On polynomial secret sharing schemes

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


Nearly all secret sharing schemes studied so far are linear or multi-linear schemes. Although these schemes allow to implement any monotone access structure, the share complexity, SC, may be suboptimal – there are access structures for which the gap between the best known lower bounds and best known multi-linear schemes is exponential. There is growing evidence in the literature, that non-linear schemes can improve share complexity for some access structures, with the work of Beimel and Ishai (CCC’01) being among the first to demonstrate it. This motivates further study of non linear schemes. We initiate a systematic study of polynomial secret sharing schemes (PSSS), where shares are (multi-variate) polynomials of secret and randomness vectors ~s,~r respectively over some finite field Fq. Our main hope is that the algebraic structure of polynomials would help obtain better lower bounds than those known for the general secret sharing. Some of the initial results we prove in this work are as follows.

Original languageEnglish
Title of host publication1st Conference on Information-Theoretic Cryptography, ITC 2020
EditorsYael Tauman Kalai, Adam D. Smith, Daniel Wichs
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771511
StatePublished - 1 Jun 2020
Event1st Conference on Information-Theoretic Cryptography, ITC 2020 - Virtual, Boston, United States
Duration: 17 Jun 202019 Jun 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs


Conference1st Conference on Information-Theoretic Cryptography, ITC 2020
Country/TerritoryUnited States
CityVirtual, Boston


  • Linear program
  • Lower bounds
  • Polynomial
  • Secret sharing

All Science Journal Classification (ASJC) codes

  • Software


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