Behold the Enigma machine!
Franklin Heath, a UK security consultancy, offers plans for printing and assembling your own papercraft Enigma machine, approximately like the ones that Alan Turing and the Polish cryptographers and co broke at Bletchley Park. Now all we need are papercraft bombes, and a papercraft Collosus, and several thousand papercraft young women to work on code intercepts through the night…
The instructions note: “Using low-tack ‘removable’ sticky tape can make it easier to swap round and reuse the rotors if you want to do that, but it’s not essential.”
If you seriously want to explore paper computing, a good followup project is the legendaryCARDiac computer.