对基于单向函数的He-Dawson多步骤秘密共享方案的改进

Improvement on the He-Dawson Multi-stage Secret Sharing Based on One-way Function

在(t,n)门限秘密共享方案中,有n个参与者,至少t个参与者拿出自己的子秘密就能够同时重构m个秘密。He-Dawson提出了一个基于单向函数的多步骤秘密共享方案。但是他们的方案是一次方案而且不能抵抗合谋攻击。每个参与者的子秘密由参与者自己选取,所以不存在秘密分发者的欺骗。并且每个参与者能够验证其他合作者的欺骗。每个参与者选取的子秘密可以复用。并且组秘密可以以任意顺序重构。此方案还能够抵抗合谋攻击。本方案的安全是基于Shamir门限方案和RSA密钥体制。

In the （t, n） threshold multi-secret sharing scheme, there are n participants in the system. At least t or more participants can easily pool their secrets shadows and reconstruct m secrets at the same time. He-Dawson proposed a multistage secret sharing based on one-way function. But their scheme is one-time-use and suffers from the conspire attack. In this paper, each participant＇s secret shadow was selected by the participant himself, so the LID cheating is not exist. And every participant can detect the cheating by any other participant. Each participant can share many secrets with other participants by holding only one reusable shadow. And the group secret can be reconstructed in free order. Furthermore, the new scheme can withstand the conspiracy attack. The security of this scheme is that of the RSA cryptosystem and Shamir＇ s （t, n） threshold secret sharing scheme.