The same way you use a private key in a computer without transmitting it?

So how are you intending to do those calculations in your mind?

There is a section in the novel Cryptonomicon where the protagonist is in a jail cell and monitored 24/7. He communicates with another person via a deck of cards, with all of the cryptography performed in the two people's minds. It's annoying to do but should certainly be possible if the fate of the world is at stake.

By being a super-advanced space alien?

I mean, or just practicing. Humans who put in the time can do pretty amazing stuff.