The problem of proving that you are the same person who sent an e-mail or wrote a message is largely solved thanks to the electronic signature.
But what about proving you are not a given person?
To take an example we are all familiar with, it would be very easy for someone to prove that he/she is the founder of Bitcoin by signing a message using Satoshi’s private key.
But how can someone prove he/she isn’t Satoshi (without compromising the anonymity of the latter)?
Note. The question is not about Satoshi Nakamoto, it is just an example.