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Does a pair of (hashing) functions for which

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

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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
    
What are you trying to achieve? –  miniBill Feb 25 at 17:03
    
@CodesInChaos yes, it is obvious. But I am earching rather pair of "cyclic" hashing functions (it can be also ONE function : f(x) = f(x+f(x)), f(x) != x and f(x) is not constant) –  ts01 Feb 26 at 8:22
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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

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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