一种有效的可验证的门限多秘密分享方案

针对多数秘密共享方案不能同时防止秘密管理者和秘密成员的欺骗，以及子秘密重构时计算量大等问题，提出了一种安全有效的解决方案。在该方案中，每个分享者只需拥有一个秘密影子就可以和其它分享者共享多个秘密信息，此外，方案提供了有效抵御秘密管理者欺骗和成员欺骗的解决方法。方案的安全性是基于求离散对数和RSA大整数因式分解的困难性。与其它已有的方案相比，此方案的优点在于计算量低和子秘密重构时采用了并行算法。

Efficient and verifiable threshold multi-secret sharing scheme

Most previous secret sharing schemes have some problems in which the schemes can not deter the cheating of the dealer and secret shadowholders simultaneously, and the computation in a secret recovery is overhead. A secure and efficient solving scheme was proposed. Each participant can share many secrets with other participants by holding only one shadow in the proposed scheme. This new scheme provides efficient solutions against cheating of the dealer and cheating of any participant. The security of the proposed scheme is based on the difficulty of computing the discrete logarithm modulo for a composite number and the factorization problem of a large integer. Compared with the other existing schemes, the proposed scheme has the advantages of lower computation and the parallel reconstruction in a secret recovery phase.