Multipartite secret sharing by bivariate interpolation

Tamir Tassa, Nira Dyn

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


Given a set of participants that is partitioned into distinct compartments, a multipartite access structure is an access structure that does not distinguish between participants that belong to the same compartment. We examine here three types of such access structures - compartmented access structures with lower bounds, compartmented access structures with upper bounds, and hierarchical threshold access structures. We realize those access structures by ideal perfect secret sharing schemes that are based on bivariate Lagrange interpolation. The main novelty of this paper is the introduction of bivariate interpolation and its potential power in designing schemes for multipartite settings, as different compartments may be associated with different lines in the plane. In particular, we show that the introduction of a second dimension may create the same hierarchical effect as polynomial derivatives and Birkhoff interpolation were shown to do in [13].

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540359079, 9783540359074
StatePublished - 2006
Event33rd International Colloquium on Automata, Languages and Programming, ICALP 2006 - Venice, Italy
Duration: 10 Jul 200614 Jul 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4052 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference33rd International Colloquium on Automata, Languages and Programming, ICALP 2006


  • Bivariate interpolation
  • Compart-mented access structures
  • Hierarchical threshold access structures
  • Monotone span programs
  • Multipartite access structures
  • Secret sharing


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