Abstract
This paper presents a simple construction of an efficient publicly verifiable secret sharing scheme (PVSS) in hierarchical settings that uses bilinear pairing (BLP) maps. Till date, hierarchical secret sharing was confined to public key infrastructure (PKI) settings. Use of BLP maps in our scheme yields better security and verifiability. Communications between the Dealer and participants is achieved using an efficient certificateless signcryption (CLSC) scheme. Comparative study with prominent schemes exhibits superior performance of our scheme.
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Notes
- 1.
In case a participant occurs in multiple groups or clusters, they will receive multiple shares of individual parents. During secret reconstruction, relevant shares of concerned groups are used. Therefore group-wise hierarchy is enough to maintained.
- 2.
The symbol \(\in _R\) is reserved for random choice of an element from a given set throughout this paper.
- 3.
Practical implementation of most systems require credential verification in person, that can be followed by this partial transmission step. Therefore in practice no extra transmission is required in most applications due to this step.
- 4.
The symbol \(:=\) denotes ‘define’. \(S^{sh}_{id_i}\) denotes share of \(id_i\).
- 5.
We assume the same threshold \(t_{hg}\) for individual groups hg at a given depth in our hierarchy. Of course polynomials \(f^{hg}\) for individual lower level groups differ due varied \(S_{\alpha }\)’s for each first level participant \(P_{\alpha }\). Analysis of threshold schemes with groups possessing varied number of members/weights is certainly more interesting. Due to page limits, we differ this analyzes for extended version of our work.
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Sarkar, P., Nandi, S., Chowdhury, M.U. (2018). Publicly Verifiable Secret Sharing Scheme in Hierarchical Settings Using CLSC over IBC. In: Abawajy, J., Choo, KK., Islam, R. (eds) International Conference on Applications and Techniques in Cyber Security and Intelligence. ATCI 2017. Advances in Intelligent Systems and Computing, vol 580. Edizioni della Normale, Cham. https://doi.org/10.1007/978-3-319-67071-3_27
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