Question: Let f : be a one-to-one function such that |f(w)| = |w| for all w . Define f

Let f : Σ∗ → Σ ∗ be a one-to-one function such that |f(w)| = |w| for all w ∈ Σ ∗ . Define f to be one-way if f is computable in polynomial time, but its inverse f −1 is not computable in polynomial time. Prove that if P = NP, then there are no such one-way functions.

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