[cryptography] Number of hash function preimages

Florian Weingarten weingarten at itsec.rwth-aachen.de
Fri Mar 9 06:25:14 EST 2012


Hello list,

first, excuse me if my questions are obvious (or irrelevant).

I am interested in the following questions. Let h be a cryptographic
hash function (let's say SHA1, SHA256, MD5, ...).

1) Is h known to be surjective (or known to not be surjective)? (i.e.,
is the set h^{-1}(x) non-empty for every x in the codomain of h?)

2) Is it known if every (valid) digest has always more than one
preimage? To state it otherwise: Does a collision exist for every
message? (i.e., is the set h^{-1}(x) larger than 1 for every x in the
image of h?).

3) Are there any cryptographic protocols or other applications where the
answers to 1) or 2) are actually relevant?


Thanks in advance!

Florian



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