I was reading about SSH key authentication and setting it up with my 3 computers at home.
I have one main computer, call it "A", and two others, call them "B" and "C".
Now based on the documentation I've read, I would run ssh-keygen on B and C and put the public keys on computer A assuming I will always SSH into computer A, if I'm on B or C.
But, I think the documentation examples I've read assumes only 1 home computer will be used with lets say some other outside computer. In my situation, does it make sense to just run ssh-keygen on one computer and copy the files over to the others? This way I only need to back up one set of keys? And when I log into an outside computer, I only have to set it up with 1 set of keys as well as opposed to setting it up with all three computers.
Does this make sense? Any flaws or cautionary notes to consider?