Efficient VSS free of computational assumption

Abstract

VSS (verifiable secret sharing) is an important security mechanism in distributed computing. It is a secret sharing technique, where each distributed share holder can verify that he obtains a share of a unique secret. Two properties are important in VSS: efficiency and security, where the security of VSS includes two requirements, bindingness and hidingness. In any application of VSS, high efficiency is desired. In applications with critical security requirements, bindingness and hidingness are desired to be achieved without any computational assumption on hard mathematical problems. No existing VSS scheme is efficient enough in both computation and communication for cost-sensitive applications, especially in the popular ubiquitous and distributed computing environment. When security is required without any hard computational assumption, efficient VSS is even more difficult. To overcome this drawback in VSS, a new secret sharing protocol is proposed in this paper. It does not need any assumption or condition like hardness of computational problems to achieve bindingness and hidingness. Especially, its privacy is information-theoretic instead of statistical in most existing VSS schemes. It is very efficient in both computation and communication and costs much less than the existing VSS schemes. Therefore, it improves the efficiency of VSS and achieves the strongest security in VSS.