Paper 2017/1032

Performing Computations on Hierarchically Shared Secrets

Giulia Traverso, Denise Demirel, and Johannes Buchmann

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.

Metadata
Available format(s)
PDF
Publication info
Preprint. MINOR revision.
Keywords
hierarchical secret sharingBirkhoff interpolationverifiable secret sharingauditingmulti-party computationdistributed storage systemscloud computing
Contact author(s)
gtraverso @ cdc informatik tu-darmstadt de
History
2017-10-29: revised
2017-10-28: received
See all versions
Short URL
https://ia.cr/2017/1032
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2017/1032,
      author = {Giulia Traverso and Denise Demirel and Johannes Buchmann},
      title = {Performing Computations on Hierarchically Shared Secrets},
      howpublished = {Cryptology ePrint Archive, Paper 2017/1032},
      year = {2017},
      note = {\url{https://eprint.iacr.org/2017/1032}},
      url = {https://eprint.iacr.org/2017/1032}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.