# Show that f(x,y)=x+y (with |x|=|y|) isn't a one way function

I have to prove that the function $$f\colon \mathbb N × \mathbb N \to \mathbb N$$ defined by $$f(x, y) = x + y$$ and $$|x| = |y|$$ isn't a one-way function. How do I go around doing that?

• Write the definition. What would it mean for $f$ not to be a one-way function? – Yuval Filmus Jun 16 '20 at 10:28

A function $$f$$ is one-way if given $$f(z)$$ for random $$z$$, it is hard to find an input $$w$$ such that $$f(w) = f(z)$$. So in order to show that $$f$$ isn't one way, you need to show that given $$f(z)$$ for random $$z$$, it is not hard to find an input $$w$$ such that $$f(w) = f(z)$$. Good luck!