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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/1145493
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- Title
- Strongly multiplicative and 3-multiplicative linear secret sharing schemes
- Related
- Lecture Notes in Computer Science, Vol. 5350 LNCS, (2008), p.19-36
- DOI
- 10.1007/978-3-540-89255-7_2
- Publisher
- Springer
- Date
- 2008
- Author/Creator
- Zhang, Z
- Author/Creator
- Liu, M
- Author/Creator
- Chee, Y M
- Author/Creator
- Ling, S
- Author/Creator
- Wang, Huaxiong
- Description
- Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multi-party computation protocols. However, it remains open whether or not there exist efficient constructions of strongly multiplicative LSSS from general LSSS. In this paper, we propose the new concept of 3-multiplicative LSSS, and establish its relationship with strongly multiplicative LSSS. More precisely, we show that any 3-multiplicative LSSS is a strongly multiplicative LSSS, but the converse is not true; and that any strongly multiplicative LSSS can be efficiently converted into a 3-multiplicative LSSS. Furthermore, we apply 3-multiplicative LSSS to the computation of unbounded fan-in multiplication, which reduces its round complexity to four (from five of the previous protocol based on multiplicative LSSS). We also give two constructions of 3-multiplicative LSSS from Reed-Muller codes and algebraic geometric codes. We believe that the construction and verification of 3-multiplicative LSSS are easier than those of strongly multiplicative LSSS. This presents a step forward in settling the open problem of efficient constructions of strongly multiplicative LSSS from general LSSS.
- Description
- 18 page(s)
- Subject Keyword
- 080200 Computation Theory and Mathematics
- Subject Keyword
- Monotone span program
- Subject Keyword
- Secure multi-party computation
- Subject Keyword
- Strongly multiplicative linear secret sharing scheme
- Resource Type
- journal article
- Organisation
- Macquarie University. Department of Computing
- Identifier
- http://hdl.handle.net/1959.14/1145493
- Identifier
- mq:54883
- Identifier
- ISSN:0302-9743
- Identifier
- mq-rm-2008990852
- Language
- eng
- Reviewed
Macquarie University ResearchOnline
