Abstract: Correlation power analysis (CPA) which is one of the most useful techniques for side channel attack can not implement a successful attack against the exponent and the message blinding countermeasures on modular exponentiation algorithm. And a successful attack against these protected implementations is performed by the high order CPA. But a lot of noise caused by the high order CPA lead to the less attack accuracy of side channel attack. Moreover, the methods of artificial observation are currently used by setting the threshold in attack process, so the attack effect is heavily dependent on the attacker's experience. In order to solve these problems, a cluster CPA is proposed by utilizing correlation characteristics difference between power consumption of modular multiplication to evaluate the effectiveness of power points. The utilization of valid information is improved and the noise and artificial participation are reduced by using the new proposed method. Experiment results demonstrate that the proposed cluster CPA can enhance attack efficiency and attack algorithm generality by comparing with other CPA methods, and only 400 power traces are required to launch the attack with the attack accuracy of 100%.