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Simple answer: of course there is. The real challenge is finding such strings. If I wanted to know the answer to that question, I'd first search some precomputed rainbow tables to see if anybody's gotten lucky: http://project-rainbowcrack.com/table.htm
Do you mean just that it is very very likely that there is, or is there some argument that the MD5 function must be surjective?
There's an infinite number of those strings, but barring an edge case in the md5 algorithm, none are known.
Imagine a simple algorithm that should hash a string to a number 0-3, but due to an extra condition it actually cannot produce "3", pseudocode:
``` Sum = sumOfAsciiCodeOfString(input); Rest = Sum % 4; Return Rest === 3 ? 2 : Rest; ```
Or due to a bug (replace `% 4` with `% 3`).
Can we prove that md5 doesn't suffer from such issues and it actually can output ffffffffffff or deaddeaddeaddead ?
Earlier quoted context omitted.
The discussion on security.SE seems to imply it's unknown: https://security.stackexchange.com/questions/107081/does-eve... so if you have a proof of your simple answer, I'm sure they'd welcome it
My statement is one of statistically-informed confidence. A physicist's proof, not a mathematician's. As I said, proving it is where the challenge lies.
Assuming you meant a 128-bit hash with all bits set to '1' (i.e., '0xffffffffffffffffffffffffffffffff'), it would still be extremely difficult, if not practically impossible, to find a string that hashes to this specific value. The MD5 algorithm is designed to produce seemingly random output for small changes in input, and there are no known methods to easily reverse-engineer an MD5 hash. That being said, MD5 is no l…
Earlier quoted context omitted.
My statement is one of statistically-informed confidence. A physicist's proof, not a mathematician's. As I said, proving it is where the challenge lies.
I believe proof-by-induction is still a mathematically valid proof. Just one to be suspicious of/can be overridden by more rigid proofs.