It really is pretty simple, at least in theory. Simply when the download stopped at x, the program tells the resume to start at x-y and overwrites the last y bytes or kb.

It would be best if you also added a few other features that should not be to difficult but would really make Furi one of the best clients.
-Remember downloads that have been queded and automatically search the network for the same file (file should have same name and size), and auto-resume.
-Split files available on multiple computers into many parts and download the different parts from different computers for faster downloads.