Performing Computations on Hierarchically Shared Secrets

  • Giulia Traverso
  • Denise Demirel
  • Johannes Buchmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10831)

Abstract

Hierarchical secret sharing schemes distribute a message to a set of shareholders with different reconstruction capabilities. In distributed storage systems, this is an important property because it allows to grant more reconstruction capability to better performing storage servers and vice versa. In particular, Tassa’s conjunctive and disjunctive hierarchical secret sharing schemes are based on Birkhoff interpolation and perform equally well as Shamir’s threshold secret sharing scheme. Thus, they are promising candidates for distributed storage systems. A key requirement is the possibility to perform function evaluations over shared data. However, practical algorithms supporting this have not been provided yet with respect to hierarchical secret sharing schemes. Aiming at closing this gap, in this work, we show how additions and multiplications of shares can be practically computed using Tassa’s conjunctive and disjunctive hierarchical secret sharing schemes. Furthermore, we provide auditing procedures for operations on messages shared hierarchically, which allow to verify that functions on the shares have been performed correctly. We close this work with an evaluation of the correctness, security, and efficiency of the protocols we propose.

Keywords

Hierarchical secret sharing Birkhoff interpolation Verifiable secret sharing Auditing Multi-party computation Distributed storage systems Cloud computing 

Notes

Acknowledgments

The authors thank Lucas Schabüser and Denis Butin for useful discussions. This work was in part funded by the European Commission through grant agreement no. 644962 (PRISMACLOUD). Furthermore, it received funding from the DFG as part of project S6 within the CRC 1119 CROSSING.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Giulia Traverso
    • 1
  • Denise Demirel
    • 1
  • Johannes Buchmann
    • 1
  1. 1.Technische Universität DarmstadtDarmstadtGermany

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