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Dynamic Threshold and Cheater Resistance for Shamir Secret Sharing Scheme

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Information Security and Cryptology (Inscrypt 2006)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4318))

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Abstract

In this paper, we investigate the problem of increasing the threshold parameter of the Shamir (t,n)-threshold scheme without interacting with the dealer. Our construction will reduce the problem of secret recovery to the polynomial reconstruction problem which can be solved using a recent algorithm by Guruswami and Sudan.

In addition to be dealer-free, our protocol does not increase the communication cost between the dealer and the n participants when compared to the original (t,n)-threshold scheme. Despite an increase of the asymptotic time complexity at the combiner, we show that recovering the secret from the output of the previous polynomial reconstruction algorithm is still realistic even for large values of t. Furthermore the scheme does not require every share to be authenticated before being processed by the combiner. This will enable us to reduce the number of elements to be publicly known to recover the secret to one digest produced by a collision resistant hash function which is smaller than the requirements of most verifiable secret sharing schemes.

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Author information

Authors and Affiliations

  1. Centre for Advanced Computing, Algorithms and Cryptography, Department of Computing, Macquarie University, NSW 2109, Australia

    Christophe Tartary

  2. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

    Huaxiong Wang

Authors
  1. Christophe Tartary
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  2. Huaxiong Wang
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Editor information

Editors and Affiliations

  1. University College London, UK

    Helger Lipmaa

  2. Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, 10027, New York, NY, USA

    Moti Yung

  3. SKLOIS Lab, Institute of Software, Chinese Academy of Sciences, 100080, Beijing, P.R. China

    Dongdai Lin

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Tartary, C., Wang, H. (2006). Dynamic Threshold and Cheater Resistance for Shamir Secret Sharing Scheme. In: Lipmaa, H., Yung, M., Lin, D. (eds) Information Security and Cryptology. Inscrypt 2006. Lecture Notes in Computer Science, vol 4318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11937807_9

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  • DOI: https://doi.org/10.1007/11937807_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49608-3

  • Online ISBN: 978-3-540-49610-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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