Universally Ideal Secret-Sharing Schemes

Amos Beimel, Benny Chor

Research output: Contribution to journalArticlepeer-review

83 Scopus citations


Given a set of parties {1, • • •, n}, an access structure is a monotone collection of subsets of the parties. For a certain domain of secrets, a secret-sharing scheme for an access structure is a method for a dealer to distribute shares to the parties. These shares enable subsets in the access structure to reconstruct the secret, while subsets not in the access structure get no information about the secret. A secret-sharing scheme is ideal if the domains of the shares are the same as the domain of the secrets. An access structure is universally ideal if there exists an ideal secret-sharing scheme for it over every finite domain of secrets. An obvious necessary condition for an access structure to be universally ideal is to be ideal over the binary and ternary domains of secrets. In this work, we prove that this condition is also sufficient. We also show that being ideal over just one of the two domains does not suffice for universally ideal access structures. Finally, we give an exact characterization for each of these two conditions.

Original languageEnglish
Pages (from-to)786-794
Number of pages9
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - 1 Jan 1994
Externally publishedYes


  • Secret-sharing
  • cryptography
  • ideal access structures
  • matroids

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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