Multi-linear secret-sharing schemes

Amos Beimel, Aner Ben-Efraim, Carles Padró, Ilya Tyomkin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

24 Scopus citations


Multi-linear secret-sharing schemes are the most common secret-sharing schemes. In these schemes the secret is composed of some field elements and the sharing is done by applying some fixed linear mapping on the field elements of the secret and some randomly chosen field elements. If the secret contains one field element, then the scheme is called linear. The importance of multi-linear schemes is that they provide a simple non-interactive mechanism for computing shares of linear combinations of previously shared secrets. Thus, they can be easily used in cryptographic protocols. In this work we study the power of multi-linear secret-sharing schemes. On one hand, we prove that ideal multi-linear secret-sharing schemes in which the secret is composed of p field elements are more powerful than schemes in which the secret is composed of less than p field elements (for every prime p). On the other hand, we prove super-polynomial lower bounds on the share size in multi-linear secret-sharing schemes. Previously, such lower bounds were known only for linear schemes.

Original languageEnglish
Title of host publicationTheory of Cryptography - 11th Theory of Cryptography Conference, TCC 2014, Proceedings
PublisherSpringer Verlag
Number of pages25
ISBN (Print)9783642542411
StatePublished - 1 Jan 2014
Event11th Theory of Cryptography Conference on Theory of Cryptography, TCC 2014 - San Diego, CA, United States
Duration: 24 Feb 201426 Feb 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8349 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th Theory of Cryptography Conference on Theory of Cryptography, TCC 2014
Country/TerritoryUnited States
CitySan Diego, CA


  • Dowling geometries
  • Ideal secret-sharing schemes
  • multi-linear matroids

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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