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manimino Sep 23, 2022 | on: The image in this post displays its own MD5 hash | context
Neat question. The best answer seems to be an HN thread from 13 years ago (!) which posits that the chance of one existing is ~63%: https://news.ycombinator.com/item?id=614079 However, it appears no one has actually discovered it yet, if it exists. A more tractable question might be to find a cycle in the MD5 hash space, like a->b->c->d->a. So one might ask, what is the shortest MD5 cycle found so far? |
My intuition tells me there's a fair chance such a fixed-point exists, if MD5 behaves as a random oracle.
Specifically, there's a 1-in-2^128 chance that any 128-bit input will give itself as the output. Over 2^128 trials the chance that no input answers itself would be:
...which mAlphaMatica helpfully calculates as...
http://www.wolframalpha.com/input/?i=(1-2^-128)^(2^128)
That is, there's about a 63% chance Kember's quest to find an input whose MD5 output is itself will succeed.
Or, is there something in MD5's construction making this impossible, making the random-oracle model inapplicable?