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How Key Exchange Works Today
Current hybrid cryptosystems like SSL/TLS use symmetric key algorithms (they are generally faster than asymmetric algorithms.) Symmetric key algorithms require a shared secret, exchanged via key-exchange algorithm.
The most famous cryptographic protocol for key exchange is Diffie–Hellman, published in 1976 by Whitfield Diffie and Martin Hellman. Diffie–Hellman allows the creation of a shared secret between a sender and receiver. This shared secret is unable to be deduced by an eavesdropper who is observing the messages between the sender and receiver, except via a brute force attack. If the keyspace for the shared secret is large enough and the secret generated is sufficiently random, brute force attacks become nearly impossible.