2560x1600 @60HZ [miniDP --> DVI-D] adapter
Solution 1:
To support that high resolution even without converting it from mini Display Port you need a Dual Link DVI adapter cable. Essentially the resolution is so high the graphics card and the display, also the cable in between must support Dual Link DVI. Chances are that the display already comes with a compatible cable and most 5 year old graphics cards have it too.
To answer your question: To get from mini display port to dual link DVI-D you can go with an unpowered one.
To get from mini display port to dual link DVI-I you most likely need an powered adapter, one that also uses power from a USB port to power the conversion. Apple sells one but I've heard they tend to die after a year or two.
Main difference is that DVI-I can output analog while DVI-D is exclusively digital, has fewer pins.
To be sure get the cheapest powered option below.
Try this one for powered dual link DVI
Cheapest option: https://www.monoprice.com/product?p_id=6904 (it is mini displayport to DVI-D make sure you have the right cable)
https://www.amazon.com/DisplayPort-Dual-Link-Adapter-Support-CAC-1051/dp/B00SOXO592
https://www.amazon.com/Accell-B087B-007B-UltraAV-DisplayPort-Dual-Link/dp/B00856WJH8
Try this one for unpowered dual link DVI (might not work)
https://www.amazon.com/DisplayPort-FOINNEX-Thunderbolt-Converter-Multi-screen/dp/B01GYC24H4
https://www.amazon.com/VisionTek-DisplayPort-DVI-D-Active-Adapter/dp/B00DYRQXNO