组合公钥体制的线性共谋攻击分析

Linear collusion attack analysis of combined public key cryptosystem

针对组合公钥(CPK)体制中的线性共谋攻击问题,从其本质出发,根据密钥产生原理提出了新的方程组构造方法。通过对方程组的系数矩阵进行线性变换,求得了方程组的秩,发现其小于私钥矩阵的种子数;同时,分析了私钥的构造,发现增广矩阵的秩不等于系数矩阵的秩。由此两方面证明了即便攻击者得到所有私钥也无法解得方程组的唯一解。因此,论证了组合公钥体制不存在线性共谋攻击的威胁。

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.