So I've had a little look at the paper and the first part of my question is addressed by their term "public deniability". Apparently they have public denyabilit

So I've had a little look at the paper and the first part of my question is addressed by their term "public deniability". Apparently they have public denyability for the receiver side, but not the sender side. So everyone can claim that they were the recipient of the message with X being its content, but only someone who knows the sender secrets can claim authorship.