Linear secret sharing with divisible shares

Josef Pieprzyk*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Citation (Scopus)


Shamir secret sharing is being considered in the broader context of linear secret sharing. It is shown that any Shamir scheme built over GF(qv) can be converted into its linear equivalent defined over GF(q). A notion of uniform perfectness is introduced and it is proved that Shamir schemes built over GF(qv) are not uniformly perfect. Probabilistic linear secret sharing is next studied and bounds on probability that the resulting secret sharing is uniformly perfect are given. The probabilistic arguments are later used to show that secret sharing with shift derived from Shamir scheme allows to achieve a secret sharing which is uniformly perfect.

Original languageEnglish
Title of host publicationInformation and Communication Security
Subtitle of host publicationSecond International Conference, ICICS’99, Sydney, Australia, November 9-11, 1999. Proceedings
EditorsVijay Varadharajan, Yi Mu
Place of PublicationBerlin
PublisherSpringer, Springer Nature
Number of pages16
ISBN (Electronic)9783540479420
ISBN (Print)9783540666820
Publication statusPublished - 1999
Externally publishedYes
Event2nd International Conference on Information and Communication Security, ICICS - 1999 - Sydney, Australia
Duration: 9 Nov 199911 Nov 1999

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other2nd International Conference on Information and Communication Security, ICICS - 1999


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