A public key cryptographic technique usable without aid of computer
Secure cryptographic protocols that can be executed by humans are considered in this paper: http://link.springer.com/chapter/10.1007%2F3-540-45682-1_4 (Hopper and Blum, "Secure Human Identification Protocols"). Reading the abstract, it sounds like they don't fully solve the problem. I suspect a satisfying solution is not known, but if you want to look into it I would start by looking at papers citing this one.