Monotone circuits for weighted threshold functions

Amos Beimel, Enav Weinreb

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

5 Scopus citations


Weighted threshold functions with positive weights are a natural generalization of unweighted threshold functions. These functions are clearly monotone. However, the naive way of computing them is adding the weights of the satisfied variables and checking if the sum is greater than the threshold; this algorithm is inherently non-monotone since addition is a non-monotone function. In this work we by-pass this addition step and construct a polynomial size logarithmic depth unbounded fan-in monotone circuit for every weighted threshold function, i.e., we show that weighted threshold functions are in mAC 1. (To the best of our knowledge, prior to our work no polynomial monotone circuits were known for weighted threshold functions.) Our monotone circuits are applicable for the cryptographic tool of secret sharing schemes. Using general results for compiling monotone circuits (Yao, 1989) and monotone formulae (Benaloh and Leichter, 1990) into secret sharing schemes, we get secret sharing schemes for every weighted threshold access structure. Specifically, we get: (1) information-theoretic secret sharing schemes where the size of each share is quasi-polynomial in the number of users, and (2) computational secret sharing schemes where the size of each share is polynomial in the number of users.

Original languageEnglish
Title of host publicationProceedings of the 20th Annual IEEE Conference on Computational Complexity
Number of pages9
StatePublished - 16 Nov 2005
Event20th Annual IEEE Conference on Computational Complexity - San Jose, CA, United States
Duration: 11 Jun 200515 Jun 2005

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159


Conference20th Annual IEEE Conference on Computational Complexity
Country/TerritoryUnited States
CitySan Jose, CA

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Mathematics


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