This article proposes a new message blinding methods requiring no multiplicative inversion for RSA. Most existing message blinding methods for RSA additionally require the multiplicative inversion, even though computational complexity of this operation is O ( n ³ ) which is equal to that of the exponentiation. Thus, this additional operation is known to be the main drawback of the existing message blinding methods for RSA. In addition to requiring no additional multiplicative inversion, our new countermeasure provides the security against various power analysis attacks as well as general differential power analysis.