A proactive secret sharing scheme based on Chinese remainder theorem

If an adversary tries to obtain a secret s in a (t, n) threshold secret sharing (SS) scheme, it has to capture no less than t shares instead of the secret s directly. However, if a shareholder keeps a fixed share for a long time, an adversary may have chances to filch some shareholders' shares. In a proactive secret sharing (PSS) scheme, shareholders are supposed to refresh shares at fixed period without changing the secret. In this way, an adversary can recover the secret if and only if it captures at least t shares during a period rather than any time, and thus PSS provides enhanced protection to long-lived secrets. The existing PSS schemes are almost based on linear SS but no Chinese Remainder Theorem (CRT)-based PSS scheme was proposed. This paper proposes a PSS scheme based on CRT for integer ring to analyze the reason why traditional CRT-based SS is not suitable to design PSS schemes. Then, an ideal PSS scheme based on CRT for polynomial ring is also proposed. The scheme utilizes isomorphism of CRT to implement efficient share refreshing.