关键词: 组合公钥, 共谋攻击, 标识认证, 种子矩阵, 线性变换

Abstract: Concerning the linear collusion attack problem in Combined Public Key (CPK) cryptosystem, on the basis of the nature of the linear collusion attack and according to the principle of key generation, a new equation set was constructed. Through the linear transformation to the coefficient matrix of the equation set, the rank of the equations can be solved, and it is less than the number of seeds of private key seed matrix. At the same time, the analysis of the private key's structure shows that the rank of the augmented matrix is not equal to the rank of coefficient matrix. Thus both sides above prove that the attacker never get the unique solution to the private key seed matrix even if he get all the private keys. Therefore, it demonstrates that there does not exist the threat of linear collusion attack in the CPK cryptosystem.

Key words: Combined Public Key (CPK), collusion attack, identity authentication, seed matrix, linear transformation