simple ssh pub key question [SOLVED]

[rsa4046]

I have a groups of Linux and Windows boxes, all running openssh (sshd), and want to have all authentication between them be via public-key. However, I'm not just logging in from a solitary host to these machines, but also leapfrogging from one to another, back and forth, etc. My question is: Can I generate one single key pair (e.g., id_rsa and id_rsa.pub) at one given (arbitrary) machine, and then add the same id_rsa.pub key to my ~/.ssh/authorized_keys files of all of the machines? Would that give me pubkey access between any given pair of machines? Or do I have to generate separate keypairs at each machine, and then copy each given public key to ~/.ssh/authorized_keys of each machine in turn? Thanks in advance ...

[frostschutz]

You can use one private/pub key for all, of course. Wether that's the most secure way to go about things is another matter.

[rsa4046]

Thanks frostschutz
Cheers.