Cultural appendix - modular arithmetic and RSA cryptography

A cultural appendix, outside the Year 5 syllabus, showing how elementary arithmetic (gcd, divisors, congruences) became — from the 1970s onwards — the basis of modern digital security. We introduce congruences modulo $n$, Fermat’s little theorem and Euler’s theorem, up to the RSA algorithm: a splendid example of “pure” mathematics that turns out to be unexpectedly applied.

• Congruences modulo n
• Modular arithmetic - sum, product, power
• Fermat’s little theorem and Euler’s theorem
• The RSA algorithm
• Toy RSA - p=11, q=13