I hope you've enjoyed our introduction to RSA and asymmetric cryptography.
It's really a very powerful idea.
In this unit, we introduced the idea of using asymmetric cryptography
both for privacy and for signatures.
There are lots more that we can do with asymmetric cryptography.
We'll talk about some of that in the next unit.
We talked about the RSA cryptosystem,
which is probably still the most widely used public key cryptosystem.
There are billions of transactions going on every day using RSA.
Nearly every time you use secure website, it's very likely that RSA is being used.
We'll talk about the protocol for that next unit.
We argue that RSA was correct, that it was invertible and had all the properties
that we needed to be able to encrypt and decrypt messages.
Its correctness depended on theorems that go back thousands of years
from Euclid--there are more recent ones, but still many hundreds of years old
from Euler and Fermat.
It's putting those things together in the right way that lead to this solution
that enables most of modern ecommerce.
We also argued that RSA is probably secure--at least for the time being.
That depends on the hardness of factoring.
Then we talked about some issues in using RSA in practice,
the dangers of encrypting small messages
or messages from a small set of known messages,
and solutions to that based on using random padding.
There's one issue that we haven't covered yet.
That's how does Bob actually know Alice's public key.
If they can get together in a room, maybe she could give it to him.
That's not usually possible, so this is a hard problem.
Until we have a solution for that, we're going to have to take away Bob's smiley face.
He's still a little bit frowny.
Until we have a solution to this problem, we don't have a good way
to use asymmetric cryptography in practice,
because it relies on being able to get all these public keys.
That's one of the things we'll talk about next unit--
how to build a public key infrastructure so Bob can learn Alice's public key
as well as lots more interesting applications of asymmetric cryptography.
Hope to see you back for unit 5.
