6. From cards to cryptography

Abstract

‘From cards to cryptography’ applies another result of Fermat – his ‘little theorem’ – to the problem of finding the number of different coloured necklaces with a given number of beads and available colours, if we use at least two colours? Euler generalized this theorem, using his so-called ‘totient function’. Multiplying two prime numbers is relatively simple, but factorizing a large number into prime factors can be very difficult. This asymmetric process led to a method for encrypting messages, discovered independently by a former Bletchley Park codebreaker and by three mathematicians with the initials R, S, and A, hence the term ‘RSA encryption’.