A Remark on One-Wayness versus Pseudorandomness

Every pseudorandom generator is in particular a one-way function. If we only consider part of the output of the pseudorandom generator is this still one-way? Here is a general setting formalizing this question. Suppose G:{0,1} n → {0,1}l(n) is a pseudorandom generator with stretch l(n). Let M R ∈ {0,1} m(n)×l(n) be a linear operator computable in polynomial time given randomness R. Consider the function $$F(x,R)=\big(M_R G(x), R \big)$$

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