How can you ask questions in such form: "anybody knows"? Many people here know this very well.
First, if keys exist, they always send somewhere. Now, I feel you did not get it. How do you think, is it possible that two parties never meet, exchange data using some open channel and still can exchange secret data even though someone spies on them from the very beginning?
Many would intuitively say this is impossible, because — whatever all of them know and tell to each other, the spy in the middle also knows. This is a subtle logical mistake. This is quite possible. The idea is well explained in this article on public-key cryptography
]. Follow the speculations about Alice and Bob and you will see that the "key extraction" techniques you're thinking of is not needed.
The key to understanding is based on one-way function
, see http://en.wikipedia.org/wiki/One-way_function
]. The data is encrypted with one key, decrypted with another one.
RSA is one of such algorithms, see http://en.wikipedia.org/wiki/RSA
], ECC is another one, see http://en.wikipedia.org/wiki/Elliptic_curve_cryptography