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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, Noordung, Mark, Xander, Rory Alsop Aug 13 at 8:00

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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 at 16:39
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What are you trying to achieve? –  miniBill Feb 25 at 17:03
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@miniBill A way to guarantee the integrity of message and its signature –  ts01 Feb 26 at 8:23
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@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 at 8:31
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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 at 22:13

1 Answer 1

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 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 at 2:57

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