I was getting errors when trying to update a LInux system that had not been updated in quite a while.

I got the error that stated that the "Signatures are invalid" when trying to "apt-get update".

The fix is simple... 

For Kali LInux just run:  wget -q -O - https://archive.kali.org/archive-key.asc  | apt-key add

After that, run: sudo apt-get update && apt-get upgrade

That should fix the issues.

Hope this helps.