There are 2 ways:
Remove the root password so you don't use one.
- SSH will be disabled over wireless so only wired connections will be allowed.
- This leaves you Edison extremely vulnerable to attack by unauthorized users
Use a terminal program which stores the user ID and password for login
- Works with wired and wireless connections
- Reduces the risk of unauthorized logins. It can happen only from machines where you have installed the capability
- I use RealTerm, but other terminal programs also do it
The correct and secure way is to connect using a private/public SSH key pair.
You create these keys on your computer. Then you store the private key on your computer and install it in Putty or another ssh client. You copy the public key to your Edison in /root/.ssh/authorized_keys.
Putty supports this method too. https://www.digitalocean.com/community/tutorials/how-to-create-ssh-keys-with-putty-to-connect-to-a-vps
But don't enter a passphrase.