How's my browser know this page is legitimately secure?

I've found a rather interesting article that details the exchange that occurs between a client and server when entering a secure (HTTPS) page. It's cool to see all the activity that takes place in such a short time frame. All users really (care to) notice is that the lock icon shows up in the bottom-right corner. But as security implementers, shouldn't we understand what's really taking place?

Read more here

Encryption is a field in itself. I've known about the existence of RSA for some years now & the possible attacks against it.

http://theory.stanford.edu/~dabo/abstra ... urvey.html

If someone ever proves P = NP, we're all screwed.