Not private key in public-key schemes (RSA, DH), because these are generally random integer and BN_mod_exp is not used in private key generation -- but it's use

Not private key in public-key schemes (RSA, DH), because these are generally random integer and BN_mod_exp is not used in private key generation -- but it's used in public key generation so the result could be an invalid key pair. In addition, I think it could produce a wrong symmetric key, as a result of a bad computation e.g. in the Diffie-Hellman protocol. So you could have insecure symmetric (e.g., AES) keys.