Analysis and Design of Multiple Threshold Changeable Secret Sharing Schemes

In a (r, n)-threshold secret sharing scheme, no group of (r − 1) colluding members can recover the secret value s. However, the number of colluders is likely to increase over time. In order to deal with this issue, one may also require to have the ability to increase the threshold value from r to r′(> r), such an increment is likely to happen several times. In this paper, we study the problem of threshold changeability in a dealer-free environment. First, we compute a theoretical bound on the information and security rate for such a secret sharing. Second, we show how to achieve multiple threshold change for a Chinese Remainder Theorem like scheme. We prove that the parameters of this new scheme asymptotically reach the previous bound.