Recently, the combined attack which is a combination of side channel analysis and fault attack has been developed to extract the secret key during the cryptographic processes using a security device. Unfortunately, an attacker can find the private key of RSA cryptosystem through one time fault injection and power signal analysis. In this paper, we diagnosed SPA/FA resistant BNP(Boscher, Naciri, and Prouff) exponentiation algorithm as having threats to a similar combined attack. And we proposed a simple countermeasure to resist against this combined attack by randomizing the private key using error infective method.