You mean to run it? I think Linux already has its built-in file permission system (which is much better than Windows). If you want, you could set up a group permission for the file and add any user you allow to use it into the group. Then in your Java, you could implement a password system to start and run the program.
My program needs administrator rights (permissions) to run properly. Thats why i need to ask password to user. For example: When you start on Ubuntu the "synaptic package manager", first it ask you a password like here: http://www.wawuk.net/sites/default/files/imagepicker/1/Ubuntu10-000056.jpg .Because it needs. My program also need to ask this question. But i don't know how.