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A message accompanied with a digital signature and a MAC.

are there any possibility to know that the digital signature and the MAC are generated from the same message?

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You have the message, so verify the signature and mac against the message, if both are valid, then they must be generated from the message (except for a negligible probability).

For signature, you need the public key, which is assumed to be public and freely available, so verifying the signature is usually not a problem.

For the MAC, since it is symmetric key based, if you have the key, then it is fine. But if you don't have the key, then you won't be able to verify. In the latter case, it would be difficult to decide the relationship between the message and the MAC, unless the sender provides e.g. a zero-knowledge proof asserting the MAC was correctly generated from the message.

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