基于特征值的无可信中心的秘密共享方案研究

Research on Secret Sharing Scheme Without Trusted Center Based on Eigenvalue

利用矩阵特征值的特性,该文提出新的无可信中心的秘密共享方案。该方案无需可信中心的参与,每个参与者提供相同的秘密份额(列向量),在黑盒子中协同产生各自的秘密份额,从而避免可信中心的权威欺骗。所有参与者提供的列向量组成一个可逆矩阵P,可逆矩阵P和对角矩阵生成一个矩阵M,并将该矩阵正交化的单位特征向量,作为子密钥分发给各参与者。由于同一个集合的参与者所对应的特征值是相同的,该方案可以有效地防止成员之间的恶意欺诈行为。分析结果表明,该方案是可行的、安全的。

By using the characteristic of matrix eigenvalues, this paper proposes a new secret sharing scheme without trusted center. The scheme does not require a trusted center, and each participant provides the same secret share （column vector） and generates its own secret share in the black box, thus avoiding the authority deception of the trusted center. Reversible matrix P consisting of column vectors provided by all participants,and diagonal matrix A generate a matrix M. Then, the orthogonalized unit eigenvectors of the matrix M is distributed to each participant as a subkey. Because the eigenvalues corresponding to the participants in the same set are the same, this scheme can effectively prevent malicious fraud among members. Analysis results show that the program is feasible and safe.