Abstract: A new multi-secret sharing scheme based on homogeneous linear recursion is proposed, and then it is converted into a verifiable scheme. In the distribution phase, very few of public values are needed to publish. In the recovery phase, each participant only needs to submit a pseudo shadow instead of his secret shadow, and his secret shadow cannot be disclosed. When secrets are changed, secret shadows don?t need to be redistributed, which makes secret shadow able to be used multiple times. The proposed scheme has many advantages, for example, the secret shares can be used multiple times and the scheme publishes very few parameters as well as the reconstructed polynomial has a low degree. This makes the proposed scheme more efficient. Therefore, it better satisfies demands of various applications.

Key words: multi-secret sharing, verifiable scheme, homogeneous linear recursion

摘要： 基于齐次线性递归提出了一个新的多秘密共享方案, 并将其扩展成一个可验证的方案。在秘密分发过程中, 只需公布很少的公开参数; 在秘密重构过程中, 每个成员只需提供伪份额, 不会暴露秘密份额; 当秘密更改时, 不需重新分配秘密份额, 实现了秘密份额的多次使用。提出的方案具有秘密份额可以多次使用、公开的参数少以及所要重构多项式的次数小的优点, 这使得方案更高效, 能够更好地满足各种应用需求。

关键词: 多秘密共享, 可验证, 齐次线性递归