[avolkov]

Wow, wait, I don't get it. You can copy from anywhere to anywhere with just one set of public private key.

for example, copy file from local machine:

scp some_file.tar.gz alex@remote_ip:~/

now copy the same file from a remote to the local machine:

scp alex@remote_ip:~/some_file.tar.gz ~/

But seamless logins form anywhere to anywhere in the way you described seems like a bad idea, unless you are willing to implement kerberos, ldap and nfs4, in this way you can just log in into a client machine using your existing credentials (see PAM) and if you have your home directory property mounted you can have public/private keypair on that machine. But this is a lot of work.