Abstract
Mehta et al. [11] recently proposed an \({{\,\mathrm{NMDS}\,}}\) code-based secret sharing scheme having a richer access structure than the traditional (t, n) threshold secret sharing schemes, and is based on two mutually nonmonotonic sets of user groups of sizes t and \(t-1\) respectively, where \(n \ge t > 1\) corresponds to the total number of users. We give a full generalization of their scheme with complete security proofs. We propose an efficient generalized secret sharing scheme constructed using \({{\,\mathrm{N^{\mu }MDS}\,}}\) codes with time complexity of \(O(n^3)\). The scheme accepts an access structure constructed using \(\mu +1\) mutually nonmonotonic sets of user groups with sizes, \(t, t-1, \dots , t-\mu \), respectively, where \(1 \le \mu < t\), and the parameter t defines the threshold such that all user groups of size greater than t can recover the secret. The proposed secret sharing scheme is perfect and ideal and has robust cheating detection and cheater identification features.
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Acknowledgments
The authors acknowledge the support of the Department of Mathematics, BITS Goa, Indian Institute of Technology, Jammu, and R. C. Bose Centre for Cryptology and Security, ISI Kolkata.
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Mehta, S., Saraswat, V. (2020). Generalized Secret Sharing Schemes Using N\(^\mu \)MDS Codes. In: Slamanig, D., Tsigaridas, E., Zafeirakopoulos, Z. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science(), vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_18
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DOI: https://doi.org/10.1007/978-3-030-43120-4_18
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