Just to say it, the four tenets are:
- Confidentiality - The message the recipient gets can be proven not to have been read by anyone else since it was encoded.
- Integrity - The message the recipient gets can be proven not to have been changed since it was encoded.
- Authenticity - The message the recipient gets can be proven to have been encoded by (edit) a positively-identified sender.
- Non-repudiation - The sender, given a message received by a recipient, cannot validly deny that the message was sent by him or that it was not the original content sent by him.
This last point seems redundant. If you can prove that the sender sent the message, and separately prove that nobody has changed (or even seen) the message while in transit, then the combination is proven by definition; that the sender and nobody else sent exactly that message and nothing else.
... At least that's my take on it. So, the question is, is there a situation (other than compromise of cryptographic secrets, which indicate a different culpability on the sender's part) in which you can verify the confidentiality and integrity of the message, and the authenticity of the message and its sender, but the sender can still validly repudiate the message?
EDIT: CodesInChaos makes a very good point; you can begin a confidential conversation with a remote party and exchange information, and prove that the information wasn't read or changed, and could only have come from the party with whom you opened the channel. All of this without having a clue who you're talking to.
This kind of undermines the point of "authenticity", though. If something is "authentic" or "genuine", it is what it looks like and/or what its supplier claims it to be. In communications, the very notion of a message being "authentic" implies that its stated source is its actual source. For the message to be "authenticated" as coming from someone, you therefore must know who that someone is in the first place.
Therefore, perhaps a change in definition of "Authenticity" is called for: "The message the recipient gets can be proven to have been encoded by a positively-identified sender". If you cannot identify the sender, you cannot authenticate the message as, in part, having that sender as its source, and therefore of course the purported sender can claim it's fake. This is true even if the message can be proven to be confidential, unchanged, and having come from a definite source location.