The Kember Identity May Not Exist

The Kember Identity May Not Exist

I used to work with Elliot Kember at Eventfinder. He recently proposed a search for the MD5 "Kember identity", a string which, when hashed, returns itself.

Something I've been thinking about: it's entirely possible such an identity doesn't exist.

Imagine a hashing algorithm that takes a two bit input and returns a two bit output. That is, the domain and range is {0, 1, 2, 3}. If the algorithm perfectly distributes its hashes over the range then, for each input value, there's a 0.25 probability of it being an identity. So, the probability of no identity being produced by the hash function over any of its domain is (0.75 ^ 4) = 0.32; about a one in three chance.

MD5 has a range of 2 ^ 128. For finding the identity, the domain must be the same as a range. So, there's a 1 in 2 ^ 128 chance of a random input being the identity. The probability of an input not being an identity is ((2 ^ 128) - 1 / (2 ^ 128)). And the probability of there not being any Kember Identity at all is ((2 ^ 128) - 1 / (2 ^ 128)) ^ (2 ^ 128).

Which, according to some quick mpmath, is:


So, there's a decent chance that there is no Kember identity. Good to know if you're considering starting to churn away on the problem.



I have a feeling that someone is going to spend far too much time trying to prove you wrong. I want to know the string that returns all 1's when it is hashed. I would actually sit there and memorise the string just because i have that much free time.

Also looks like someone may get a lot of money if they prove you wrong. Snap.
I hope you mean you have a feeling someone is going to spend far too much time trying to find the identity rather than prove false Dom's contention that it is unlikely to exist.
To clarify my contention: there is a 63 percent chance that MD5 has a fixed point.
heh, whoops. Oh well, I take solace in the fact that I was less mistaken than Chicken. This is a guy s'posed to be teaching Probability to fifth formers...
By which I mean I am that guy; deixis be damned.
What the hell does all of this mean?
I lol'd
Also, is there a proof for uniqueness, should it exist?
or, "should one exist", rather