[Cryptography] Solving Matt's hash problem

[Jerry Leichter]

> In Matt Levine's long article about cryptocurrencies, he describes in
> accurate detail how hashing works, and mentions in an aside that he
> cannot include the hash of the article in the article itself, you (the
> reader) figure out why.
> 
> I know this is a preimage problem, but is there anything about making
> the hash itself part of the input that would make it harder or easier
> to solve?
Call the article with all 0's (say) as a placeholder for the hash A0.  Now replace the 0's with H(A0) to create A1.  Almost certainly, H(A0) != H(A1).  You can replace replace H(A0) with H(A1) to get A2, but hash changes again.  What you're looking for is essentially a fixed point - but even assuming it exists (there's no particular reason I can see why it has to) - how would you find it?

                                                        -- Jerry