一种可验证的 $ (k,n) $门限多秘密共享方案

基于排列和 Diffie-Hellman 问题，文章提出一种可验证的 $ (k, n) $ 门限多秘密共享方案。该方案中排列的使用确保了计算生成的秘密份额的安全性，在 Diffie-Hellman 问题的假设下，各参与者的伪份额均由自己生成，基于相关等式是否成立实现了方案的可验证性。各参与者只需维护 1 个彼此不同的伪份额即可根据门限值 k 进行多个秘密的重构。结果表明，该方案不需要安全信道，各参与者的伪份额可重复使用，且可以抵抗合谋攻击和外部攻击。

Based on the permutation and Diffie-Hellman problem, a verifiable $ (k,n) $ threshold multi-secret sharing scheme is proposed. In the scheme, the application of the permutation ensures the security of the secret shares generated by calculation. Under the assumption of the Diffie-Hellman problem, participants' pseudo-shares are generated by themselves. The verifiability of the scheme is achieved based on whether the relevant equation holds. Each participant only needs to maintain a pseudo-share that is different from each other to reconstruct multiple secrets according to the threshold value k. Further analysis shows that the scheme does not need a secure channel, the pseudo-share of each participant can be reused, and it can resist collusion and external attacks.