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ASIACRYPT
2008
Springer

Strongly Multiplicative and 3-Multiplicative Linear Secret Sharing Schemes

10 years 4 months ago
Strongly Multiplicative and 3-Multiplicative Linear Secret Sharing Schemes
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 ...
Zhifang Zhang, Mulan Liu, Yeow Meng Chee, San Ling
Added 12 Oct 2010
Updated 12 Oct 2010
Type Conference
Year 2008
Where ASIACRYPT
Authors Zhifang Zhang, Mulan Liu, Yeow Meng Chee, San Ling, Huaxiong Wang
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