Hmm. So basically any protocol with a shared key? I.e. a symmetric key is shared between you and me. If I receive a message with that key, I know it's from you

Hmm. So basically any protocol with a shared key? I.e. a symmetric key is shared between you and me. If I receive a message with that key, I know it's from you because the key is only known by you and me, and I know I wasn't the sender, so it must be you. But any third party can only say that the message was by one of us.