# Hardness amplification of PRFs by increasing key length

I was reading the GGM construction for PRFs and wondering the relation between key length and hardness. GGM construction does not seem to yield any significant improvements. Are there any PRF constructions which take into account key length for increasing hardness? Alternatively, are there any constructions which transform a $(t, \epsilon)$ PRF of key length $k$ to something like $(t^2, \epsilon)$ PRF of key length $2k$ or $k^2$?

There are some examples of techniques that given a $(t,\epsilon)$-scheme construct a new scheme that is something like $(t,\epsilon^2)$-secure, but that's different. (If you're interested in that, spend some quality time with Google and Google Scholar looking at results on "hardness amplification"; see, e.g., Yao's XOR lemma.) I don't know of any techniques that given a $(t,\epsilon)$-scheme construct a $(t^2,\epsilon)$-scheme.