Score:1

Can a one-way permutation be used to stretch a pseudorandom generator?

lu flag

Consider a secure PRG $G:\{0,1\}^\lambda \to \{0,1\}^n$ and a one-way permutation $f:\{0,1\}^{n-\lambda} \to \{0,1\}^{n-\lambda}$. I'm wondering if the following construction $G': \{0,1\}^\lambda \to \{0,1\}^{2n-\lambda}$ is a valid stretch of the PRG output:

  1. Apply $G$ to the input $x \in \{0,1\}^\lambda$ to obtain $y \in \{0,1\}^n$.
  2. Apply $G$ to the first $\lambda$ bits of $y$ to obtain $z \in \{0,1\}^n$.
  3. Apply $f$ to the last $n-\lambda$ bits of $y$ to obtain $w \in \{0,1\}^{n-\lambda}$.
  4. Return $z || w$.
fgrieu avatar
ng flag
Perhaps (not sure): first settle if $G'$ is a PRG when $f$ is identify.
fgrieu avatar
ng flag
Simpler [related question](https://crypto.stackexchange.com/q/106924/555).
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