Symmetric and Asymmetric ciphers, non-repudiation?

Question

Hello, I have read on wikipedia "However, symmetric ciphers also can be used for non-repudiation purposes by ISO 13888-2 standard."

Then again and I read on another wiki page, "Non-repudiation, or more specifically non-repudiation of origin, is an important aspect of digital signatures. By this property an entity that has signed some information cannot at a later time deny having signed it. Similarly, access to the public key only does not enable a fraudulent party to fake a valid signature. This is in contrast to symmetric systems, where both sender and receiver share the same secret key, and thus in a dispute a third party cannot determine which entity was the true source of the information."

This means one page says symmetric algorithms have non-repudiation and another page says they don't have it and therefore they are not used for digital signatures. So do symmetric keys have non-repudiation or not? It makes sense that they can not be used for signatures and non-repudiation since symmetric keys are the same and thus the system can't distinguish which one belongs to which person and which one is first etc. In that case I think symmetric keys are only a tool for confidentiality and not used for non-repudiation or digital signatures.

Answer 1

I think the answer depends on whether the shared key is public or not. If the parties agree to public source (third party) for their shared key there is non-repudiation of origin.

Answer 2

ISO 13888-2 introduces structures and protocols which can be used to introduce non-repudiation services, in the context of symmetric techniques. However all these "tricks" rely on the existence of a Trusted Third Party.

The point of the second Wikipedia citation in the question is that asymmetric key systems intrinsically [and without the need of thrid parties] offer non-repudiation features (specifically NRO i.e. non-repudation of the the Origin).