An Integratable Verifiable Secret Sharing Mechanism

Threshold secret sharing (SS), also denoted as (t, n) SS, has been used extensively in the area of information security, such as for group authentication, cloud storage schemes, secure parallel communication and wireless multipath routing protocols. However, a (t, n) SS cannot detect any deceptions among the dealer and shareholders. Verifiable secret sharing (VSS) overcomes the weakness of (t, n) SS in such a way that it is able to detect cheaters by verifying the validity of shares or the correctness of the recovered secret under the condition that both shares and the secret are not compromised. Recently, two noninteractive VSSs based on Asmuth-Bloom’s SS were proposed by Harn et al. and Liu et al., respectively. Both VSSs require shareholders to examine the range of values of some integers related to the secret before recovering the secret, which is a time-consuming operation. In this paper, we propose a novel integratable VSS mechanism that integrates the concepts of the generalized Chinese remainder theorem (GCRT), Shamir’s SS and AsmuthBloom’s SS. Our proposed VSS can verify that the secret reconstructed by any t or more shareholders is the same as the one that the dealer has generated. Analysis shows that our proposed VSS can provide perfect secrecy and better efficiency.