可公开验证的短份额秘密共享算法

Public verifiable algorithm of threshold secret sharing with short share

为弥补传统秘密共享方案秘密长度不能太长的缺点,同时又能防止参与者作弊,利用Jordan矩阵理论,结合拉格朗日插值公式,提出了一种可验证的短份额门限秘密共享算法。算法能有效抵抗统计攻击和任意少于r个腐败的分享者的合谋攻击;各分享者保存的份额很短。当秘密是一个大的隐私文件、在一个不可信链路上传输的大消息、几个分享者共享的一个秘密数据库或者分布式存储的海量数据时,都具有重要的应用。

To make up the limitation that the length of secret can not be too long and prevent the action of cheating, using the theory of Jordan matrix, and combining with the formulary of Lagrange, the authors put forward an algorithm of threshold secret sharing with short share. It could effectively resist the statistical attack and the united attack of corrupt participants less than r. The length of secret share that each participator needed to conserve was very short. It had a very important application when the secret was a big privacy file, a big message transmitted in an insecure channel, a secret database shared by several participants or enormous data in distributed storage.