It is impossible to prove that somebody is Satoshi.
Yes, it is difficult because no one knows the true Satoshi Nakamoto. And only his personal acquaintances, friends, and relatives can prove it.
Even if Satoshi presents his privatekeys, signs messages, shows his passwords, e-mail account accesses... it could be someone else who has all these privatekeys, passwords, accesses now.
He would only prove the ownership of these but it is impossible for somebody to prove that he is Satoshi.
What else should we base on who the real Satoshi Nakamoto is? This is the only way because it is difficult and impossible to crack Satoshi Nakamoto's wallet.