Based on the structure of the side channel attacks (SCAs) to RSA cryptosystem can resist the fault attack andcombine with the randomization method for the message and secret exponent, a new implementation scheme of CRT-based(the Chinese remained theorem) RSA is proposed. The proposed scheme can prevent simple power analysis (SPA), differentialpower analysis (DPA) and time attack, and is compatible with the existing RSA-CRT cryptosystem as well. In addition, animprovement for resisting fault attack is proposed, which can reduce extra computation time.