Multi-linear Secret-Sharing Schemes

Liangliang Xiao

Zhifang Zhang, Mulan Liu, Liangliang Xiao

Carlo Blundo, Alfredo De Santis, Giovanni Di Crescenzo +2 more

Ronald Cramer, Ivan Damgård, Ueli M. Maurer

Zhifang Zhang, Mulan Liu, Liangliang Xiao

Abstract. As an extension of multi-party computation (MPC), we propose the concept of secure parallel multi-party computation which is to securely compute multi-functions against an adversary with multistructures. Precisely, there are m functions f1,..., fm and m adversary structures A1,..., Am, where fi is required to be securely computed against an Ai-adversary. We give a general construction to build a parallel multi-party computation protocol from any linear multi-secret sharing scheme (LMSSS), provided that the access structures of the LMSSS allow MPC at all. When computing complicated functions, our protocol has more advantage in communication complexity than the “direct sum” method which actually executes a MPC protocol for each function. The paper also provides an efficient and generic construction to obtain from any LMSSS a multiplicative LMSSS for the same multi-access structure. 1

Mulan Liu

In the paper, through a complete description of secret sharing schemes, we give definitions respectively for perfect secret sharing schemes, statistical secret sharing schemes and computational secret sharing schemes in an uniform way. Furthermore, we analyze why and how multiplicative linear secret sharing schemes are used in secure multi-party computation protocols, and explain the security of secure multi-party computation in detail.