It is not logical to try to do it this way - here is why.
System A (your 'Nix box) stores a password in a variable. To access that information, the other systems (B, C, D, ...) would have to FIRST access system A to find the variable to get the password to gain access....and since the other 'system' has gained access to read the variable, why bother since it's gained access?
If you are looking for access without using passwords (once it's all set up) try ssh which can be loaded onto different OS systems and will give you 'trusted' accounts/hosts which will allow your automatic logins.