基于特征值的黑盒子意义下的特殊门限秘密共享方案

摘 要: 基于Shamir(n,t)秘密共享方案，提出一个新的门限秘密共享方案。利用n阶矩阵的特征方程具有重根的特点，实现了不同集合中参与者的秘密共享。同一参与集合所对应的次主密钥是相同的，即特征值是相同的，将同一个特征值所对应的不同特征向量作为子密钥，分发给同一参与集合的参与成员。而且，利用黑盒子，同一集合内部成员可以验证自己手中的子密钥的真实性，从而达到了防欺诈的目的。分析结果表明，本方案是安全的理想秘密共享方案。

Special threshold secret sharing scheme in the sense of black box based on eigenvalue

Abstract: This paper proposed a new threshold secret sharing scheme based on the Shamir(n,t) threshold secret sharing scheme. Used the characteristic that the characteristic equation of the n-th order matrix has multiple roots, realized the secret sharing of participants in different sets.The secondary master key corresponding to the same participation set is the same, that is, the eigenvalue are the same.The algorithm firstly used the feature vector corresponding to the same eigenvalue as a subkey ,then it distributed the subkey to the participating members of the same participating set.what''s more, the members of the same collection can use the black box to verify the authenticity of the sub-keys in their own hands so as to achieve the purpose of fraud prevention. The analysis result shows that this scheme is safe and ideal .