I have a simple question:
Are we certain that the md5 hashing algorithm can produce $2^{128}$ different outputs ?
If so, how ?
Note: Sorry if this has already been asked, I really couldn't find it.
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Related question from StackOverflow: Do cryptographic hash functions reach each possible value, e.g. are they surjective? – mikeazo Jul 12 '18 at 13:42
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@mikeazo Thank you very much, that word (surjectivity) helped me find my question : https://cs.stackexchange.com/questions/43205/is-it-known-whether-the-md5-algorithm-is-surjective – Lynesth Jul 12 '18 at 13:47
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1That's how it goes some times, just need the right word. Also related Are common cryptographic hashes bijective when hashing a single block of the same size as the output? – mikeazo Jul 12 '18 at 13:49
1 Answers
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MD5 processes a message into a fixed-length output of 128 bits, typically represented as a sequence of 32 hexadecimal digits.
This process is not random, but it’s a so called „pseudo-random“-process (A pseudo-random process is a process that appears to be random but is not 100% random).
There is actually no proof that every hash-value of the MD5-process is reachable for some input, but it is expected to be true.
So MD5 can hash every input to an „arbitrary“ hash-value of 128 bits, bits can be 1 or 0, so $2^{128}$ possible outputs.
AleksanderCH
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1... and note that there are infinite inputs, so the hash function is very likely to produce each and every value if the output is pseudo-random, otherwise a small bias is clearly present. +1 for answering before it was put on hold :) – Maarten Bodewes Jul 12 '18 at 15:52