[Solved]: What will i obtain if i apply a xor-ing a one way function and it's input?

Problem Detail: 

I know that a one-way function is informally a function that it's easy to compute but hard to invert.
If f(x) is a one way function the function $g(x) = x\oplus f(x)$ is a one-way function? My intuition is that it's but i not really sure.

Asked By : dbonadiman

Answered By : Yuval Filmus

Let $h$ be any one-way function, and define $f(x) = 0^{|x|} h(x)$. Note that $f$ is also one-way: it is easy to compute, and if you can invert $f$ you can invert $h$ (so since $h$ is hard to invert, so is $f$). But $g(x) = xh(x)$ is easy to invert.

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Question Source : http://cs.stackexchange.com/questions/7160