一个可验证的门限多秘密共享方案

A verifiable threshold multi-secret sharing scheme

针对Lin-Wu方案容易受恶意参与者攻击的缺点,基于大整数分解和离散对数问题的难解性,提出了一个新的可验证(t,n)门限多秘密共享方案,有效地解决了秘密分发者和参与者之间各种可能的欺骗.在该方案中,秘密分发者可以动态的增加共享的秘密;各参与者的秘密份额可以重复使用,每个参与者仅需保护一个秘密份额就可以共享多个秘密.与现有方案相比,该方案在预防各种欺骗时所需的指数运算量更小,而且,每共享一个秘密仅需公布3个公共值.分析表明该方案比现有方案更具吸引力,是一个安全有效的秘密共享方案.

Based on the intractability of the factorization problem and the discrete logarithm problem, a verifiable （t, n）-threshold multi-secret sharing scheme is presented to overcome the drampack of Lin-Wu scheme that is easy to be attacked by any malicious participant. The proposed scheme provides an efficient solution to the cheating problems .between the dealer and each participant. In this scheme, the dealer can share any new secret among these participants dynamically, and only one reusable secret shadow is required to be kept by each participant for sharing multiple secrets. Compared with the existing schemes, the proposed scheme reduces the number of modular exponentiation operations in preventing the dealer or each participant from cheating, and only 3 public values are required for sharing a secret, which makes the proposed scheme more attractive in computation and communication than the existing ones. Analyses show that this scheme is a secure and efficient secret sharing scheme.