Linear secret sharing with divisible shares

Josef Pieprzyk

doi:10.1007/978-3-540-47942-0_7

Linear secret sharing with divisible shares

Josef Pieprzyk^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Citation (Scopus)

Abstract

Shamir secret sharing is being considered in the broader context of linear secret sharing. It is shown that any Shamir scheme built over GF(q^v) 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(q^v) 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 language	English
Title of host publication	Information and Communication Security
Subtitle of host publication	Second International Conference, ICICS’99, Sydney, Australia, November 9-11, 1999. Proceedings
Editors	Vijay Varadharajan, Yi Mu
Place of Publication	Berlin
Publisher	Springer, Springer Nature
Pages	71-86
Number of pages	16
ISBN (Electronic)	9783540479420
ISBN (Print)	9783540666820
DOIs	https://doi.org/10.1007/978-3-540-47942-0_7
Publication status	Published - 1999
Externally published	Yes
Event	2nd International Conference on Information and Communication Security, ICICS - 1999 - Sydney, Australia Duration: 9 Nov 1999 → 11 Nov 1999

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer Berlin Heidelberg
Volume	1726
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	2nd International Conference on Information and Communication Security, ICICS - 1999
Country/Territory	Australia
City	Sydney
Period	9/11/99 → 11/11/99

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10.1007/978-3-540-47942-0_7

Cite this

Pieprzyk, J. (1999). Linear secret sharing with divisible shares. In V. Varadharajan, & Y. Mu (Eds.), Information and Communication Security: Second International Conference, ICICS’99, Sydney, Australia, November 9-11, 1999. Proceedings (pp. 71-86). (Lecture Notes in Computer Science; Vol. 1726). Springer, Springer Nature. https://doi.org/10.1007/978-3-540-47942-0_7

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abstract = "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.",

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year = "1999",

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Pieprzyk, J 1999, Linear secret sharing with divisible shares. in V Varadharajan & Y Mu (eds), Information and Communication Security: Second International Conference, ICICS’99, Sydney, Australia, November 9-11, 1999. Proceedings. Lecture Notes in Computer Science, vol. 1726, Springer, Springer Nature, Berlin, pp. 71-86, 2nd International Conference on Information and Communication Security, ICICS - 1999, Sydney, New South Wales, Australia, 9/11/99. https://doi.org/10.1007/978-3-540-47942-0_7

Linear secret sharing with divisible shares. / Pieprzyk, Josef.
Information and Communication Security: Second International Conference, ICICS’99, Sydney, Australia, November 9-11, 1999. Proceedings. ed. / Vijay Varadharajan; Yi Mu. Berlin: Springer, Springer Nature, 1999. p. 71-86 (Lecture Notes in Computer Science; Vol. 1726).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AB - 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.

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T3 - Lecture Notes in Computer Science

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T2 - 2nd International Conference on Information and Communication Security, ICICS - 1999

Y2 - 9 November 1999 through 11 November 1999

ER -

Linear secret sharing with divisible shares

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