Secret Sharing Extensions based on the Chinese Remainder Theorem

In this paper, we investigate how to achieve verifiable secret sharing (VSS) schemes by using the Chinese Remainder Theorem (CRT). We first show that two schemes proposed earlier are not secure from an attack where the dealer is able to distribute inconsistent shares to the users. Then we propose a new VSS scheme based on the CRT and prove its security. Using the proposed VSS scheme, we develop joint random secret sharing (JRSS) and proactive SSS protocols, which, to the best of our knowledge, are the first secure protocols of their kind based on the CRT.