This is from my homework:

  • Prove that if there exists a one-way function, then there exists a one-way function f such that

    $f(0^n ) = 0^n$ for every $n$.

    Note that now for infinitely many values $y$, it is trivial to compute $f^{−1}(y)$.

While I don't expect someone to spell the answer out for me, setting f as the inverse function, we can say the inverse exists. As a result, it is not a one-way function.

  • 1
    $\begingroup$ Welcome to Cryptography. For Homeworks we only provide hints. However, It is not clear what do you mean by ` f(0 n ) = 0 n`. Note: You can use $LaTeX$/MathJax in out site. $\endgroup$ – kelalaka Nov 17 '19 at 20:29

One-way function doesn't mean that it's impossible to reverse on EVERY output. One-way function means that's it's hard to invert on an output picked at random over the set of the outputs.

You can read in more details the definitions given in the following link:


| improve this answer | |
  • $\begingroup$ Please see Our current homework policy $\endgroup$ – kelalaka Nov 19 '19 at 21:00
  • $\begingroup$ The question was not about how to solve the exercise, the homework was just the context about the question (If I didn't misunderstood). $\endgroup$ – Ievgeni Nov 20 '19 at 8:45

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