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 ...

• Type: Conference
• Year: 2008
• Where: ASIACRYPT
• Authors: Zhifang Zhang, Mulan Liu, Yeow Meng Chee, San Ling, Huaxiong Wang
• Keywords: 3-multiplicative Lsss, ASIACRYPT 2008, Cryptology, Multiplicative Linear, Multiplicative Lsss