I have the 800:1 version of that monitor. The HDCP DVI input will work just like an HDMI input (with the correct cable/adapter). I have never had an issue with any HDCP stuff through it, but I also have never run a 1080p HDCP signal to it either.
For a cable you need either a DVI-I or a DVI-D cable, and you don't need a dual link either unless you want one.