Zero-Knowledge Interactive Proof Schemes Based on Subset Sum Promblem

Abstract

The concept of zero-knowledge interactive proof (ZKIP) scheme was first proposed by Goldwasser, Micali and Rackoff in 1985. Since then many practical ZKIP schemes have been proposed. One common feature among all these schemes is that the security of the schemes is based on factoring or discrete logarithms. In 1991, Simmons proposes an alternative practical ZKIP scheme whose security is based on subset sum problem. However, there is a very strong assumption existed in the scheme, i.e., Simmons’s scheme would be secure under the assumption that an indistinguishable box is existed. Unfortunately, nobody, including Simmons, can tell us how to implement the indistinguishable box until now. In this paper, we propose a method to implement the indistinguishable box and then two concrete ZKIP protocols whose security is based on knapsack problem are proposed. It is shown that the proposed indistinguishable box is very simple, flexible and secure in the applications of ZKIP protocols.