A generalized Chinese remainder theorem-based proactive multi-secret sharing scheme for global wide area network

A generalized Chinese Remainder Theorem (GCRT)-based multi-secret sharing (MSS) scheme, which can solve a tricky problem that the correspondences between multi-secret and their remainders in each share are unclear, has been proposed recently. But potential security issues should be taken into accounts in the design and implementation of MSS. To protect long-lived multi-secret against intended attacks, in this paper, we propose a proactive multi-secret sharing (PMSS) scheme. It consists of share generation, share refreshing, and secret recovery phases. Compared with those existing MSS schemes, unordered shares in the proposed PMSS scheme are refreshed at a fixed period while the multi-secret remains intact. This can lead to a higher security level because an adversary must capture at least t shares from total n shares during a period to crack the secrets. Both the share generation and refreshing phases can be easily realized by using modular operation. What is more, the proposed PMSS scheme has a much less computational load thanks to the use of a lightweight GCRT-based algorithm in the secret recovery phase. Finally, some examples are provided to illustrate the efficiency, and some analyses regarding security are also given.