Open Access
Research Article
A new ideal secret sharing scheme based on a tree
Ghanem Meriemghanem.meriem@gmail.comL’IFORCE Laboratory Faculty of Mathematics USTHB University P. O. Box 32, El Alia Bab-Ezzouar Algiers 16111 AlgeriaView full profile → , *Sadek BouroubiCorresponding authorsbouroubi@usthb.dz, bouroubis@gmail.comL’IFORCE Laboratory Faculty of Mathematics USTHB University P. O. Box 32, El Alia Bab-Ezzouar Algiers 16111 AlgeriaAlgiers, 16111, AlgeriaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 30 Sep 2020
- Accepted:
- 28 Feb 2021
- Published Online:
- 27 Oct 2021
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-1335
- Pages:
- 121–138
Abstract
One of the methods used in order to protect a secret K is a secret sharing scheme. In this method, the secret K is distributed among a finite set of participants P by a special participant called the dealer, assumed to be honest, in such a way that only predefined subsets of participants can recover the secret after collaborating with their secret shares. The construction of secret sharing schemes has received a considerable attention of many researchers whose main goal was to improve the information rate. In this paper, we focused on the hierarchical secret sharing. Related to the previous works, we propose a novel simpler construction of a secret sharing scheme, where the access structure is a tree according to the hierarchical concept of companies illustrated through its organization chart. We prove that the proposed scheme is ideal by showing that the information rate equals 1. In order to show the efficiency of the proposed scheme, we discuss all possible kinds of attacks and prove that the security is ensured. Finally, we include a detailed didactic example of a small company organization chart.
Keywords
Subject Classifications
Primary 11T71Secondary 94A60
References
- Adi Shamir, How to share a secret, Communications of the ACM, 22, 612-613 (1979) doi: https://doi.org/10.1145/359168.359176 [Crossref], [Web of Science ®], [Google Scholar]
- Abhishek Mishra, Ashutosh Gupta, Multi secret sharing scheme using iterative method, Journal of Information and Optimization Sciences, 39.3, 631-641 (2018) doi: https://doi.org/10.1080/02522667.2017.1385161 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- AL-Saidi NMG, Rajab NA, Said MRMd, Kadhim KA, Perfect secret sharing scheme based on vertex domination set. International Journal of Computer Mathematics, 92, 1755-1763 (2014) doi: https://doi.org/10.1080/00207160.2014.941360 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Blundo C, De Santis A, Stinson DR, Vaccaro U, Graph decomposition and secret sharing schemes, Journal of Cryptology, 8, 39-64 (1995) doi: https://doi.org/10.1007/BF00204801 [Crossref], [Web of Science ®], [Google Scholar]
- Brickell EF, Stinson DR, Some improved bounds on the information rate of perfect secret sharing schemes, Journal of Cryptology, 5, 153-166 (1992) doi: https://doi.org/10.1007/BF02451112 [Crossref], [Google Scholar]
- Blakley GR, Safeguarding cryptographic keys, AFIPS National Computer Conference, 313-317 (1979) [Google Scholar]
- Di Crescenzo G, Galdi C, Hyper-graph decomposition and secret sharing. Discrete Applied Mathematics, 157, 928-946 (2009) doi: https://doi.org/10.1016/j.dam.2008.04.001 [Crossref], [Web of Science ®], [Google Scholar]
- Ernest F, Brickell, Some ideal secret sharing schemes,Advances in Cryptology EUROCRYPT 89, 468-475. Springer, Berlin, Heidelberg (1990) [Google Scholar]
- Farras O, Padr C, Ideal hierarchical secret sharing schemes, IEEE transactions on information theory, 58(5), 3273-3286 (2012) doi: https://doi.org/10.1109/TIT.2011.2182034 [Crossref], [Web of Science ®], [Google Scholar]
- Feng Jen-Bang, et al, Visual secret sharing for multiple secrets, Pattern Recognition 41.12, 3572-3581 (2008) doi: https://doi.org/10.1016/j.patcog.2008.05.031 [Crossref], [Web of Science ®], [Google Scholar]
- Fu Zheng-xin, Bin Yu, Ideal secure multi-secret Visual Cryptography scheme with ring shares, Transactions on Data Hiding and Multimedia Security IX, 42-56 (2014) [Google Scholar]
- Gustavus J, Simmons, How to (really) share a secret, Advances in Cryptology-CRYPTO’88, 390-448.Springer, New York, NY (1990) [Google Scholar]
- Ito M, Saito A, Nishizeki T, Multiple assignment scheme for sharing secret, Journal of Cryptology, 6, 15-20 (1993) doi: https://doi.org/10.1007/BF02620229 [Crossref], [Google Scholar]
- Ito M, Saito A, Nishizeki T, Secret sharing scheme realizing general access structure, Electronics Communications in Japan, 72, 56-64 (1989) doi: https://doi.org/10.1002/ecjc.4430720906 [Crossref], [Google Scholar]
- Josh C, Benaloh, Leichter Jerry, Generalized secret sharing and monotone functions, Advances in Cryptology-CRYPTO’88, 27-35. Springer, New York, NY (1990) [Crossref],
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