu, A.N., Ch Venkaiah, V.: Reusable multi-stage multi-secret sharing schemes based on CRT. 15–24 (2015)
Wang, K., Zou, X., Sui, Y.: A multiple secret sharing scheme based on matrix projection. In: 2009 33rd Annual IEEE International Computer Software and Applications Conference, COMPSAC’09, vol. 1, pp. 400–405, IEEE, 20 July 2009
Basit, A., Chaitanya Kumar, N., Ch Venkaiah, V., Moiz, S.A., Tentu, A.N., Naik, W.: Multi-stage multi-secret sharing scheme for hierarchical access structure. In: 2017 International Conference on Computing, communication and automation (IC-CCA), pp. 557–563. IEEE (2017)
Singh, N., Tentu, A.N., Basit, A., Ch Venkaiah, V.: Sequential secret sharing scheme based on Chinese remainder theorem. In: 2016 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC), pp. 1–6. IEEE (2016)
Zhang, T., Ke, X., Liu, Y.: (t, n) multi-secret sharing scheme ex-tended from Harn-Hsu’s scheme. EURASIP J. Wirel. Commun. Netw. 2018(1), 71 (2018)
Simmons, G.J.: How to (really) share a secret. In: Conference on the Theory and Application of Cryptography, pp. 390–448. Springer, New York, NY (1988)
Tassa, T., Dyn, N.: Multipartite secret sharing by bivariate interpolation. J. Cryptol. 22(2), 227–58 (2009)
Ghodosi, H., Pieprzyk, J., Safavi-Naini, R.: Secret sharing in multilevel and compartmented groups. Information Security and Privacy, pp. 367–378. Springer (1998)
Nojoumian, M., Stinson, D.R.: Sequential secret sharing as a new hierarchical access structure. J. Internet Serv. Inf. Secur. 5(2), 24–32 (2015)
Tentu, A.N., Basit, A., Bhavani, K., Ch Venkaiah, V.: Multi-secret sharing scheme for level-ordered access structures. In: International Conference on Number-Theoretic Methods in Cryptology, pp. 267–278. Springer, Cham (2017)
Wang, X., Xiang, C., Fu, F.W.: Secret sharing schemes for compartmented access structures. Crypt. Commun. 9(5), 625–635 (2017)
Selcuk, A.A., Yilmaz, R.: Joint compartmented threshold access structures. IACR Cryptol ePrint Arch. 2013, 54 (2013)
Duari, B., Giri, D.: An ideal and perfect (t, n) Multi-secret sharing scheme based on finite geometry. In: Information Technology and Applied Mathematics, pp. 85–94. Springer, Singapore (2019)
Fathimal, P.M, Arockia Jansi Rani, P.: Threshold secret sharing scheme for compartmented access structures. Int. J. Inf. Secur. Privacy (IJISP) 10(3), 1–9 (2016)
Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing general access structure. Electron. Commun. Jpn. (Part III: Fundam. Electron. Sci.) 72(9), 56–64 (1989)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Basit, A., Venkaiah, V.C., Moiz, S.A. (2020). Multi-secret Sharing Scheme Using Modular Inverse for Compartmented Access Structure. In: Raju, K.S., Senkerik, R., Lanka, S.P., Rajagopal, V. (eds) Data Engineering and Communication Technology. Advances in Intelligent Systems and Computing, vol 1079. Springer, Singapore. https://doi.org/10.1007/978-981-15-1097-7_31
Download citation
DOI: https://doi.org/10.1007/978-981-15-1097-7_31
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-1096-0
Online ISBN: 978-981-15-1097-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)