A cheater identifiable multi-secret sharing scheme based on the Chinese remainder theorem

摘要

There are many researches on the polynomial-based verifiable (k, n) multi-secret sharing scheme (VMSSS), but none of them focuses on the Chinese remainder theorem (CRT)-based VMSSS so far. For the first time, we provide a cheater identifiable multi-secret sharing scheme based on CRT as an alternative method for VMSSS, which is unconditionally secure when the number of cheaters t <= (k - 1)/3. We adopt an encoding method, which makes multiple secrets to be transferred as a single one. In addition, we utilize a single keyed message authenticated code (MAC) to detect and identify cheaters in the reconstruction phase. Then, combine these two methods with a CRT-based Asmuth-Bloom's SSS to achieve our design goals. In our scheme, all participants share a single key of MAC rather than each participant possesses an independent key to check the validity of shares, and the size of share is independent in any of n, k, and t. Analyses show that our scheme is more efficient and secure than existing ones. Finally, as an example of the practical impact of our work, we present how our techniques can be applied to secure sum computation. Copyright (C) 2015 John Wiley & Sons, Ltd.