Did Amalek Really Exist?

The title of this post is self-explanatory. I don't think that there is any extra-Biblical evidence for Amalek. Do you know of any? (Arab traditions cite Amalek as an extremely powerful group, but I'm thinking more of archaeology than other people's mesorahs.)

Possibilities:

1. Amalek existed as described in Tanach
2. Amalek existed, but was nothing like what the Torah describes
3. Amalek never existed

Ideas:

In Ages in Chaos, Immanuel Velikovsky identified the Amalekites with the Hyksos. If this is true it royally screws with those who believe that Hyksos = Jews in Egypt.

Apologetic view: The Jews followed God's commandment, wiping out Amalek and leavinging behind no evidence that they ever existed.

If anyone here reads and understands German, I found this reference which possibly addresses this question: "Nöldeke, Ueber die Amalekiter und einige andere Nachbarvölker der Israeliten, Göttingen, 1864."

So two questions: Did Amalek actually exist? Do you have any extra-Biblical evidence to back up the contention that they did?