Efficient and unconditionally secure verifiable threshold changeable scheme

Abstract

In this paper, we describe how to construct an efficient and unconditionally secure verifiable threshold changeable scheme, in which any participants can verify whether the share given by the dealer is correct or not, in which the combiner can verify whether the pooled shares are correct or not, and in which the threshold can be updated plural times to the values determined in advance. An optimal threshold changeable scheme was defined and given by Martin et. al., and an unconditionally secure verifiable threshold scheme was given by Pedersen. Martin’s scheme is based on Blakley’s threshold scheme whereas Pedersen’s is based on Shamir’s. Hence these two schemes cannot directly be combined. Then we first construct an almost optimal threshold changeable scheme based on Shamir’s, and after that using Pedersen’s scheme, construct a unconditionally secure verifiable threshold scheme in which the threshold can be updated plural times, say N times. Furthermore, our method can decrease the amount of information the dealer has to be publish, comparing with simply applying Pedersen’s scheme N times.