Efficient explicit constructions of compartmented secret sharing schemes
- 81 Downloads
Multipartite secret sharing schemes have been an important object of study in the area of secret sharing schemes. Two interesting families of multipartite access structures are hierarchical access structures and compartmented access structures. This work deals with efficient and explicit constructions of ideal compartmented secret sharing schemes, while most of the known constructions are either inefficient or randomized. We construct ideal linear secret sharing schemes for three types of compartmented access structures, such as compartmented access structures with upper bounds, compartmented access structures with lower bounds, and compartmented access structures with upper and lower bounds. There exist some methods to construct ideal linear schemes realizing these compartmented access structures in the literature, but those methods are inefficient in general because non-singularity of many matrices has to be determined to check the correctness of the scheme. Our constructions do not need to do these computations. Our methods to construct ideal linear schemes realizing these access structures combine polymatroid-based techniques with Gabidulin codes. Gabidulin codes play a fundamental role in the constructions, and their properties imply that our methods are efficient.
KeywordsSecret sharing schemes Multipartite access structures Compartmented access structures Matroids Polymatroids Gabidulin codes
Mathematics Subject Classification94A62 94B05
The authors are very grateful to the reviewers and Dr. Yue Zhou for their detailed comments and suggestions that much improved the presentation and quality of this paper. Special thanks to the reviewer who suggests to use polymatroid–based techniques and gives many guidance to improve the presentation of our main result by using polymatroid-based techniques.
This research was supported in part by the Foundation of National Natural Science of China (Nos. 61772147, 61702124), Guangdong Province Natural Science Foundation of major basic research and Cultivation project (No. 2015A030308016) and Project of Ordinary University Innovation Team Construction of Guangdong Province (No. 2015KCXTD014).
- 2.Beimel A.: Secret-sharing schemes: a survey. In: Chee Y.M., Guo Z., Ling S., Shao F., Tang Y., Wang H., Xing C. (eds.) IWCC 2011. LNCS, vol. 6639, pp. 11–46. Springer, Heidelberg (2011).Google Scholar
- 5.Ben-Or M., Goldwasser S., Wigderson A.: Completeness theorems for noncryptographic fault-tolerant distributed computations. In: Proceedings of the 20th ACM Symposium on the Theory of Computing, pp. 1–10 (1988).Google Scholar
- 7.Blakley G.R.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference’79, AFIPS Proceedings, vol. 48, pp. 313–317 (1979).Google Scholar
- 10.Chaum D., Crépeau C., Damgård I.: Multiparty unconditionally secure protocols. In: Proceedings of the 20th ACM Symposium on the Theory of Computing, pp. 11–19 (1988).Google Scholar
- 14.Desmedt Y., Frankel Y.: Threshold cryptosystems. In: Brassard G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990).Google Scholar
- 18.Fehr S.: Efficient construction of the dual span program. Manuscript, May (1999).Google Scholar
- 21.Goyal V., Pandey O., Sahai A., Waters B.: Attribute-based encryption for fine-grained access control of encrypted data. In: Proceedings of the 13th ACM Conference on Computer and Communications Security, pp. 89–98 (2006).Google Scholar
- 24.Ito M., Saito A., Nishizeki T.: Secret sharing schemes realizing general access structure. In: Proceedings of the IEEE Global Telecommunication Conference, Globecom 1987, pp. 99–102 (1987).Google Scholar
- 25.Kothari S.C.: Generalized linear threshold scheme. In: Blakley G.R., Chaum D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 231–241. Springer, Heidelberg (1985).Google Scholar
- 27.Massey J.L.: Minimal codewords and secret sharing. In: Proceedings of the 6th Joint Swedish-Russian Workshop on Information Theory, pp. 276–279 (1993).Google Scholar
- 28.Massey J.L.: Some applications of coding theory in cryptography. Codes Ciphers Cryptogr Coding 4, 33–47 (1995).Google Scholar
- 29.Naor M., Wool A.: Access control and signatures via quorum secret sharing. In: 3rd ACM Conference on Computer and Communications Security, pp. 157–167 (1996).Google Scholar
- 34.Simmons G.J.: How to (really) share a secret. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 390–448. Springer, Heidelberg (1990).Google Scholar