—Fault attacks constitute a major threat toward cryptographic products supporting RSA-based technologies. Most often, the public exponent is unknown, turning resistance to fault attacks into an intricate problem. Over the past few years, several techniques for secure implementations have been published, but none of them is fully satisfactory. We propose a completely different approach by embedding the public exponent into [the description of] the private key. As a result, we obtain a very efficient countermeasure with a 100% fault detection. Keywords- RSA cryptosystem; fault attacks; countermeasures.