BackupPC http://backuppc.sourceforge.net/ is probably what you're looking for, although I can't tell you about the encryption part. I am just starting to look into serious backup solutions myself.
I have set up BackupPC before. It is not quite the same as dropbox and probably won't fill the client file-sharing and change tracking need; it is a backup system, that you can retrieve files and directories via a browser. It is more like SonicWall's CDP or something (it is not continuous and on-the-fly like SonicWall's product, the last I checked, but with the newer linux kernels having inotify built in, it is technically possible to do it).
