This principle is called Diffie-Hellman key exchange ( http://en.wikipedia.org/wiki/Diffie–Hellman_key_exchange http://en.wikipedia.org/wiki/Diffie–Hellman_key_

This principle is called Diffie-Hellman key exchange ( http://en.wikipedia.org/wiki/Diffie–Hellman_key_exchange http://en.wikipedia.org/wiki/Diffie–Hellman_key_exchange ) and is vulnerable to a man in the middle attack. The man in the middle would complete key exchanges with both Alice and Bob. All that A and B see are valid key exchanges. This is why we have trusted third parties like Verisign. The further problems with this are discussed in the article.