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Does a pair of (hashing) functions for which

enter image description here

where neither g(x) nor f(x) are constants exists?

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closed as off-topic by Gilles, TildalWave, Mark, Xander, Rory Alsop Aug 13 '14 at 8:00

  • This question does not appear to be about Information security within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

Defining f as "take the last <output size of g> bytes of the input" works with arbitrary g. Another variant for f is "take everything except the last <output size of g> bytes of the input and feed it to g". – CodesInChaos Feb 25 '14 at 16:39
What are you trying to achieve? – miniBill Feb 25 '14 at 17:03
@miniBill A way to guarantee the integrity of message and its signature – ts01 Feb 26 '14 at 8:23
@miniBill for given message m and hash h(m) = x, there is function f which outputs f(m + x) = x. If you are asking for practical use, there is probably any. – ts01 Feb 26 '14 at 8:31
This question appears to be off-topic because it is about mathematics, possibly (but not clearly) about cryptography, but has no application to security. – Gilles Aug 12 '14 at 22:13

How about:

  • g(x)=x, f(x)=x/2
  • g(x)=x^2, f(x) = 1/4 * (sqrt(1+4*x)-1)^2
  • g(x)=x^n, f(x) = RootOf(Z^n+Z-x)^n
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This isn't a cryptographic hash (which is all the hashes we care about on Information Security). – Gilles Aug 12 '14 at 22:09
As you yourself pointed out above, this question appears to be a mathematics question, though it may have some security application. Having no further information, I answered the question as stated; making unstated assumptions is as bad a practice in security as it is in science. – Ari Trachtenberg Aug 13 '14 at 2:57

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