Cryptography and Statistics: A Didactical Project

Cryptography is a stimulating way to introduce and consolidate ideas in statistics, computational linguistics, combinatorics and modular arithmetic. Two of the authors have been carrying out didactical experiences starting back in 1989 at a primary school level, without any special technology. A game is set up which involves cryptographers and cryptanalysts. Simple substitution ciphers are broken by building letter frequency hystograms by parallel work, so as to achieve what is being felt as statistical significance. Pupils quickly discover Markov models and the slight non-stationarity of the linguistic process. We have initiated a new round of experiments at a different level of age, 14-16, and technology. We take advantage of computer software to deepen our analysis of cipher systems and Markov models. The friendly (and cheap) technology of graphing calculators is used to analyse perfect and pseudo-perfect ciphers and to discuss the elusive notion of randomness.