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Secret Sharing Using Near-MDS Codes

  • Sanyam Mehta
  • Vishal SaraswatEmail author
  • Smith Sen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11445)

Abstract

We propose a generalized secret sharing scheme based on NMDS codes. The proposed scheme is efficient and the computational complexity for setup and reconstruction phase is only \(O(n^3)\), where n is the number of participants. The scheme admits an access structure based on two mutually exclusive sets of participant combinations of sizes t and \(t-1\) respectively. The parameter t for the access structure is independent of the field size. The proposed scheme is ideal and perfect and has desirable security features of cheating detection and cheater identification. We also provide a cryptanalysis of the \((t+1, n)\) threshold secret sharing scheme based on NMDS codes proposed in [12]. We show that their scheme is insecure and that there always exists a set of m participants, where \(m <t+1\), which can reconstruct the secret.

Keywords

Secret sharing Generalized access structure MDS codes Near-MDS codes 

Notes

Acknowledgements

This work has been partially supported by DST-FIST Level-1 Program, Grant No. SR/FST/MSI-092/2013. The authors would like to thank Department of Mathematics, BITS Goa, R. C. Bose Centre for Cryptology and Security, ISI Kolkata, and Indian Institute of Technology, Jammu, for their support.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Robert Bosch Engineering and Business Solutions Pvt. Ltd. (RBEI/ESY)BangaloreIndia
  2. 2.Birla Institute of Technology and Science, Pilani, K. K. Birla Goa CampusGoaIndia

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