Computer Science – Cryptography and Security
Scientific paper
2008-12-13
Advances in Cryptology - Asiacrypt 2008, vol. 5350 of Lecture Notes in Computer Science, pp. 19-36, Springer-Verlag, 2008
Computer Science
Cryptography and Security
18 pages
Scientific paper
10.1007/978-3-540-89255-7
Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multiparty 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 a 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 strongly 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.
Chee Yeow Meng
Ling San
Liu Mulan
Wang Huaxiong
Zhang Zhifang
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