Are hashing algorithms constructed to guarantee that no fixed point exists?

My assumption is not, because I don’t see what utility that would have. (Please correct me if I’m wrong.) As such, purely for curiosity’s sake, have any fixed points of common algorithms (e.g., MD5, SHA-256, etc.) been found?

  • $\begingroup$ What is the point of knowing whether a hashing algorithm has a fixed point or not? I am not able to see it. What I mean, there are some questions that we can ask which, however, might not make much sense. For example, we can ask whether the world population at the point of the very start of year 2000 is an even number or odd number. $\endgroup$
    – John L.
    Jan 22, 2019 at 21:51
  • $\begingroup$ As I say, for curiosity’s sake. $\endgroup$ Jan 22, 2019 at 21:52

1 Answer 1


No, they are not constructed, to avoid having fixed point because it will not leverage extension attack, as of now, even making counter of lenght equal to some weak hash is infeasible and preimage attack is hard (otherwise we would call it compression, not hashing).

As of today, there are methods for collisions finding, and for SHA 256 for finding fixed points. Yes, it was found, take a look at crypto post.


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