[Nathan]

In think in such a case you wouldn't really say good luck, but the oh-so-useful phrase 頑張る（がんばる）(ganbaru)

When wishing someone luck on something, a short conversation in my experience would always go like this.

A: 　そうか？頑張ってください！ (sou ka? ganbatte kudasai!) "That so? Do your best!"
B: はい、頑張ります。 (hai, ganbarimasu) "Yeah, I will (do my best)."