Q:

Is it possible to perform a rudimentary asymmetric key encryption algorithm by hand?

I have at least three, distinct motivations for having a simple way to use asymmetric key encryption by hand or without modern computers.
First, I was recently demonstrating to a 12-year-old how encryption works. I created some basic cyphers and had him figure them out. (I recommend this; it's quite fun.) Wanting to up the ante, I looked for ways to send messages back and forth using public-private key encryption, and I failed with flying colors.
Second reason for wanting this is that it would really help me understand how asymmetric encryption works. At the moment, I can't figure out a way to do solve this on my own, and I feel that betrays my lack of understanding in the subject.
Finally, (this one may be a stretch) I'm writing a fantasy story, and I'd like to do something unique with the form of exchange. One thought was to have a memorized key that the owner held, which she would use to sign her (paper) payment of 30 units for a loaf of bread, or whatever, combining her key with the shopkeeper's public key. (UPDATE: Note that this gets into digital signatures, rather than asymmetric key encryption. I'm hoping they are related, but if they're not, forget it.)
Any ideas how to accomplish this? If it's simply not feasible, I would appreciate an explanation as to why.
There are two similar questions on this site, but neither of them address asymmetric key encryption, unless I'm more misinformed than I thought:

Is there a secure cryptosystem that can be performed mentally?
What is the most secure hand cipher?

A:

Yes, you can perform rudimentary asymmetric encryption or signing by hand, but no it won't be secure.
Textbook RSA with small enough numbers is easy to do by hand. Diffie-Hellman to exchange a symmetric key is even easier. However, the kinds of numbers for which this is feasible are far from those needed for real security.
There are a lot of other asymmetric systems, but those tend to use even more complicated (to humans) math. Generally asymmetric encryption on a computer is something like an order of magnitude slower than symmetric and like the question you linked shows even secure symmetric encryption is barely doable, maybe, by hand.

