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Generalized Secret Sharing Schemes Using N\(^\mu \)MDS Codes

  • Sanyam Mehta
  • Vishal SaraswatEmail author
Conference paper
  • 33 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11989)

Abstract

Mehta et al. [11] recently proposed an \({{\,\mathrm{NMDS}\,}}\) code-based secret sharing scheme having a richer access structure than the traditional (tn) 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.

Keywords

Secret sharing schemes Generalized access structure Near MDS codes Almost MDS codes 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Goldman Sachs Services Pvt LtdBangaloreIndia
  2. 2.Robert Bosch Engineering & Business Solutions Pvt LtdBangaloreIndia

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