Keep it public, but use a very good passphrase. That's not impossible to do. I'm not a crypto type but I believe what you want is a password-based key derivati

Keep it public, but use a very good passphrase. That's not impossible to do. I'm not a crypto type but I believe what you want is a password-based key derivation function such as scrypt, the output of which you can then use as the symmetric key to encrypt/decrypt the private key. (This might even be what GPG/SSH does for you; I'm not at all sure)