X'
so that H(X') = H(X)
given H(X)
. So if an X
is found it is computationally certain that it was indeed the input message. Otherwise you would have performed a collision attack after all. Rainbow tables can be used to speed up the attacks and there are specialized internet resources out there that will help you find a password given a specific hash.H(X)
to verify passwords that were generated on other systems. The only thing that the receiving system has to do is to store the result of a deterministic function F
that takes H(X)
as input. When X
is given to the system then H(X)
and therefore F
can be recalculated and the results can be compared. In other words, it is not required to decrypt the hash value to just verify that a password is correct, and you can still store the hash as a different value.H(X)
even if H(X)
is a password hash. Password hashes are still deterministic, so if anybody has knows all the input and the hash algorithm itself then X
can be used to calculate H(X)
and - again - the results can be compared.