A proactive secret sharing scheme based on Chinese remainder theorem

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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 share-holder 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 re-fresh shares at fixed period without changing the secret.In this way,an adversary can recover the secret if and only if it cap-tures 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 effi-cient share refreshing.
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