Paper 2011/386

How to share secrets simultaneously

Laszlo Csirmaz

Abstract

Each member of a team consisting of $n$ person has a secret. The $k$ out of $n$ simultaneous threshold secret sharing requires that any group of $k$ members should be able to recover the secret of the other $n-k$ members, while any group of $k-1$ or less members should have no information on the secret of other team members. We show that when all secrets are independent and have size $s$ then each team member must receive a share of size at least $(n-k)s$, and we present a scheme which achieves this bound. This result shows a significant saving over $n$ independent applications of the $k$ out of $n-1$ threshold schemes which assigns shares of size $(n-1)s$ to each team member independently of $k$.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
simultaneous secret sharingcomplexitythreshold schemesecret sharinginterpolation
Contact author(s)
csirmaz @ degas ceu hu
History
2011-07-18: received
Short URL
https://ia.cr/2011/386
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2011/386,
      author = {Laszlo Csirmaz},
      title = {How to share secrets simultaneously},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/386},
      year = {2011},
      url = {https://eprint.iacr.org/2011/386}
}
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