The chosen-message method used to be employed in conducting SPA attack by means of selecting special input messages.However, it is difficult to make distinction by visual observation i.e.SPA in practical hardware environment.In this paper, we proposed a practical chosen-message CPA attack which combines the chosenmessage method with correlation power analysis (CPA) for side channel attack.And we introduce other two practical chosen-messages 1 and n + 1 and utilize them to attack Boschers right-to-left binary exponentiation algorithm which used to be considered as an efficient side channcl resistant cxponcntiation algorithm.Further we also propose a countermeasure to resist the chosen-message CPA attack over Boschers algorithm without nullifying its countermeasure features to DPA and DFA.To validate the proposed attack method and countermeasure, we designed a 1024-bit RSA coprocessor on the Xilinx FPGA with the Side-channel Attack Standard Evaluation Board (SASEBO) to implement Boschers algorithm as well as our proposed algorithm and launched the proposed attack on it separately.The experiment results show that the proposed attack and countermeasure is feasible and efficient.