I was thinking about the private key s. The computer I'm using everyday should be safe but I wouldn't trust it for something risky.
If I use your method, the computer may keep s somewhere (HDD, RAM, bash history, etc) and if it's compromised the attacker might be able to retrieve it and decrypt the message.
Now that I'm writing it I realize that the same goes for the message and the random N...
If you are trusting your computer with your message, you can trust it to hold a secret for a fraction of a second. Once you send out a message, simply clear the secret from memory, so it's not swapped on disk or otherwise extracted due to some corruption later on (it's a standard security practice, btw: put some secret in memory, use it, then zero it out ASAP).