@inbook{30df238e8811478391790705ae45ccf4,
title = "Strongly multiplicative and 3-multiplicative linear secret sharing schemes",
abstract = "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.",
author = "Zhifang Zhang and Mulan Liu and Chee, {Yeow Meng} and San Ling and Huaxiong Wang",
year = "2008",
doi = "10.1007/978-3-540-89255-7_2",
language = "English",
isbn = "3540892540",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer, Springer Nature",
pages = "19--36",
editor = "Josef Pieprzyk",
booktitle = "Advances in Cryptology - ASIACRYPT 2008",
address = "United States",
note = "14th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2008 ; Conference date: 07-12-2008 Through 11-12-2008",
}