Signing a message
Send to the receiver after encrypting with your private
key.
Sending a signed private message
Encrypt a message with your private key, and then the
receiver's public key. Send that.
Electronic Commerce
Each party chooses a random private key, and derives
a public key from that. They send the public keys to each other.
Then each side can send encoded messages to the other including details
of the transaction. After their finished, forget the keys used (or
not, that's OK too).