Or do cheap ECDSA instead of expensive RSA. Even if the backdoor is hidden inside RSA decryption and the rest of the system thinks the thing being decrypted sho

Or do cheap ECDSA instead of expensive RSA. Even if the backdoor is hidden inside RSA decryption and the rest of the system thinks the thing being decrypted should be encrypted with RSA, you don't have to use it for the back door.