What is and amplification factor in pseudo-random generators?
Amplification is equivalent to &quot;stretch&quot;, the number of (seemingly) random bits that your algorithm generates given the truly random seed.
Let $G:\{0,1\}^*\rightarrow\{0,1\}^*$ be a PRG that maps strings of length $n$ to strings of length $l(n)$, then $l(n)$ is said to be the stretch function of $G$. If $l(n)&gt;n$ and $l$ is injective, then you have $\forall n :|Im(G)\cap\{0,1\}^n|\le 2^{n-1}$.  You can use this to construct a language $L\in NP$, such that $L\in P$ allows you to break $G$ (construct a distinguisher with success probability $\ge\frac{1}{2})$. Note that you can relax the injectivity requirement by ignoring some of the output (i.e. given a PRG with stretch $l(n)&gt;n$, you can construct a PRG with stretch $l'(n)=n+1$).