
Since Kali Linux is based on Debian, some of the tips could apply to your scenario. There is also this question on AskUbuntu where you can find interesting stuff about dual booting Ubuntu 32-bit EFI and 64-bit EFI. Take a look at the related stuff section of this answer. Note also that when talking about EFI, there are some machines that have 32bit EFI, but run amd64 processor so, there are some tweaks that need to be made to make this kind of "boot freak machines" work.


If you have 32bit machines, it is safer to download a 32bit OS to boot on both architecture options. You will probably get the following error message(or some message that is similar to this one):
