Can I use OpenSSL's private/public key idea for local/offline security?

If I am asked for a sudo password, I will have to copy it to a file, unencrypted, so I can copy and paste it, because I have a bad memory. What I need is the ability to encrypt the password that is in the file, and be able to have it accepted in the terminal. So, even if there is a guy standing behind me, resting a pair of binoculars on my shoulder, he will not be able to see my password. Of course, he could knock me unconscious with the binoculars, and steal my laptop.