When using a cipher with RSA authentication, an ephemeral RSA key exchange can take place. In this case the session data are negotiated using the ephemeral/temporary RSA key and the RSA key supplied and certified by the certificate chain is only used for signing.
Under previous export restrictions, ciphers with RSA keys shorter (512 bits) than the usual key length of 1024 bits were created. To use these ciphers with RSA keys of usual length, an ephemeral key exchange must be performed, as the normal (certified) key cannot be directly used.
Using ephemeral RSA key exchange yields forward secrecy, as the connection can only be decrypted, when the RSA key is known. By generating a temporary RSA key inside the server application that is lost when the application is left, it becomes impossible for an attacker to decrypt past sessions, even if he gets hold of the normal (certified) RSA key, as this key was used for signing only. The downside is that creating a RSA key is computationally expensive.
Additionally, the use of ephemeral RSA key exchange is only allowed in the TLS standard, when the RSA key can be used for signing only, that is for export ciphers. Using ephemeral RSA key exchange for other purposes violates the standard and can break interoperability with clients. It is therefore strongly recommended to not use ephemeral RSA key exchange and use EDH (Ephemeral Diffie-Hellman) key exchange instead in order to achieve forward secrecy (see SSL_CTX_set_tmp_dh_callback(3)).
On OpenSSL servers ephemeral RSA key exchange is therefore disabled by default and must be explicitly enabled using the SSL_OP_EPHEMERAL_RSA option of SSL_CTX_set_options(3), violating the TLS/SSL standard. When ephemeral RSA key exchange is required for export ciphers, it will automatically be used without this option!
An application may either directly specify the key or can supply the key via a callback function. The callback approach has the advantage, that the callback may generate the key only in case it is actually needed. As the generation of a RSA key is however costly, it will lead to a significant delay in the handshake procedure. Another advantage of the callback function is that it can supply keys of different size (e.g. for SSL_OP_EPHEMERAL_RSA usage) while the explicit setting of the key is only useful for key size of 512 bits to satisfy the export restricted ciphers and does give away key length if a longer key would be allowed.
The tmp_rsa_callback is called with the keylength needed and the is_export information. The is_export flag is set, when the ephemeral RSA key exchange is performed with an export cipher.