There are lots and lots of other interesting applications of asymmetric cryptography.
We'll see some of those later in unit 5,
but for now I want to focus on how to actually build an asymmetric cryptosystem.
What we want to build is what's known as a "trap door" one-way function.
A one-way function would be a function that is easy to compute in one direction
and hard to compute in another direction.
With asymmetric crypto we need to reveal this function.
We want the reverse to still be hard, but we want some way to be able to do the reverse easily
if we know some secret. That's our trap door.
We want to be able to--if you have some secret key, you can do the inverse.
If you don't, you can't. That's what makes an asymmetric cryptosystem.
It's hard to do in the reverse direction unless you have this extra key.
But revealing the easy way to do the forward direction
does not reveal the easy way to do the reverse direction.
Diffe and Hellman envisioned such a cryptosystem
in the 1976 paper that we talked about last unit,
but they didn't devise a function that had this property.
The first cryptosystem to successfully have this property, is the RSA cryptosystem.
That'll be the focus for the rest of this unit.
