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Now let's look at a couple applications, if we could build a cryptosystem like this.
First we'll look at a standard use of it to send private messages.
This is what our goal was initially for the symmetric cryptosystems.
That assumed that we had a shared key to begin with.
Now let's assume that we don't.
Let's assume Alice wants to send a private message to Bob.
She doesn't have a secure channel, and she doesn't have a key shared with Bob,
but she does know Bob's public key.
We'll call that KUB.
Bob knows his private key that corresponds to the public key that Alice
as well as anyone else who wants to know knows is associated with Bob.
Now Alice can send a message to Bob,
encrypting it with Bob's public key knowing that the only one who can decrypt it
is someone who knows Bob's private key, which should be only known to Bob.
Bob decrypts the message using his private key.
Now we'll have a quiz to see that everyone is understanding asymmetric cryptosystems.
What correctness property does this rely on?
Here are the three choices.
Pick the one that this private messaging system is relying about the E and the D functions.