一个完善的可公开验证秘密分享方案*

利用离散对数问题的难解性和Williams体制，在假设初始化阶段和秘密恢复阶段始终有一位值得信赖的分发者参与的情况下，提出了一个可公开验证的门限秘密分享方案。在方案中，各用户只需公布其秘密份额的盲化值，每个参与者甚至第三者都可以对这一盲化的秘密份额进行验证；不但能有效地阻止密码分析者窃取秘密或子秘密，也能有效地防止内部成员之间的相互欺诈，而且任一分享者能在多项式时间内恢复密钥。

Publicly Verifiable Secret Sharing Scheme with Perfect Secrecy Feature

By means of the intractability of the discrete logarithm problem and Williams scheme, a publicly verifiable threshold secret sharing scheme is proposed with a trusted dealer distributing the secret information in the initialization phase and recoving phases. Every participant only show his own blind sub-secret and other participants are able to verify it. This scheme can prevent adversaries from getting the secret or sub-secrets and the participants from cheating each other efficiently. Furthermore, each share can get the secret in a polynomial time to set orders lastly. It solves some critical questions safely and effi- ciently.