# Can a One way function also be its inverse?

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.

• 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. Nov 17 '19 at 20:29