Lattice-based threshold-changeability for standard CRT secret-sharing schemes

Ron Steinfeld, Josef Pieprzyk, Huaxiong Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a non-standard scheme designed specifically for this purpose, or to have secure channels between shareholders. In contrast, we show how to increase the threshold parameter of the standard CRT secret-sharing scheme without secure channels between the shareholders. Our method can thus be applied to existing CRT schemes even if they were set up without consideration to future threshold increases. Our method is a positive cryptographic application for lattice reduction algorithms, and we also use techniques from lattice theory (geometry of numbers) to prove statements about the correctness and information-theoretic security of our constructions.

Original languageEnglish
Pages (from-to)653-680
Number of pages28
JournalFinite Fields and their Applications
Issue number4
Publication statusPublished - Nov 2006


  • Changeable threshold
  • Geometry of numbers
  • Lattice reduction
  • Secret-sharing


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