PRG is Injective

Question

I read this: Prove there is PRG that is not necessarily one-to-one. Now my question is: is there such PRG that is injective?

Answer 1

Recall the classical Goldreich-Levin PRG construction from a one-way permutation $f$ and a seed $s = s_1s_2\dots s_{2n}$ of even length:

• Compute $b = \sum_{i=1}^n s_i \times s_{n+i}$ (with arithmetic in $\mathbf{F}_2$).
• Output $G(s) = f(s_1\dots s_n)s_{n+1}\dots s_{2n}b$.

It is easily seen that $G(s) = G(s')$ implies $s = s'$.