Communication efficient and strongly secure secret sharing schemes based on algebraic geometry codes

Umberto Martinez Peñas

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20 Citations (Scopus)

Abstract

Secret-sharing schemes with optimal and universal communication overheads have been obtained independently by Bitar et al. and Huang et al. However, their constructions require a finite field of size q n, where n is the number of shares, and do not provide strong security. In this paper, we give a general framework to construct communication efficient secretsharing schemes based on sequences of nested linear codes, which allows to use, in particular, algebraic geometry codes and allows to obtain strongly secure and communication-efficient schemes. Using this framework, we obtain: 1) schemes with universal and close to optimal communication overheads for arbitrarily large lengths n and a fixed finite field; 2) the first construction of schemes with universal and optimal communication overheads and optimal strong security (for restricted lengths), having, in particular, the component-wise security advantages of perfect schemes and the security and storage efficiency of ramp schemes; and 3) schemes with universal and close to optimal communication overheads and close to optimal strong security defined for arbitrarily large lengths n and a fixed finite field.
Original languageEnglish
JournalI E E E Transactions on Information Theory
Volume64
Issue number6
Pages (from-to)4191-4206
Number of pages16
ISSN0018-9448
DOIs
Publication statusPublished - Apr 2018

Keywords

  • algebraic geometry codes
  • asymptotic secret sharing
  • communication bandwidth
  • communication efficiency
  • Secret sharing
  • strong security

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