I am reading this article (pdf) on the Diffie–Hellman key exchange. It states the following:
At this point, the Diffie-Hellman operation could be considered complete. The shared secret is, after all, a cryptographic key that could encrypt traffic. But completion at this point is very rare, because the shared secret is an asymmetric key by its mathematical nature, and all asymmetric key systems are inherently slow.
In most real applications of the DH protocol (SSL, TLS, SSH, and IPSec in particular), the shared secret encrypts a symmetric key for one of the symmetric algorithms, then transmits it securely, and the distant end decrypts it with the shared secret.
I'm trying to understand the point in an authentication scheme where two parties have exchanged keys with Diffie-Hellman, and now have the "shared secret".
How is the shared secret asymmetric if the "shared secret" is used to both encrypt and decrypt?
How exactly do i encrypt an AES key with the "shared secret" key?
Is it not possible to directly create a symmetric AES key with the DH key exchange?