基于线性单向函数的可验证的多秘密共享方案

基于Shamir的门限秘密共享方案和线性单向函数的安全性以及离散对数问题的困难性，提出了一个可验证的多秘密共享方案。该方案中每个参与者只需保护一个秘密份额，就可共享多个秘密。秘密恢复之前，参与者可验证其他参与者所提供的影子份额的正确性。秘密恢复后，参与者的秘密份额不会泄露，可重复使用，并且所需的公开参数较少，秘密分发过程不需要安全信道。

Verifiable multi-secret sharing scheme based on linear one-way function

Based on Shamir's threshold secret sharing scheme, the security of the linear one-way function and the difficulty of the discrete logarithm problem, a verifiable multi-secret sharing scheme was proposed．In this scheme, each participant needed just one secret share to share a set of secrets．Before recovering the secrets, participants could verify the correctness of the shadow shares provided by other participants．After recovering all of the secrets, the secret shares of the participants were still kept confidential and the secret shares could be used to share a new set of secrets．At the same time，the proposed scheme had fewer public parameters，and it did not require secure communication channels．