How to share secrets simultaneously

Laszlo Csirmaz

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 sharing complexity threshold scheme secret sharing interpolation
Contact author(s): csirmaz @ degas ceu hu
History: 2011-07-18: received
Short URL: https://ia.cr/2011/386
License: 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}
}